Four Fours Problem
Compiled by Paul Bourke
Contributions by Frank Primer, Chris Smith, Guido Roach, Dhruv Chand,
Jim Millar, Vijay Kailas, David Bevan,
Ewald R. de Wit, Martin Olivella, Heiner Marxen,
Scott Forschler, Wayne Goode, Jörg Wiegels, Ben Rudiak-Gould,
Charles Dillingham, Peter Karsanow, Brad McInnes,
Richard Schorn, Ewart Shaw, Rick Hevener, Toufic Batouli, Sven Peterson
and Rizvan Dadaev.
This classical problem is most commonly formulated as follows:
"Given no more than four instances of the digit 4,
represent all integers using a finite number of
mathematical symbols and operators in common use."
|
The central issue then is which symbols may one use and which ones
may not, the rules that will be applied to the following lists are
outlined below.
In situations where more than one solution can be found the
challenge is to find the simplest, least number of symbols and
operators as well as the simplest operators.
- Acceptable symbols and operators
+,- addition subtraction
*,/ multiplication, division
sqrt,^ square root, power
! factorial, eg: n! = n * (n-1) * (n-2) * ... * 2 * 1
. decimal point, eg: .4
` repeating decimal, eg: .4` = .444444444...
- Other Symbols
Cannot use representations for other numbers, eg: use of [pi] in
sin(π / 4) = 1
- Infinity
Cannot use ... to represent an infinite number of operations eg:
sqrt(sqrt(sqrt(...4))) = 1
- Subfactorials
Many solutions to this problem in the past have relied on an operator called
the subfactorial, defined as follows.
!n = n! (1 - 1/1! + 1/2! - 1/3! + 1/4! - ... +/-1/n!)
Note that !n is always an integer.
In particular
!1 = 0
!2 = 1
!3 = 2
!4 = 9
Since the subfactorial is not considered a symbol in "common" use it will not be
used here.
- Gamma function
The gamma function can be used to get an expression for 6 with only one 4.
Γ(4) = 6
Γ(√4) = 1
Nora Grider proposed a simple soloution for the elusive 113, 4(4!+4)+Γ(√4).
Gamma function will only be used here as a last resort.
- Concatenation operator
Nora Grider proposed the concatenation operator "||" which is already being used
implicitely in 4||4 and 4||4||4. This can also be used as a solution for 113.
((Γ(√4)) || (Γ(√4)) || (4-Γ(√4))
- 0.4th root (Courtesy of Scott Forschler)
The 0.4th root of a number, normally written as 
This will be represented in the ASCII form as sqrt.4(x).
It gives a shorter solution for 32, namely root.4(4) = 4^(5/2) = 32.
Solutions are also listed below for 766, 770, and 772.
- Arbitrary root (Courtesy of Frank Mrazik)
An arbitrary root "b" of a number "a" may be written as root(a,b)
where, in this context, a and b are made up entirely of the digit 4.
This gives a four 4 solution for 657 for example.
- Percent (Courtesy of Scott Forschler)
While "%" is not strictly a mathematical symbol it is "in common use".
It is shown below as alternative solutions for some numbers but still
the primary solution for the problematic 113.
This has been extended by Frank Mrazik to the following
.4% (.004),
.4'% (.00444444....),
and even 4!% (0.24).
- Percent-percent (Courtesy of Frank Mrazik)
Getting a bit weird, 1%% = 1/10000.
So for example 10000 = 4 / 4%%
- Summation (Courtesy of Scott Forschler)
A summation can be used to give various solutions, in particular, 303.
Because solutions based upon summations use additional symbols, namely "i",
they will not be used here.
- Using five 4's
Some of the gaps in the numbers below (numbers for which a solution
with only four 4's hasn't yet been found) have solutions listed that
use five 4's.
Note that variations of the problem allow 'free' squaring (eg: 4^2 uses
only one 4). In this case those five 4 solutions
that use sqrt(4) in the rules used here
become solutions with four or less fours. For example,
163 = (4^2+4^2+.4'^2)/.4'^2
uses only four 4's but eight if the 2's are replaced by
sqrt(4) as required here.
- 2/9 (First introduced by Richard Schorn for 113)
This and the next repeating decimals are pushing the limits of
what is acceptable. In this case it is written as .(sqrt(4))' = 0.22222222...
otherwise known as 2/9.
- 24/99 (Introduced by Rick Hevener)
Hardly standard but some of the difficult numbers can be solved
with .(4!)' which is supposed to represent 24/99 or 0.2424242424.....
For example 99 then can be solved with two 4's as 4! / .(4!)'.
- Mille (Proposed by Frank Mrazik)
Frank Mrazik proposed use of the mille notation %o to mean 1/1000.
Initially used for the elusive 713.
- n!! (Proposed by Gerard
Schildberger)
Double factorial !! for even and odd numbers, for example
8!! = 8 * 6 * 4 * 2
9!! = 9 * 7 * 5 * 3
For example, Jim Millar gave the following solution for 113
113 = (4!! - 4/4)!! + 4!!
A further list by Frank Mrazik.
8 = 4!!
15 = 5!!
48 = 6!!
105 = 7!!
384 = 8!!
945 = 9!!
3840 = 10!!
Including a double double !, by Frank Wrazik
384 = (4!!)!!
113 = ((4!!)! / (4!!)!!) + 4!!
- !!n (Proposed by Gerard
Schildberger)
!!n = 0! + 1! + 2! + 3! + ... + n!
For example !!4 = 10
- Any number with three 4's
(Contributed by Ben Rudiak-Gould)
A cute solution to any number using just 3 fours. By admitting
natural logarithms "ln()" then any positive integer n can be represented as
n = -ln[ ln( sqrt(sqrt(...(sqrt(4))...))) / ln(4) ] / ln(4)
where the number of nested sqrt() functions is twice n. Or if base 4
logarithms are permitted "log4()" then the expression becomes
n = -log4(log4(sqrt(sqrt(...(sqrt(4))...))))
- Any number with two 4's
(Contributed by "whetstone")
Using log10, any number can be represented using two fours
and creative use of % as shown below:
log(srqt(4/(4%))) = log(sqrt(100)) = log(10) = 1
log(sqrt(4/(4%%))) = log(sqrt(10000)) = log(100) = 2
log(sqrt(4/(4%%...%))) = n
- Any number with one 4
(Contributed by Jim Millar)
Another cunning idea sees any number created using only one 4 and a lot of
nested trigonometric functions (atan and sec). The principle lies in the relationship
tan2(x)+1 = sec2(x)
from which
sec(atan(x)) = sqrt(x2+1)
Repeated and nested application k times gives
sec(atan(...(sec(atan(x))...)) = sqrt(x2+k)
So if x=4 we can get any number (greater than 4) by only using a single 4. For example
5 is represented as
sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(4))))))))))))))))))
To get a particular number n requires k = n2-16 nestings.
For more information, including how to derive numbers up to 4,
see this description by Jim Millar.
- Primorial (Suggested by Chris Smith)
The primorial function, often written using the "#" symbol and it is the prime equivalent for
factorial. So, for example, 4# is the product of the first 4 primes, 2*3*5*7=210.
(4+4/4)=3210 and (4+(4+4)/4)=30030.
- ceiling() and floor() (Suggested by Bruno Curfs)
An option that provides another solution for the pesky 113, namely the "ceiling(x)" function
defined as the smallest integer greater than or equal to x. Written as //x\\, then //.4\\ = 1.
113 can be written as 4 * (4 + 4!) + //.4\\
Along the same lines, if floor(x) is the largest integer less than or equal to x, if
floor(x) is written as \\x// then
113 = \\exp(4.4)// + root.4(4)
- Exactly 4 fours
A variation to the problems description above is to use exactly 4 fours.
A list compiled by Sven Peterson is given here: 4_4_4_4.docx.
- Rizvan Dadaev
Suggested using 4/9900 = (4%)'% as well as other fractions, for example:
- 4/99900 = (.4%)'%
- 24/99900 = (4!‰)'%
- 2/9900 = (sqrt(4)%)'%
Also pointed out that from the definition of the gamma function,
factorials can be defined for non-integer values, in particular
- Tetration (Suggested by Rizvan Dadaev)
Another candidate operator is tetration, repeated exponentiation.
For example.
5a = a^(a^(a^(a^(a))))
See also: Tetration fractal.
Here we will use the operator "^^" to represent tetration.
This leads to some alternative solutions as follows.
- sqrt(4)^^4 = 2^^4 = 2^(2^(2^2) = 2^16 = 65536
- (sqrt(4)^^4)/4! - sqrt(.4') = 2730
- (sqrt(4) /.4)^^sqrt(4) = 5^5 = 3125
- (4!/4)^^sqrt(4) = 6^6 = 46656
- ((4!/4)^^sqrt(4) )/4! = 1944
- sqrt( (sqrt(4/.4'))^^sqrt(4) ) = 19683
- sqrt( (sqrt(4/.4'))^^sqrt(4) ) * .4' = 8748
- sqrt( (sqrt(4/.4'))^^sqrt(4) ) * sqrt(.4') = 13122
- (sqrt(4) ^^ 4) * .4 - .4 = 26214
- (sqrt(4) ^^ 4) * .sqrt(4) - .sqrt(4) = 13107
- (sqrt(4) ^^ 4) * (.sqrt(4))' + .4' = 14564
- (sqrt(4) ^^ 4 + sqrt(4) ) * .4!' = 15888
- sqrt( sqrt(sqrt(sqrt((4!/sqrt(.4'))^^sqrt(4))))/.4! ) = 6840
- sqrt( sqrt(sqrt(sqrt((4!/sqrt(.4'))^^sqrt(4)))) * 4! ) = 15552
And there is a more esoteric solution for 2, namely the infinite
tetration of the square root of 2.
sqrt(sqrt(4))^^(4/(4-4)) = sqrt(2)^^infinity = sqrt(2)^(sqrt(2)^(sqrt(2)^(sqrt(2)^ ... )))) = 2
The solutions so far
0 2 4 - 4
4 (4+4) - (4+4)
1 2 4 / 4
4 (4+4) / (4+4)
2 1 sqrt(4)
4 ((4+4) ÷ sqrt(4)) / sqrt(4)
3 2 sqrt(4 / .4`)
3 4 - 4 / 4
4 (4+4+4) / 4
π 3 sqrt((-sqrt(4) / 4)!)^4
4 sqrt((sqrt(4)/4)!^4)*4
4 1 4
4 (4+4) - (sqrt(4)+sqrt(4))
5 2 sqrt(4) / .4
4 (4+sqrt(4)) - (4/4)
6 2 4 + sqrt(4)
4 (4+sqrt(4)) / (4/4)
7 3 (4! + 4) / 4
4 4 + 4 - 4 / 4
8 2 4 + 4
4 (sqrt(4)+sqrt(4)) + (sqrt(4)+sqrt(4))
9 2 4 / .4`
4 (4+4) + (4/4)
10 2 4 / .4
4 (4+4) + (4/sqrt(4))
11 3 44 / 4
4 (4! / sqrt(4)) - (4/4)
12 2 4! / sqrt(4)
3 4 + 4 + 4
4 (4×4) - (sqrt(4)+sqrt(4))
13 3 (4! + sqrt(4)) / sqrt(4)
4 (4! / sqrt(4)) + (4/4)
14 3 4 * 4 - sqrt(4)
4 (4×4) - (4 / sqrt(4))
15 3 (4 + sqrt(4)) / .4
4 4 * 4 - 4 / 4
2 sqrt(.4') / 4' %
16 2 4 * 4
4 (sqrt(4) * sqrt(4)) × (sqrt(4) * sqrt(4))
17 4 4 * 4 + 4/4
3 (4 - .(sqrt(4))`) / .(sqrt(4))`
3 sqrt(4) + root(-sqrt(4), .4`%)
18 3 4 * 4 + sqrt(4)
2 4 / .(sqrt(4))'
4 (4 * 4) + (4 /sqrt(4))
19 3 4! - sqrt(4) /.4
4 4! - (4 + (4/4))
20 2 4! - 4
4 (4 * 4) + (sqrt(4)+sqrt(4))
21 3 4! - sqrt(4) / sqrt(.4`)
4 4! - (4 - (4/4))
22 2 4! - sqrt(4)
4 (4 * 4) + (4+sqrt(4))
23 3 4! - 4 / 4
4 (4!-sqrt(4)) + (4/4)
24 1 4!
4 (4*4) + (4+4)
25 3 4! + 4 / 4
2 .(sqrt(4))^(-sqrt(4))
2 sqrt(4% ^ -sqrt(4))
4 (4!+sqrt(4)) - (4/4)
26 2 4! + sqrt(4)
4 4! + (sqrt(4) × (4/4))
27 3 4! / (.4` * sqrt(4))
4 4! + ((4+ sqrt(4)) / sqrt(4))
28 2 4! + 4
4 4! + ((4 * 4) / 4)
29 3 4! + sqrt(4) / .4
4 (4!+4) + (4/4)
30 3 4! + 4 + sqrt(4)
2 sqrt(4) / sqrt(.4' %)
4 (4!+4) + (4+sqrt(4))
31 4 4! + (4! + 4) / 4
3 (sqrt(4) + sqrt(.4' %)) / sqrt(.4' %)
32 3 4 * (4 + 4)
2 root.4(4)
4 (4*4) + (4*4)
33 4 (4!+4) + (sqrt(4) / 0.4)
3 4! + 4 / .4`
2 sqrt(.4') /(sqrt(4)%)'
34 3 4! + 4 / .4
4 (4!+sqrt(4)) + (4+4)
35 3 (4! - sqrt(.4`)) / sqrt(.4`)
4 ((4!+4) / 0.4) / sqrt(4)
36 4 4 * (4 + 4) + 4
3 4! + 4! / sqrt(4)
2 4! / sqrt(.4`)
37 3 (4! + sqrt(.4`)) / sqrt(.4`)
4 4! + ((4!+sqrt(4)) / sqrt(4))
38 3 4! / sqrt(.4`) + sqrt(4)
4 (4!-sqrt(4)) + (4 * 4)
39 3 (sqrt(4) + 4!) / sqrt(.4`)
4 ((4 * 4) + 0.4) / 0.4
40 3 44 - 4
4 (4!+4!) - (4+4)
41 4 (4 * 4 + .4) / .4
3 (sqrt(4%) / .4`%) - 4
42 3 44 - sqrt(4)
4 (4!+4!) - (4+sqrt(4))
43 4 44 - 4/4
3 (sqrt(4%) / .4`%) - sqrt(4)
44 2 44
4 (4!+4!) - (sqrt(4)+sqrt(4))
45 3 (4! - 4) / .4`
2 sqrt(4) / 4' %
4 ((4 * 4) + sqrt(4)) / 0.4
46 3 44 + sqrt(4)
4 (4!+4!) - (4 / sqrt(4))
47 4 4! + 4! - 4 / 4
3 sqrt(4) + (sqrt(4%) / .4`%)
48 2 4! + 4!
4 (4!+4!) ÷ (4/4)
49 4 4! + 4! + 4 / 4
3 .(sqrt(4))^(-sqrt(4)) + 4!
3 (sqrt(4) - 4%) / 4%
50 3 4! + 4! + sqrt(4)
2 sqrt(4) / 4 %
4 (4!+4!) + (4 / sqrt(4))
51 4 (.4 + 4! - 4) / .4
3 (sqrt(4) + 4%) / 4%
52 3 4! + 4! + 4
4 (4!+4!) + (sqrt(4)+sqrt(4))
53 3 (4! - .4`) / .4`
4 (4!+4!) + (sqrt(4) / .4)
54 2 4! /.4`
4 (4!+4!) + (sqrt(4)+4)
55 4 (4!/0.4) - (sqrt(2) / 0.4)
3 (4! - sqrt(4)) / .4
2 (sqrt(4))'% /(4%)'%
56 3 4! / .4 - 4
57 4 (4! + .4) / .4 - 4
3 (4 - sqrt(4%)) / sqrt(.4`%)
58 3 4! / .4 - sqrt(4)
59 3 (4! - .4) /.4
60 2 4! / .4
61 3 (4!+ .4) / .4
62 3 4! / .4 + sqrt(4)
63 3 (4! + 4) / .4`
64 2 sqrt(sqrt(sqrt(4^(4!))))
65 3 (4! + sqrt(4)) / .4
66 3 sqrt(sqrt(sqrt(4^(4!)))) + sqrt(4)
3 44 / sqrt(.4`)
67 4 sqrt(4) + (4! + sqrt(4)) / .4
68 3 44 + 4!
69 4 (4! + 4 - .4) / .4
3 4! + (sqrt(4%) / .4`%)
70 3 (4! + 4) / .4
71 4 (4! + 4.4) / .4
72 3 4! + 4! + 4!
73 4 sqrt(sqrt(sqrt(4^(4!)))) + 4 / .4`
74 4 4! + 4! + 4! + sqrt(4)
3 (sqrt(4) / 4%) + 4!
75 4 (4! + 4 + sqrt(4)) / .4
3 4! / root(.4, 4)%
76 4 4! + 4! + 4! + 4
3 4! / .(4!) - 4!
3 (4 / 4%) - 4!
77 4 4! / (.4` * sqrt(.4`)) - 4
78 3 4! + 4! / .4`
79 4 4! + (4! - sqrt(4)) / .4
80 3 4 * (4! - 4)
81 3 (4 / .4')^sqrt(4)
82 4 4 * (4! - 4) + sqrt(4)
83 4 4! - (.4 - 4!) / .4
84 3 4! / .4 + 4!
85 4 (4! + 4 / .4) / .4
3 (.4` - sqrt(.4`%)) / .4`%
86 4 44 * sqrt(4) - sqrt(4)
3 (.4 / .4`%) - 4
87 4 4 * 4! - 4 / .4`
88 3 44 * sqrt(4)
89 4 (4! + sqrt(4)) / .4 + 4!
3 (.4 - .4`%) / .4`%
90 3 4 / (.4` - .4)
2 .4 / .4`%
91 4 4 * 4! - sqrt(4) / .4
3 (.4` - 4%) / .4`%
92 3 4 * 4! - 4
93 4 4 * 4! - sqrt(4) / sqrt(.4`)
94 3 4 * 4! - sqrt(4)
95 4 4 * 4! - 4/4
3 (4 - sqrt(4%)) / 4%
96 2 4 * 4!
97 4 4 * 4! + 4/4
3 (sqrt(.4`) - sqrt(4)%) / sqrt(.4`)%
98 3 4 * 4! + sqrt(4)
99 3 44 / .4`
2 4! / .(4!)'
100 3 4 * 4! + 4
2 4! / .(4!)
2 4 / 4%
101 4 4 * 4! + sqrt(4) / .4
3 (4 + 4%) / 4%
102 4 4 * 4! + 4 + sqrt(4)
3 4! / .(4!) + sqrt(4)
3 (4 / 4%) + sqrt(4)
103 4 44 / .4` + 4
3 (sqrt(4)% + sqrt(.4`)) / sqrt(.4`)%
104 3 4 * (4! + sqrt(4))
105 4 (44 - sqrt(4)) / .4
3 (4 + sqrt(4%)) / 4%
106 4 44 / .4 - 4
3 (4 + 4!%) / 4%
107 4 (4! + 4! - .4`) / .4`
3 (4! - .(sqrt(4))`) / .(sqrt(4))`
108 3 (4! + 4!) / .4`
2 4!/.(sqrt(4))`
109 4 (44 - .4) / .4
3 (4! + .(sqrt(4))`) / .(sqrt(4))`
3 (4% + .4`) / .4`%
110 3 44 / .4
111 4 444/4
112 3 4 * (4! + 4)
113 4 4!/.(sqrt(4))` + sqrt(4)/.4
4 (.4 - .4`%) / .4`% + 4!
4 ( sqrt(4) / .4' + sqrt(4)% ) / 4%
4 (sqrt(4) + (sqrt(4) + 4!)%) / (sqrt(4))%
3 (.(sqrt(4))' / (.(sqrt(4)) % )') + sqrt(4)
114 4 44 / .4 + 4
3 4! + (.4 / .4`%)
115 4 (44 + sqrt(4)) / .4
3 (.4` + sqrt(.4`%)) / .4`%
116 3 (sqrt(4) / .4)! - 4
117 4 (4! + 4! + 4) / .4`
118 3 (sqrt(4) / .4)! - sqrt(4)
119 4 (4! + 4! - .4) / .4
3 (4! - sqrt(4%)) / sqrt(4%)
120 2 (sqrt(4) / .4)!
121 4 (44 / 4) ^ sqrt(4)
3 (4! + sqrt(4%)) / sqrt(4%)
122 3 (sqrt(4) / .4)! + sqrt(4)
123 4 44 / .4` + 4!
124 3 (sqrt(4) / .4)! + 4
125 4 (4! - 4) / (.4 * .4)
3 sqrt(sqrt(sqrt((sqrt(4) / .4)^(4!))))
2 sqrt(sqrt(sqrt(.(sqrt(4))))^(-4!)
126 4 4^4 / sqrt(4) - sqrt(4)
3 (4! + 4) / .(sqrt(4))`
3 (sqrt(.4`) / .4`%) - 4!
127 4 (4^4 - sqrt(4)) / sqrt(4)
128 3 4^4 / sqrt(4)
129 4 (4^4 + sqrt(4)) / sqrt(4)
130 4 4^4 / sqrt(4) + sqrt(4)
3 (sqrt(4) + 4!) / sqrt(4%)
131 4 4! / (.4 * .4`) - 4
132 4 4^4 / sqrt(4) + 4
133 4 4! / (.4 * .4`) - sqrt(4)
134 4 4! + 44 / .4
135 3 4! / (.4 * .4`)
136 4 4 * ( 4! + 4 / .4)
3 (4!% + sqrt(.4`)) / sqrt(.4`)%
137 4 4! / (.4 * .4`) + sqrt(4)
138 4 (4! * 4! - 4!) / 4
139 4 4! / (.4 * .4`) + 4
140 4 4 * 4! + 44
3 (4! + 4) / .(sqrt(4))
3 (4 + 4!) / sqrt(4%)
141 4 (4 * 4! - sqrt(4)) / sqrt(.4`)
3 (sqrt(.4`) - 4%) / .4`%
142 4 4! * 4! / 4 - sqrt(4)
143 4 (4! * 4! - 4) / 4
144 3 4! * 4! / 4
145 4 (4 + 4! * 4!) / 4
3 (sqrt(4%) + .4`) / .4`%
146 4 4! / .4 / .4 - 4
3 (sqrt(.4`) / .4`%) - 4
147 4 (4 * 4! + sqrt(4)) / sqrt(.4`)
148 4 4 + 4! * 4! / 4
3 (sqrt(.4`) / .4`%) - sqrt(4)
149 4 (4! / .4 - .4) / .4
3 (sqrt(.4`) - .4`%) / .4`%
150 3 4! / (.4 * .4)
2 sqrt(.4') / .4' %
151 4 (4! / .4 + .4) / .4
3 (sqrt(.4`) + .4`%) / .4`%
152 4 4 * 44 - 4!
3 sqrt(4) + (sqrt(.4`) / .4`%)
153 4 (44 + 4!) / .4`
154 4 4 + 4! / .4 / .4
3 4 + (sqrt(.4`) / .4`%)
155 4 (4! / .4 + sqrt(4)) / .4
156 4 (4! + sqrt(4)) * (4 + sqrt(4))
157 4 4^4 - 4! / .(4!)'
4 ((4% + sqrt(.4`)) / .4`%) - sqrt(4)
158 4 sqrt(sqrt(sqrt(4^4!))) / .4 - sqrt(4)
159 4 4! / .4 / .4` + 4!
3 (4% + sqrt(.4`)) / .4`%
160 3 sqrt(sqrt(sqrt(4^4!))) / .4
161 4 (sqrt(sqrt(sqrt(4^4!))) + .4) / .4
162 4 (4! * 4 - 4!) / .4`
3 4! / sqrt(.4') / .(sqrt(4))'
163 4 (4! / sqrt(.4`) + .(sqrt(4))`) / .(sqrt(4))`
4 ((4 + 4!)% + .4`) / .4`%
164 4 (sqrt(4) / .4)! + 44
165 4 44 / .4 / sqrt(.4`)
2 .4 / .(4!)' %
3 (sqrt(.4`) - sqrt(.4`)%) / .4%
166 4 4! / (sqrt(.4') * .(sqrt(4))') + 4
4 (sqrt(.4)^(-4) + sqrt(.4')) * 4!
3 (sqrt(.4`) / .4%) - sqrt(.4`)
167 4 (sqrt(.4') / .4 % ) + (sqrt(.4') / sqrt(4))
4 .4 / (.4!' - .4!) + sqrt(4)
168 4 (4! + 4) * (4 + sqrt(4))
169 4 (4! + sqrt(4))^sqrt(4) / 4
170 4 (44 + 4!) / .4
171 4 (.4 / .(4!)' %) + sqrt(4) + 4
4 ((4 / 4%) - 4!) / .4`
172 4 4 * 44 - 4
173 4 ((4!/4)! * .(4!)) + .(sqrt(4))
4 (4 - (4! / .4`)%) / sqrt(4)%
174 4 4 * 44 - sqrt(4)
3 4! + (sqrt(.4`) / .4`%)
175 4 (4! + 4) / (.4 * .4)
176 3 4 * 44
177 4 ((sqrt(4) / .4)! - sqrt(4)) / sqrt(.4`)
178 4 4 * 44 + sqrt(4)
179 4 ((4! / 4)! - 4) / 4
180 3 (4 + sqrt(4))! / 4
2 .4 / .(sqrt(4))' %
181 4 ((4! / 4)! + 4) / 4
182 4 sqrt(4) + (4! / 4)! / 4
183 4 ((sqrt(4) / .4)! + sqrt(4)) / sqrt(.4`)
184 4 4 * (sqrt(4) + 44)
185 4 44.4 / .(4!)
4 44.4 / 4!%
186 4 ((4! / 4)! + 4!) / 4
187 4 (4 - .(4!) - sqrt(4) % ) / sqrt(4) %
4 (4 - (sqrt(4) + 4!)%) / sqrt(4)%
4 (4 - .(sqrt(4))') / (.(4!)' - .(sqrt(4))')
188 4 4 * (4! + 4!) - 4
3 (4 - 4!%) / sqrt(4)%
189 4 (4! / .4 + 4!) / .4`
190 4 4! (4 + 4) - sqrt (4)
3 (.4 + .4`) / .4`%
191 4 (.4' % + .4 + .4') / .4' %
192 3 4 * (4! + 4!)
193 4 (4 + .(sqrt(4))' + sqrt(.4' % )) / (sqrt(4) % )'
4 sqrt(.4`% ^ -sqrt(4)) - root(.4, 4)
194 4 4! (4 + 4) + sqrt (4)
195 4 (4! / .4` + 4!) / .4
3 (sqrt(4%) + sqrt(.4`)) / .4`%
196 4 sqrt(4) * (4 * 4! + sqrt(4))
3 (4 / sqrt(4)%) - 4
197 4 (44 - .(sqrt(4)')) / .(sqrt(4)')
4 (4 - (4 + sqrt(4))%) / sqrt(4)%
198 4 (4! - sqrt(4)) * 4 / .4`
3 44 / .(sqrt(4)')
3 (4 / sqrt(4)%) - sqrt(4)
199 4 (44 + .(sqrt(4)')) / .(sqrt(4)')
4 4!/.(4!)' + 4!/(4!)
3 (4 - sqrt(4)%) / sqrt(4)%
200 4 4 * 44 + 4!
2 .4' / .(sqrt(4))' %
2 4 / sqrt(4)%
201 4 ((4!) - (sqrt(sqrt(sqrt(.4))))^(-4!)) * (4!)
3 (4 + sqrt(4)%) / sqrt(4)%
202 4 4^4 - 4! / .4`
3 (4 / sqrt(4)%) + sqrt(4)
203 3 (.4' + sqrt(.4') % / .(sqrt(4))' %
4 (4 + (4 + sqrt(4))%) / sqrt(4)%
204 4 4! + (4! / 4)! / 4
3 4 + (4 / sqrt(4)%)
205 4 ((sqrt(4) / 4' %) - 4) / .(sqrt(4))
4 (4 + (.4 / 4)) / sqrt(4)%
206 4 (4! / .(4!)' + 4) * sqrt(4)
4 4 ^ 4 - (sqrt(4) / 4%)
207 4 (4 * 4! - 4) / .4`
208 4 4^4 - 4! - 4!
209 4 ((sqrt(4) / 4 % ) + sqrt(.4')) / .(4!)'
4 (4 / sqrt(4)%) + (4 / .4`)
210 4 (4! / .4 + 4!) / .4
3 (4 + sqrt(4%)) / sqrt(4)%
211 4 ((.4 * 4!) - .sqrt(4))') / 4' %
4 4 ^ 4 - (sqrt(4%) / .4`%)
212 4 4^4 - 44
3 (4 + 4!%) / sqrt(4)%
213 4 (4! * sqrt(4) - sqrt(.4')) / .(sqrt(4))'
4 (4 + (sqrt(4) + 4!)%) / sqrt(4)%
214 4 4! * 4 / .4` - sqrt(4)
215 4 (4 * 4! - .4`) / .4`
216 3 4 * 4! / .4`
217 4 (4 * 4! + .4') / .4'
218 4 4! * 4 / .4` + sqrt(4)
219 4 (root.4(4/.4')) - 4!
220 4 44 * sqrt(4) / .4
3 44 / sqrt(4%)
221 4 (44 + .(sqrt(4))) / .(sqrt(4)
3 sqrt(.4`% ^ -sqrt(4)) - 4
222 4 444 / sqrt(4)
223 4 ((4! / .(4!)) / .4') - sqrt(4)
3 sqrt(.4`% ^ -sqrt(4)) - sqrt(4)
224 4 (4 + 4) * (4! + 4)
3 (4 / sqrt(4)%) + 4!
225 4 ((sqrt(4) + 4) / .4)^sqrt(4)
2 sqrt(.4`% ^ -sqrt(4))
226 4 ((4! / .(4!)) + .4') / .4'
3 sqrt(.4% ^ -sqrt(4)) - 4!
227 4 ((4! / .(4!)) / .4') + sqrt(4)
3 sqrt(4) + sqrt(.4`% ^ -sqrt(4))
228 4 4^4 - 4! - 4
229 4 ((4! / .(4!)) / .4') + 4
3 4 + sqrt(.4`% ^ -sqrt(4))
230 4 (4 * 4! - 4) / .4
231 4 (sqrt(4) + 4! / .4') / .(4!)'
4 ((4 / .4`%) + 4!) / 4
232 3 4^4 - 4!
233 4 (4! / .(sqrt(4))') + sqrt(sqrt(sqrt(.(sqrt(4)))) ^ (- 4!)
4 4 + 4 + sqrt(.4`% ^ -sqrt(4))
234 4 4^4 - 4! + sqrt(4)
235 4 (4 * 4! - sqrt(4)) / .4
236 4 4^4 - 4! + 4
237 4 (4 * 4) - .(sqrt(4)) / sqrt(.4' %)
4 ((4 * 4) - sqrt(4%)) / sqrt(.4`%)
238 4 4! * 4 /.4 - sqrt(4)
239 4 (4 * 4! - .4) / .4
240 3 4 * 4! / .4
241 4 (4 * 4! + .4) / .4
242 4 4! * 4 / .4 + sqrt(4)
243 4 sqrt(4) * 4! / (.4` * .4`)
3 root(sqrt(4%), sqrt(4 / .4`))
244 4 4^4 - 4! / sqrt(4)
245 4 (4 * 4! + sqrt(4)) / .4
246 4 4^4 - 4 / .4
3 sqrt(.4% ^ -sqrt(4)) - 4
247 4 4^4 - 4 / .4`
248 4 4^4 - 4 - 4
3 sqrt(.4% ^ -sqrt(4)) - sqrt(4)
249 4 ((4!/.4) - .(4!)) / .(4!)
3 4! + sqrt(.4`% ^ -sqrt(4))
250 4 (4 * 4! + 4) / .4
2 sqrt(.4% ^ -sqrt(4))
251 4 4^4 - sqrt(4) / .4
252 3 4^4 - 4
253 4 4^4 - sqrt(4) / sqrt(.4`)
254 3 4^4 - sqrt(4)
255 4 4^4 - 4/4
256 2 4^4
257 4 4^4 + 4/4
258 3 4^4 + sqrt(4)
259 4 4^4 + sqrt(4) / sqrt(.4`)
260 3 4^4 + 4
261 4 4^4 + sqrt(4) / .4
262 4 4^4 + 4 + sqrt(4)
263 4 (sqrt(sqrt(sqrt(4^4!))) - .(4!)') / .(4!)'
4 (sqrt(4) - (4! + sqrt(.4`))%) / sqrt(.4`)%
264 4 44 * (4 + sqrt(4))
3 (sqrt(4) - 4!%) / sqrt(.4`)%
265 4 4^4 + 4 / .4`
266 4 4^4 + 4 / .4
267 4 (root.4(4/.4')) + 4!
268 4 4^4 + 4! / sqrt(4)
269 4 ((sqrt(4) / .4)! - .4`) / .4`
270 3 (sqrt(4) / .4)! / .4`
271 4 ((sqrt(4) / .4)! + .4`) / .4`
272 4 4^4 + 4 * 4
273 4 ((4! / .4) + .4') / .(sqrt(4))'
4 ((sqrt(4) - sqrt(4)%) / sqrt(.4`)%) - 4!
274 4 (sqrt(4) / .4)! / .4` + 4
3 4! + sqrt(.4% ^ -sqrt(4))
275 4 44 / .4 / .4
2 sqrt(.4') / .(4!)' %
276 4 4^4 + 4! - 4
3 (sqrt(4) / sqrt(.4`)%) - 4!
277 4 ((sqrt(.4') + .(sqrt(4))' % ) / .(sqrt(4))' % ) - 4!
4 ((sqrt(4) + sqrt(.4`)%) / sqrt(.4`)%) - 4!
278 4 4^4 + 4! - sqrt(4)
279 4 ((sqrt(4) / .4)! + 4) / .4`
4 (((sqrt(sqrt(sqrt(.4))))^(-4!)) - (4)) * (4!)
280 3 4^4 + 4!
281 4 .(sqrt(4))^(-sqrt(4)) + 4^4
4 4 ^ 4 + sqrt(4% ^ -sqrt(4))
282 4 4^4 + 4! + sqrt(4)
283 4 (sqrt(.4') - 4 % + .(sqrt(4))' % / .(sqrt(4))' %
4 sqrt (.4') / .4!'% + 4 + 4
284 4 4^4 + 4! + 4
285 4 (sqrt(sqrt(sqrt(4^4!))) - .4') / .(sqrt(4))'
4 (4! + (.4 / .4`%)) / .4
286 4 (4! * 4! / sqrt (4)) - sqrt (4)
287 4 (4! * 4! - sqrt(4)) / sqrt(4)
288 3 (4 + sqrt(4))! * .4
289 4 (sqrt(4) + 4! * 4!) / sqrt(4)
290 4 (4! * 4! / sqrt (4)) + sqrt(4)
3 (sqrt(4) - sqrt(.4`%)) / sqrt(.4`)%
291 4 (sqrt(sqrt(sqrt(4^4!))) + .4') / .(sqrt(4))'
4 (sqrt(4 * .4`) - 4%) / .4`%
292 4 (4! * 4! / sqrt (4)) + 4
293 4 ((sqrt(.4') - sqrt(4) % ) / .(sqrt(4))' % ) + sqrt(4)
4 ((sqrt(4) - sqrt(4)%) / sqrt(.4`)%) - 4
294 4 (sqrt(4) / .4)! / .4` + 4!
3 (sqrt(4) - 4%) / sqrt(.4`)%
295 4 ((sqrt(4) / .4)! - sqrt(4)) / .4
296 4 (sqrt(4) / .4)! / .4 - 4
3 (sqrt(4) / sqrt(.4`)%) - 4
297 4 4! / .(4!)' * sqrt(4 / .4')
3 (sqrt(4) - sqrt(4)%) / sqrt(.4`)%
298 4 (sqrt(4) / .4)! / .4 - sqrt(4)
3 (sqrt(4) / sqrt(.4`)%) - sqrt(4)
299 4 ((sqrt(4) / .4)! - .4) / .4
3 (sqrt(4) - sqrt(.4`)%) / sqrt(.4`)%
300 3 (sqrt(4) / .4)! / .4
2 sqrt(.4') / .(sqrt(4))' %
2 sqrt(4) / sqrt(.4`)%
301 4 (.4 + (sqrt(4) / .4)!) / .4
3 (sqrt(4) + sqrt(.4`)%) / sqrt(.4`)%
302 4 sqrt(4) + (sqrt(4) / .4)! / .4
3 sqrt(4) + (sqrt(4) / sqrt(.4`)%)
303 4 ((4! / sqrt(4)) + .(4!)') / .4'%
3 (sqrt(4) + sqrt(4)%) / sqrt(.4`)%
304 4 4^4 + 4! + 4!
3 4 + (sqrt(4) / sqrt(.4`)%)
305 4 (sqrt(4) + (sqrt(4) / .4)!) / .4
306 4 (4 + sqrt(sqrt(sqrt(4^4!)) / .(sqrt(4))'
3 (sqrt(4) + 4%) / sqrt(.4`)%
307 4 (.(4!) + .4' - .(sqrt(4))' % ) / .(sqrt(4))' %
4 4 + ((sqrt(4) + sqrt(4)%) / sqrt(.4`)%)
308 4 (4 + (sqrt(.4') / .4' % )) * sqrt(4)
309 4 (sqrt(.4' * 4) + 4 % ) / .4' %
310 4 (4 + (sqrt(4) / .4)!) / .4
3 (sqrt(4) + sqrt(.4`%)) / sqrt(.4`)%
311 4 (sqrt(.4') + (4 % )' - sqrt(4) % ) / .(sqrt(4))' %
4 (sqrt(sqrt(4) - 4%) / .4`%) - 4
312 4 (4 + sqrt(4))! * .4 + 4!
313 4 (.(sqrt(4)) + (.(sqrt(4)) ^ -(sqrt(sqrt(sqrt((4!))))) / .4
4 (sqrt(sqrt(4) - 4%) / .4`%) - sqrt(4)
314 4 ((sqrt(.4') - sqrt(4)' % ) / .(sqrt(4)' % ) + 4!
4 4 + ((sqrt(4) + sqrt(.4`%)) / sqrt(.4`)%)
315 4 (4! / sqrt(.4' %)) - (sqrt(4) / 4' %)
3 sqrt(sqrt(4) - 4%) / .4`%
316 4 4^4 + 4! / .4
317 4 ((sqrt(.4') + 4 % - .(sqrt(4))' % ) / .(sqrt(4))' %
4 sqrt(4) + (sqrt(sqrt(4) - 4%) / .4`%)
318 4 (4 + sqrt(4))! * .4` - sqrt(4)
319 4 (sqrt(sqrt(sqrt(4 ^ 4!)))) - .(sqrt(4))) / .(sqrt(4))
4 4 + (sqrt(sqrt(4) - 4%) / .4`%)
320 3 (4 + sqrt(4))! * .4`
321 4 (sqrt(sqrt(sqrt(4 ^ 4!) + .(sqrt(4))) / .(sqrt(4)
4 ((sqrt(.4`) / .4%) - 4!) / .4`
322 4 (4 + sqrt(4))! * .4` + sqrt(4)
323 4 ((sqrt(.4') - .(sqrt(4))' % ) / .(sqrt(4))' % ) + 4!
4 ((sqrt(4) - sqrt(.4`)%) / sqrt(.4`)%) + 4!
324 4 (4 * 4 + sqrt(4))^sqrt(4)
3 (sqrt(4) / sqrt(.4`)%) + 4!
325 4 (4! + sqrt(4))! / (4!)! / sqrt(4)
326 4 (4! - sqrt(4)) / sqrt(.4' %)) - 4
327 4 ((sqrt(sqrt(sqrt(.4))))^(-4!) - sqrt(4)) * 4!
328 4 (4! / sqrt(.4' % )) - root.4(4)
329 4 (4! - (sqrt(4) + sqrt(.4' %))) / sqrt(.4' %)
330 4 (root.4(4) / .4) / .(4!)'
3 (4! - sqrt(4)) / sqrt(.4`%)
331 4 (sqrt(.4' %) - sqrt(4) + 4!) / sqrt(.4' %)
332 4 (4! / sqrt(.4' %)) - (4 + 4!)
333 4 (4! - sqrt(4) + .(sqrt(4))) / sqrt(.4' % )
3 (sqrt(.4`) - sqrt(.4`%)%) / sqrt(4%)%
334 4 (4! / sqrt(.4' %)) - (sqrt(4) + 4!)
3 (sqrt(.4`) / sqrt(4%)%) + sqrt(.4`)
335 4 (4! / sqrt(.4' %)) - .(sqrt(4)) ^ - (sqrt(4))
4 (4 + sqrt(4)%) / (sqrt(4) / .4)!%%
336 4 4! * (4! + 4) / sqrt(4)
3 (4! / sqrt(.4`%)) - 4!
337 4 ((4! + sqrt(.4' % )) / sqrt(.4' % )) - 4!
338 4 (4! + sqrt(4))^sqrt(4) / sqrt(4)
339 4 ((sqrt(.4') / 4' % ) + sqrt(.4' % )) / 4' %)
340 4 (4! / sqrt(.4' %)) - (4! - 4)
4 (sqrt (sqrt (sqrt (4 ^ 4!))) + 4) / .sqrt (4)
341 4 (sqrt(4) - .4' - 4 % ) / .4' %
342 4 (root(.(sqrt(4))' ,4) * sqrt(.4')) + sqrt(.4')
4 (4 - sqrt(4%)) * .4 / .4`%
343 4 sqrt(sqrt(sqrt((sqrt(4) + sqrt(4) / .4))))^4!
344 4 (4 + sqrt(4))! * .4` + 4!
345 4 (4! / sqrt(.4' %)) - (sqrt(.4') / 4' %)
346 4 ((4! - sqrt(.4')) / sqrt(.4' % )) - 4
347 4 ((4! - sqrt(.4') - .(sqrt(4))) / sqrt(.4' % )
4 (4! - (sqrt(4%) + sqrt(.4`))) / sqrt(.4`%)
348 4 ((4! / 4)! - 4!) / sqrt(4)
349 4 ((4! - sqrt(.4') - sqrt(.4' % )) / sqrt(.4' % )
350 4 (4! - (4 / .4)) / 4%
3 (sqrt(4) - .4`) / .4`%
4 (4! /. 4 + 4!) / .4!
351 4 4! / sqrt(sqrt(sqrt(.4^(4!)))) - 4!
352 4 44 * (4 + 4)
353 4 ((4! - sqrt(.4') + .(sqrt(4))) / sqrt(.4' % )
4 ((4! - sqrt(4%)) / sqrt(.4`%)) - 4
354 4 (sqrt(4) / .4' %) - (4 * 4!)
3 (4! - .4) / sqrt(.4`%)
355 4 4^4 + 4! / .(4!)'
4 ((4 * .4`) - sqrt(4%)) / .4`%
356 4 (4! / 4)! / sqrt(4) - 4
3 (4! / sqrt(.4`%)) - 4
357 3 (4! - .(sqrt(4))) / sqrt(.4' %)
3 (4! - sqrt(4%)) / sqrt(.4`%)
358 4 ((4! / 4)! - 4) / sqrt(4)
3 (4! / sqrt(.4`%)) - sqrt(4)
359 4 ((4! / 4)! - sqrt(4)) / sqrt(4)
3 (4! - sqrt(.4`%)) / sqrt(.4`%)
360 3 (sqrt(4) + 4)! / sqrt(4)
2 4! / sqrt(.4' % )
361 4 (sqrt(4) + (4! / 4)!) / sqrt(4)
3 (4! + sqrt(.4`%)) / sqrt(.4`%)
362 4 ((4! / 4)! + 4) / sqrt (4)
3 sqrt(4) + (4! / sqrt(.4`%))
363 4 44 * sqrt(4) / .(4!)'
3 (4! + sqrt(4%)) / sqrt(.4`%)
364 4 4 + (4! / 4)! / sqrt(4)
3 4 + (4! / sqrt(.4`%))
365 4 (4! / sqrt(.4' %)) + (sqrt(4) / .4)
366 4 (4! / sqrt(.4' %)) + (4! / 4)
3 (4! + .4) / sqrt(.4`%)
367 4 (4! + sqrt(.4') - .(sqrt(4))) / sqrt(.4' % )
4 4 + ((4! + sqrt(4%)) / sqrt(.4`%))
368 4 4 * (4 * 4! - 4)
369 4 .(sqrt(4))^(-4) - 4^4
4 4% ^ -sqrt(4) - 4 ^ 4
370 4 (4! / sqrt(.4' %)) + (4 / .4)
3 (4! + sqrt(.4`)) / sqrt(.4`%)
371 4 4! / sqrt(sqrt(sqrt(.4^(4!)))) - 4
372 4 (4! + (4! / 4)!) / sqrt(4)
373 4 4! / sqrt(sqrt(sqrt(.4^(4!)))) - sqrt(4)
374 4 (.(sqrt(4)) ^ - (sqrt(4)) - (sqrt(.4' %)) / sqrt(.4' %)
4 ((sqrt(4) - .4`) / .4`%) + 4!
375 4 .4 * 4! / .4^4
3 4! / sqrt(sqrt(sqrt(.4 ^ (4!)))
376 4 (4! - 4)^sqrt(4) - 4!
377 4 4! / sqrt(sqrt(sqrt(.4^(4!)))) + sqrt(4)
378 4 (4^4 - 4) / sqrt(.4`)
379 4 4! / sqrt(sqrt(sqrt(.4^(4!)))) + 4
380 4 4 * 4 * 4! - 4
381 4 (4^4 - sqrt(4)) / sqrt(.4`)
382 4 4 * 4 * 4! - sqrt(4)
383 4 (4^4 - sqrt(.4`)) / sqrt(.4`)
384 3 4 * 4 * 4!
385 4 (4^4 + sqrt(.4`)) / sqrt(.4`)
386 4 4 * 4 * 4! + sqrt(4)
387 4 (4^4 + sqrt(4)) / sqrt(.4`)
388 4 4 * 4 * 4! + 4
389 4 (sqrt(4) + 4! - sqrt(.4`%)) / sqrt(.4`%)
390 4 (4^4 + 4) / sqrt(.4`)
3 (sqrt(4) + 4!) / sqrt(.4`%)
391 4 (sqrt(.4' %) + sqrt(4) + 4!) / sqrt(.4' %)
392 4 4 * (4 * 4! + sqrt(4))
393 4 (.(sqrt(4)) + sqrt(4) + 4!) / sqrt(.4' %)
4 (sqrt(4) + 4! + sqrt(4%)) / sqrt(.4`%)
394 4 ((4*4!) / .(4!)') - sqrt(4)
4 ((4 * 4) - 4!%) / 4%
395 4 ((4*4!) - .(4!)') / .(4!)'
4 ((4 * 4) - sqrt(4%)) / 4%
396 4 (4! - 4)^sqrt(4) - 4
3 ((4*4!) / .(4!)')
3 (sqrt(4) - 4!%) / .4`%
397 4 ((4*4!) + .(4!)') / .(4!)'
4 (sqrt(4) - (4! - .4`)%) / .4`%
398 4 (4! - 4)^sqrt(4) - sqrt(4)
399 4 (4! / sqrt(sqrt(sqrt(.4^(4!))))) + 4!
400 3 (4! - 4)^sqrt(4)
401 4 (.(4!) + (4! * 4)) / .(4!)
4 ((4 * 4) + 4%) / 4%
402 4 (4! - 4)^sqrt(4) + sqrt(4)
403 4 ((sqrt(4) - .(sqrt(4))) / .4' % ) - sqrt(4)
3 (4 + 4)!% - sqrt(4%)
404 4 (4! - 4)^sqrt(4) + 4
405 4 (4 + sqrt(4))! / 4 / .4`
3 (sqrt(4) - sqrt(4%)) / .4`%
406 4 ((sqrt(4) - .(sqrt(4)) + .4' % ) / .4' %
4 (sqrt(4) / .4`%) - 44
407 4 ((sqrt(4) - .(sqrt(4))) / .4' % ) + sqrt(4)
4 4 + (4 + 4)!% - sqrt(4%)
408 4 4 * 4 * 4! + 4!
409 4 ((sqrt(4) - .(sqrt(4))) / .4' % ) + 4
4 ((4 * .4`) + 4%) / .4`%
410 4 ((4 * 4) + .4) / 4%
411 4 ((sqrt(4) - sqrt(.4' % )) / .4' % ) - 4!
412 4 ((4! / .(4!)') + 4) * 4
4 (4 + 4 + 4!%) / sqrt(4)%
413 4 root(.(sqrt(4))' ,4) - (4! / .(4!)')
414 4 ((4*4!) - 4) / .(sqrt(4)')
4 (sqrt(4) - (4 * 4)%) / .4`%
415 4 (sqrt(4) - .(sqrt(4)) + 4' % ) / .4' %
4 ((4 / 4%) - .4) / 4!%
4 (4! /. 4! - .4) / .4!
416 4 4 * 4 * (4! + sqrt(4))
417 4 (4 - .(sqrt(4)) + 4!) / sqrt(.4'%)
4 ((sqrt(4) - 4%) / .4`%) - 4!
418 4 (sqrt(4) / .4' %) - root(.4,4)
419 4 (4 + 4! - sqrt(.4' %)) / sqrt(.4' %)
420 4 444 - 4!
3 (4 + 4!) / sqrt(.4`%)
421 4 (sqrt(.4') + 4 + 4!) / sqrt(.4' %)
4 4 ^ 4 + .4 / .4!'%
422 4 (sqrt(4) / .4' %) - (4 + 4!)
423 4 (((sqrt(sqrt(sqrt(.4))))^(-4!)) + (sqrt(4))) * (4!)
424 4 (4! - 4)^sqrt(4) + 4!
425 4 ((sqrt(4) - .4' % ) / .4' % ) - 4!
426 4 4! * (4! - .4^(-sqrt(4)))
3 (sqrt(4) / .4`%) - 4!
427 4 ((sqrt(4) + .4' % ) / .4' % ) - 4!
4 (4 + 4)!% + 4! - .sqrt(4)
428 4 (4*4!) / .sqrt(4)' - 4
4 sqrt(4) + (sqrt(4) / .4`%) - 4!
429 4 ((4*4!) - .4') / .(sqrt(4))'
4 (4! + (sqrt(.4`) / .4%)) / .4`
430 4 (4*4!) / .sqrt(4)' - sqrt(4)
4 ((4 / .4`) - .4) / sqrt(4)%
431 4 ((4*4!) - .sqrt(4)') / .sqrt(4)'
4 ((sqrt(4) - sqrt(.4`%)) / .4`%) - 4
432 4 4! * (4 * 4 + sqrt(4))
3 (4*4!) / .sqrt(4)'
433 4 ((4*4!) + .sqrt(4)') / .sqrt(4)'
4 ((sqrt(4) - sqrt(.4`%)) / .4`%) - sqrt(4)
434 4 (4*4!) / .sqrt(4)' + sqrt(4)
4 (sqrt(4) / .4`%) - (4 * 4)
435 4 ((4*4!) + .4') / .(sqrt(4))'
3 (sqrt(4) - sqrt(.4`%)) / .4`%
436 4 (4*4!) / .sqrt(4)' + 4
4 4 * (4% + .4`) / .4`%
437 4 ((sqrt(4) - 4 %) / .4' % ) - 4
438 4 (sqrt(4) / .4' %) - (4! / sqrt(4))
4 sqrt(4) /. 4'% - 4! / sqrt(4)
439 4 ((sqrt(4) - 4 % ) / .4' % ) - sqrt(4)
440 4 444 - 4
3 (sqrt(4) - 4!%) / .4%
441 4 (4! - sqrt(4) / sqrt(.4`))^sqrt(4)
3 (sqrt(4) - 4%) / .4`%
442 4 444 - sqrt(4)
443 4 ((sqrt(4) - 4 % ) / .4' % ) + sqrt(4)
444 3 444
445 4 (sqrt(4) / .4' %) - (sqrt(4) / .4)
446 4 444 + sqrt(4)
3 (sqrt(4) / .4`%) - 4
447 4 ((sqrt(4) / .4'% ) - (sqrt(4 / .4')
4 (4! /.4! - sqrt(.4 ')) / .sqrt(4)'
448 4 444 + 4
3 (sqrt(4) / .4`%) - sqrt(4)
449 4 (4! / .(sqrt(4))' - .(4!)) / .(4!)
3 (sqrt(4) - .4`%) / .4`%
450 4 (4! / 4)! / 4 / .4
2 sqrt(4) / .4' %
451 4 (4! / .(sqrt(4)) + .(4!)) / .(4!)
3 (sqrt(4) + .4`%) / .4`%
452 4 root(.(sqrt(4))' ,4) - (4! / .4)
3 sqrt(4) + (sqrt(4) / .4`%)
453 4 ((4! / .(4!)) + sqrt(.4')) / .(sqrt(4))'
4 4 + ((sqrt(4) - .4`%) / .4`%)
454 4 (4! / .(4!) / .(sqrt(4))') + 4
3 4 + (sqrt(4) / .4`%)
455 4 (sqrt(4) / .4' %) + (sqrt(4) / .4)
456 4 4! * (4! - sqrt(4) / .4)
457 4 ((sqrt(4) + 4 % ) / .4' % ) - sqrt(4)
458 4 (4*4!) / .sqrt(4)' + 4!
4 4 + 4 + (sqrt(4) / .4`%)
459 4 ((4! / .(4!)) + sqrt(4)) / .(sqrt(4))'
3 (sqrt(4) + 4%) / .4`%
460 4 (4! - sqrt(4))^sqrt(4) - 4!
3 (4!% + sqrt(.4`%)) / sqrt(.4`%)%
461 4 ((sqrt(4) + 4 % ) / .4' % ) + sqrt(4)
462 4 (4! - sqrt(4))! / (4! - 4)!
463 4 ((sqrt(4) + 4 % ) / .4' % ) + 4
464 4 (4^4 - 4!) * sqrt(4)
465 4 (sqrt(4) / .4' %) + (sqrt(.4') / 4' %)
3 (sqrt(4) + sqrt(.4`%)) / .4`%
466 4 (sqrt(4) / .4' %) + (4 * 4)
467 4 ((sqrt(4) + sqrt(.4' % )) / .4' % ) + sqrt(4)
468 4 444 + 4!
469 4 ((sqrt(4) + sqrt(.4' % )) / .4' % ) + 4
470 4 (sqrt(4) / .4' %) + (4! - 4)
4 (4! * 4 - sqrt (4)) / .sqrt(4)
471 4 (((sqrt(sqrt(sqrt(.4))))^(-4!)) + (4)) * (4!)
472 4 (4! - 4) * (4! - .4)
473 4 ((sqrt(4) - .4' % ) / .4' % ) + 4!
474 4 (4! / .(4!) / .(sqrt(4))') + 4!
3 (sqrt(4) / .4`%) + 4!
475 4 ((4! / .(4!)') - 4) / .(sqrt(4))
4 (sqrt(4) - (.4 / 4)) / .4%
476 4 4! * (4! - 4) - 4
3 (sqrt(4) / .4%) - 4!
477 4 4! * 4! - 4! / .(4!)'
4 (4 + 4!%) / (sqrt(4) * .4`)%
478 4 4! * (4! - 4) - sqrt(4)
479 4 (4 * 4!) - .(sqrt(4)) / .(sqrt(4))
4 ((4 * 4!) - sqrt(4%)) / sqrt(4%)
480 3 4! * (4! - 4)
481 4 (4 * 4!) + .(sqrt(4)) / .(sqrt(4))
4 ((4 * 4!) + sqrt(4%)) / sqrt(4%)
482 4 sqrt(4) + 4! * (4! - 4)
483 4 (4! / .(sqrt(4))' - sqrt(.4')) / .(sqrt(4))'
4 ((sqrt(4) + 4%) / .4`%) + 4!
484 3 (4! - sqrt(4))^sqrt(4)
485 4 ((4! / .(sqrt(4))') - .(sqrt(4))') / .(sqrt(4))'
4 (sqrt(4) - (4 + sqrt(4))%) / .4%
486 4 4 * 4! / (.4` * .4`)
487 4 (((4! / .(sqrt(4))') + .(sqrt(4))') / .(sqrt(4))'
488 4 sqrt(4) * 4 ^ 4 - 4!
489 4 ((4! / .(sqrt(4))') + sqrt(.4') / .(sqrt(4))'
4 (sqrt(4) - 4.4%) / .4%
490 4 (4! / .(sqrt(4))' / .(sqrt(4))') + 4
3 (sqrt(4) - 4%) / .4%
491 4 ((sqrt(4) / .4)! / .(4!)' - 4
4 (sqrt(4) / .4%) - (4 / .4`)
492 4 root(.(sqrt(4))' ,4) - (4 / .(sqrt(4)))
4 (sqrt(4) / .4%) - (4 + 4)
493 4 ((sqrt(4) / .4)! / .(4!)' - sqrt(4)
4 ((sqrt(4) - sqrt(4)%) / .4%) - sqrt(4)
494 4 (((sqrt(4) / .4)! - .(4!)') / .(4!)'
4 (sqrt(4) / .4`%) + 44
495 4 (4! - sqrt(4)) / (.4` - .4)
3 ((sqrt(4) / .4)! / .(4!)'
3 (sqrt(4) - sqrt(4)%) / .4%
496 4 4 * (4 + (sqrt(4) / .4)!)
3 (sqrt(4) / .4%) - 4
497 4 ((sqrt(4) / .4)! / .(4!)' + sqrt(4)
4 ((sqrt(4) + .4%) / .4%) - 4
498 4 ((4! / .(4!) - .4) / .(sqrt(4))
3 (sqrt(4) / .4%) - sqrt(4)
499 4 ((sqrt(4) / .4)! / .(4!)' + 4
3 (sqrt(4) - .4%) / .4%
500 4 4 * sqrt(sqrt(sqrt((sqrt(4) / .4)^4!)))
2 sqrt(4) / .4%
501 4 ((sqrt(4) / .4)! + .(4!)) / .(4!)
3 (sqrt(4) + .4%) / .4%
502 4 root(.(sqrt(4))' ,4) - (4 /.4)
3 sqrt(4) + (sqrt(4) / .4%)
503 4 root(.(sqrt(4))' ,4) - (4 / .4')
4 4 + ((sqrt(4) - .4%) / .4%)
504 4 (4^4 - 4) * sqrt(4)
3 4 + (sqrt(4) / .4%)
505 4 .(sqrt(4))^(-4) - (sqrt(4) / .4)!
3 (sqrt(4) + sqrt(4)%) / .4%
506 4 root(.(sqrt(4))' ,4) - (4 / sqrt(.4'))
4 4 + sqrt(4) + (sqrt(4) / .4%)
507 4 root(.(sqrt(4))' ,4) - (sqrt(4) / .4)
4 sqrt(4) + ((sqrt(4) + sqrt(4)%) / .4%)
508 4 4^4 * sqrt(4) - 4
509 4 root(.(sqrt(4))' ,4) - (sqrt(4 / .4'))
4 (4 / .4`) + (sqrt(4) / .4%)
510 4 sqrt(4) * 4^4 - sqrt(4)
3 (sqrt(4) + 4%) / .4%
511 4 root(.(sqrt(4))' ,4) - (4 / 4)
4 (4.4% + sqrt(4)) / .4%
512 3 sqrt(4) * 4^4
2 root(.(sqrt(4))',4)
513 4 root(.(sqrt(4))' ,4) + (4 / 4)
4 (sqrt(4) + root(sqrt(4%), 4)) / sqrt(4)
514 4 sqrt(4) * 4 ^ 4 + sqrt(4)
515 4 root(.(sqrt(4))' ,4) + (sqrt(4 / .4'))
4 ((4 + sqrt(4))% + sqrt(4)) / .4%
516 4 sqrt(4) * 4 ^ 4 + 4
517 4 root(.(sqrt(4))' ,4) + (sqrt(4) / .4))
518 4 root(.(sqrt(4))' ,4) + (4 / sqrt(.4'))
4 ((4 + sqrt(4))!%% + sqrt(4)) / .4%
519 4 ((sqrt(4) / .4)! / .(4!)' + 4!
4 ((sqrt(4) - sqrt(4)%) / .4%) + 4!
520 4 sqrt(4) * (4 + 4^4)
521 4 root(.(sqrt(4))' ,4) + (4 / .4')
522 4 (4^4 - 4!) / .4`
523 4 ((sqrt(4) - .4 % ) / .4 % ) + 4!
524 4 4! * (4! - sqrt(4)) - 4
3 (sqrt(4) / .4%) + 4!
525 4 (4! - sqrt(.4`)) / (.4` - .4)
526 4 4! * (4! - sqrt(4)) - sqrt(4)
527 4 ((4! - sqrt(.4')) / 4' % ) + sqrt(4)
528 3 (4! - sqrt(4)) * 4!
529 4 (4! - 4 / 4) ^ sqrt(4)
530 4 sqrt(4) + 4! * (4! - sqrt(4))
531 4 (4! - .4) / (.4` - .4)
532 4 4!^sqrt(4) - 44
533 4 (4! * .4' - sqrt(.4)%) / sqrt(4)%
534 4 root(.(sqrt(4))' ,4) + (4! - sqrt(4))
4 (4 - 44%) / sqrt(.4`)%
535 4 (4! - .(sqrt(4))') / (.4' - .4)
4 4% ^ -sqrt(4) - (.4 / .4`%)
536 4 sqrt(4) * 4 ^ 4 + 4!
537 4 ((sqrt(4) / .4')! - .4') / .(sqrt(4))'
4 (4 - (sqrt(4)% + .4)) / sqrt(.4`)%
538 4 4! / (.4` - .4) - sqrt(4)
539 4 (((sqrt(4) / .4)! - .(sqrt(4)')) / .(sqrt(4)')
4 (sqrt(4) + .4 - .4`%) / .4`%
540 3 4! / (.4` - .4)
2 4! / 4' %
541 4 (((sqrt(4) / .4)! + .(sqrt(4)')) / .(sqrt(4)')
4 (sqrt(4) - 4% + .4`) / .4`%
542 4 4! / (.4` - .4) + sqrt(4)
543 4 ((sqrt(4) / .4)! + .4') / .(sqrt(4))'
4 (4 + sqrt(4)% - .4) / sqrt(.4`)%
544 4 4! / (.4` - .4) + 4
545 4 (4! + .(sqrt(4))') / (.4' - .4)
4 (4! - sqrt(4)%) / 4.4%
546 4 ((4! - sqrt(4)) / 4%) - 4
547 4 (4! + .(sqrt(4))') / 4' % ) + sqrt(4)
548 4 4!^sqrt(4) - 4! - 4
549 4 (4! + .4) / (.4` - .4)
550 4 4!^sqrt(4) - 4! - sqrt(4)
3 (4! - sqrt(4)) / 4%
551 4 4! * 4! - .(sqrt(4))^(-sqrt(4))
4 (4! - sqrt(4) + 4%) / 4%
552 3 4!^sqrt(4) - 4!
553 4 ((4! + sqrt(.4')) / 4' % ) - sqrt(4)
4 (sqrt(sqrt(sqrt(4!^4!))) * 4)% + 4%
554 4 4!^sqrt(4) - 4! + sqrt(4)
555 4 (4! + sqrt(.4`)) / (.4` - .4)
556 4 4!^sqrt(4) - 4! + 4
557 4 ((4! + sqrt(.4')) / 4' % ) + sqrt(4)
558 4 (4! - sqrt(.4`)) * 4! - sqrt(4)
559 4 (sqrt(4) + .(4!) - .4 % ) / .4 %
4 (sqrt(4) + (4! - .4)%) / .4%
560 3 (4! - sqrt(.4`)) * 4!
561 4 .(sqrt(4))^(-4) - (sqrt(sqrt(sqrt(4^4!)
4 (sqrt(4) + (4! + .4)%) / .4%
562 4 (4! - sqrt(.4`)) * 4! + sqrt(4)
563 4 ((4! - 4' % ) / 4' % ) + 4!
564 4 4!^sqrt(4) - 4! / sqrt(4)
3 (4 - 4!%) / sqrt(.4`)%
565 4 .(sqrt(4))^(-4) - (4! / .4)
4 4% ^ -sqrt(4) - (4! / .4)
566 4 4!^sqrt(4) - 4 / .4
567 4 (4^4 - 4) / .4'
568 4 4!^sqrt(4) - 4 - 4
569 4 ((4! + .(sqrt(4))') / 4' % ) + 4!
4 (4 - (sqrt(4%) + sqrt(.4`)%)) / sqrt(.4`)%
570 4 4!^sqrt(4) - 4 - sqrt(4)
3 (4 - sqrt(4%)) / sqrt(.4`)%
571 4 4!^sqrt(4) - sqrt(4) / .4
572 3 4!^sqrt(4) - 4
573 4 4!^sqrt(4) - sqrt(4 / .4`)
574 3 4!^sqrt(4) - sqrt(4)
575 4 4!^sqrt(4) - 4/4
576 2 4!^sqrt(4)
577 4 4!^sqrt(4) + 4/4
578 3 4!^sqrt(4) + sqrt(4)
579 4 4!^sqrt(4) + sqrt(4) / sqrt(.4`)
580 3 4!^sqrt(4) + 4
581 4 4!^sqrt(4) + sqrt(4) / .4
582 4 4!^sqrt(4) + 4 + sqrt(4)
583 4 ((sqrt(4) + 4!) / 4' % ) - sqrt(4)
3 (4! - .4') / (4%)'
584 4 4!^sqrt(4) + 4 + 4
585 4 (4^4 + 4) / .4`
586 4 4!^sqrt(4) + 4 / .4
587 4 ((sqrt(4) + 4!) / 4' % ) + sqrt(4)
588 4 4!^sqrt(4) + 4! / sqrt(4)
3 (4! - .4!') / (4%)'
589 4 .(sqrt(4))^(-4) - (4! / sqrt(.4'))
4 (4! - 44%) / 4%
590 4 (4! + sqrt(.4`)) * 4! - sqrt(4)
3 (4! - .4) / 4%
591 4 (4! / 4%) - (4 / .4')
592 3 4! (sqrt(.4') + 4!)
593 4 .(sqrt(4))^(-4) - root(.4,4)
4 4% ^ -sqrt(4) - root(.4, 4)
594 4 (4! + sqrt(.4`)) * 4! + sqrt(4)
3 4! - .(4!)) / 4 %
3 (4! - 4!%) / 4%
595 4 (4!/4)! - sqrt(sqrt(sqrt(.(sqrt(4)))))^(-4!)
3 (4! - sqrt(4%)) / 4%
596 4 4!^sqrt(4) + 4! - 4
3 (4! / 4%) - 4
597 4 .(sqrt(4))^(-4) - (4! + 4)
3 (4 - sqrt(4)%) / sqrt(.4`)%
598 4 4!^sqrt(4) + 4! - sqrt(4)
3 (4! / 4%) - sqrt(4)
599 4 .(sqrt(4))^(-4) - (4! + sqrt(4))
3 (4! - 4%) / 4%
600 3 4!^sqrt(4) + 4!
2 4! / 4%
601 4 (sqrt(4) / .4)^4 - 4!
3 (4! + 4%) / 4%
602 4 4!^sqrt(4) + 4! + sqrt(4)
3 sqrt(4) + (4! / 4%)
603 4 .(sqrt(4))^(-4) - (4! - sqrt(4))
3 (4 + sqrt(4)%) / sqrt(.4`)%
604 4 4!^sqrt(4) + 4! + 4
3 4 + (4! / 4%)
605 4 .(sqrt(4))^(-4) - (4! - 4)
3 (4! + sqrt(4%)) / 4%
606 4 (4! + .(4!)' + .(4!)') / .4'%
3 (4! + 4!%) / 4%
607 4 (4 % + .(4!) + 4!) / 4 %
4 ((4 + 4!)% + 4!) / 4%
608 4 (4! + sqrt(.4`) + sqrt(.4`)) * 4!
609 4 .(sqrt(4))^(-4) - (4 * 4)
4 (4 / .4`) + (4! / 4%)
610 4 ((sqrt(4) / .4)! + sqrt(4)) / .(sqrt(4))
3 (4! + .4) / 4%
611 4 root(.(sqrt(4))' ,4) + (4! / .(4!)')
4 (4! + 44%) / 4%
612 4 4! * (4! + sqrt(.4`) / .4`)
613 4 .(sqrt(4))^-(4) - (4! / sqrt(4))
4 4% ^ -sqrt(4) - (4! / sqrt(4))
614 4 ((4! - .4) / 4 % ) + 4!
615 4 .(sqrt(4))^(-4) - (4 / .4)
4 (4 + (.4 / 4)) / sqrt(.4`)%
616 4 4^4 / .4 - 4!
617 4 .(sqrt(4))^(-4) - (4 + 4)
4 4% ^ -sqrt(4) - (4 + 4)
618 4 (4! / 4 % ) + (4 / .(sqrt(4))')
4 4! + ((4! - 4!%) / 4%)
619 4 .(sqrt(4))^(-4) - (4 / sqrt(.4'))
4 4% ^ -sqrt(4) - (4 + sqrt(4))
620 4 4!^sqrt(4) + 44
621 4 (sqrt(4) / .4)^4 - 4
3 4% ^ -sqrt(4) - 4
622 4 4! * (4! + sqrt(4)) - sqrt(4)
623 4 (sqrt(4) / .4)^4 - sqrt(4)
3 4% ^ -sqrt(4) - sqrt(4)
624 3 4! * (4! + sqrt(4))
625 3 (sqrt(4) / .4) ^ 4
2 .(sqrt(4))^-(4)
2 4% ^ -sqrt(4)
626 4 sqrt(4) + 4! * (4! + sqrt(4))
4 (4! + sqrt(4) )! / (4!)! - 4!
627 4 sqrt(4) + (sqrt(4) / .4)^4
3 sqrt(4) + 4% ^ -sqrt(4)
628 4 4 + 4! * (4! + sqrt(4))
629 4 4 + (sqrt(4) / .4)^4
3 4 + 4% ^ -sqrt(4)
630 4 (4 / .4')! / (4! * 4!)
3 (4 + sqrt(4%)) / sqrt(.4`)%
631 4 .(sqrt(4))^(-4) + (4 / sqrt(.4'))
4 4 + sqrt(4) + 4% ^ -sqrt(4)
632 4 root(.(sqrt(4))' ,4) + (sqrt(4) / .4)!
4 (4! / 4%) + root(.4, 4)
633 4 .(sqrt(4))^(-4) + 4 + 4
4 4 + 4 + 4% ^ -sqrt(4)
634 4 .(sqrt(4))^(-4) + (4 / .4')
4 4! + ((4! + .4) / 4%)
635 4 (4^4 - sqrt(4)) / .4
636 4 4^4 / .4 - 4
3 (4 + 4!%) / sqrt(.4`)%
637 4 .(sqrt(4))^-(4) + (4! / sqrt(4))
4 (4! / sqrt(4)) + 4% ^ -sqrt(4)
638 4 4^4 / .4 - sqrt(4)
639 4 (4^4 - .4) / .4
640 3 4^4 / .4
641 4 (.4 + 4^4) / .4
642 4 sqrt(4) + 4^4 / .4
643 4 .(sqrt(4)) ^ (- 4) + (4 / .(sqrt(4))')
4 ((sqrt(4%) - 4!)% + sqrt(.4`)) / sqrt(.4`%)%
644 4 4 + 4^4 / .4
645 4 (sqrt(4) + 4^4) / .4
646 4 (4! + sqrt(4))! / (4!)! - 4
647 4 .(sqrt(4))^(-4) + (4! - sqrt(4))
4 4! - sqrt(4) + 4% ^ -sqrt(4)
648 4 (sqrt(4) + 4)^4 / sqrt(4)
649 4 4! + (sqrt(4) / .4)^4
3 4! + 4% ^ -sqrt(4)
650 3 (4! + sqrt(4))! / (4!)!
651 4 (4! + sqrt(4))! + (4!)!) / (4!)!
652 4 (4! + sqrt(4))^sqrt(4) - 4!
653 4 .(sqrt(4))^(-4) + 4! + 4
4 4 + 4! + 4% ^ -sqrt(4)
654 4 4 + (4! + sqrt(4))! / (4!)!
655 4 (.(sqrt(4)) + sqrt(4) + 4!) / 4 %
4 (sqrt(4) + 4! + sqrt(4%)) / 4%
656 4 4! * (4! + 4 - sqrt(.4`))
657 4 (4!) * (4!) + root( - (sqrt(.4')), .4')))
658 4 (44 / sqrt(.4' % )) - sqrt(4)
659 4 (44 - sqrt(.4' %)) / sqrt(.4' %)
660 4 (4! / 4)! - 4! / .4
3 44 / sqrt(.4`%)
661 4 .(sqrt(4))^(-4) + (4! / sqrt(.4'))
4 (44 + sqrt(.4`%)) / sqrt(.4`%)
662 4 (44 / sqrt(.4' %)) + sqrt(4)
663 4 (44 + .(sqrt(4))) / sqrt(.4' %)
4 (sqrt(4%) + 44) / sqrt(.4`%)
664 4 4! + 4^4 / .4
665 4 (4! / 4' %) + (.(sqrt(4)) ^ - (sqrt(sqrt(sqrt(4!)))))
4 ((4 * sqrt(.4`)) - sqrt(.4`)%) / .4%
666 4 444 / sqrt(.4`)
3 (.4` / sqrt(.4`%)%) - sqrt(.4`)
667 4 (sqrt(4) - sqrt(.4') +(sqrt(.4' % ) % ) / .(sqrt(4)) %
4 (4 + sqrt(4%)%) / (4! / .4)%%
668 4 4! * (4! + 4) - 4
669 4 .(sqrt(4))^(-4) + 44
4 4% ^ -sqrt(4) + 44
670 4 4! * (4! + 4) - sqrt(4)
671 4 (sqrt(4) / .4' % / sqrt(.4')) - 4
672 4 (4 + 4)! /4! * .4
3 4! * (4! + 4)
673 4 .(sqrt(4))^(-4) + (4! * sqrt(4))
4 (4! / (4 - .4`)%) - sqrt(4)
674 4 (4! + sqrt(4))^sqrt(4) - sqrt(4)
675 4 (sqrt(4) / .4)! / (.4 * .4`)
3 4! / (4 - .4`)%
676 3 (4! + sqrt(4))^sqrt(4)
677 4 (sqrt(4) / .4' % / sqrt(.4')) + sqrt(4)
678 4 (4! + sqrt(4))^sqrt(4) + sqrt(4)
679 4 .(sqrt(4))^(-4) + (4! / .4')
4 4 + (4! / (4 - .4`)%)
680 4 (4! + sqrt(4))^sqrt(4) + 4
681 4 ((sqrt(4) / 4' %) + .4) / sqrt(.4' %)
682 4 (sqrt(4) - .4' - 4 % ) / .(sqrt(4))' %
4 (root(sqrt(4%), 4) * sqrt(.4`)) - sqrt(.4`)
683 4 ((.(4!)' + (4 % )') / (4 % % )') - 4!
4 (.4! + (4%)' - .4'%) / (4%)'%
684 4 4! * (4! + sqrt(4) / .4`)
685 4 .(sqrt(4))^(-4) + (4! / .4)
4 (4! / .4) + 4% ^ -sqrt(4)
686 4 ((.(4!) + sqrt(.4' % ) / (4 % )' % ) - 4
4 root(sqrt(.4`), sqrt(4) - 4%) / .4%
687 4 (((sqrt(.4') / .(4!)% )% ) - .(sqrt(4)% ) / .4 %
4 (sqrt(.4') / .4!'% - .sqrt (4) ) /.4
688 4 (4! + 4 + sqrt(.4`)) * 4!
689 4 .(sqrt(4))^(-4) + sqrt(sqrt(sqrt(4)^4!)))
690 4 (4! / 4)! - ((sqrt(4) / sqrt(.4' %))
691 4 (sqrt(4) - .4' - sqrt(4) % ) / .(sqrt(4))' %
692 4 (4 + sqrt(4))! - 4! - 4
693 4 ((sqrt(.4') / .4' % ) + 4) / .(sqrt(4))'
694 4 (4 + sqrt(4))! - 4! - sqrt(4)
695 4 (4! / 4)! - .(sqrt(4))^(-sqrt(4))
4 (4 + 4! - sqrt(4%)) / 4%
696 3 (4 + sqrt(4))! - 4!
697 4 (sqrt(4) - .4' - sqrt(.4') % ) / .(sqrt(4))' %
4 (4 - sqrt(4)% + sqrt(.4`)) / sqrt(.4`)%
698 4 (4 + sqrt(4))! - 4! + sqrt(4)
699 4 (sqrt(.4') / .4' % / .(sqrt(4))') + 4!
4 (4 + 4! - 4%) / 4%
700 4 (4^4 + 4!) / .4
3 (4 + 4!) / 4%
701 4 (sqrt(sqrt(sqrt(.(sqrt(4))))^(-4!))) + 4! * 4!
4 (4 + 4! + 4%) / 4%
4 sqrt(((4! +4)! + (4!)!) / (4!)!)
702 4 (4!/4)! - (4/.(sqrt(4))')
4 ((4 + 4!) / 4%) + sqrt(4)
703 4 (sqrt(4) - .4' + sqrt(.4') % ) / .(sqrt(4))' %
4 (4 + sqrt(4)% + sqrt(.4`)) / sqrt(.4`)%
704 4 4 * 4 * 44
705 4 (sqrt(sqrt(sqrt(4/.4')))^(4!)) - 4!
706 4 (.(4!) + 4 + 4!) / 4 %
4 4 ^ 4 + (sqrt(4) / .4`%)
707 4 (sqrt(4) - .4') / ((4! - sqrt(4)) % % )'
4 (4 + .4!') / (.4!%)' * .4
708 4 (4 + sqrt(4))! - 4! / sqrt(4)
709 4 (sqrt(4) - .4' + sqrt(4) % ) / .(sqrt(4))' %
710 4 (4 + sqrt(4))! - 4 / .4
711 4 (4 + sqrt(4))! - 4 / .4`
712 4 (4 + sqrt(4))! - 4 - 4
713 4 ((.(4!) - sqrt(.4' % )) / .(4!)' %o ) - sqrt(4)
5 (sqrt(sqrt(sqrt(4/.4')))^(4!)) - (4 * 4)
4 (.(sqrt(4)) '+ sqrt(.4'%)) / (4%)'% - sqrt(4)
714 4 (4 + sqrt(4))! - 4 - sqrt(4)
715 4 (4 + sqrt(4))! - sqrt(4) / .4
716 3 (4 + sqrt(4))! - 4
717 4 (4 + sqrt(4))! - sqrt(4) / sqrt(.4`)
718 3 (4 + sqrt(4))! - sqrt(4)
719 4 (4 + sqrt(4))! - 4/4
720 2 (4 + sqrt(4))!
721 4 (4 + sqrt(4))! + 4/4
722 3 (4 + sqrt(4))! + sqrt(4)
723 4 (4 + sqrt(4))! + sqrt(4) / sqrt(.4`)
724 3 (4 + sqrt(4))! + 4
725 4 (4 + sqrt(4))! + sqrt(4) / .4
726 4 (4 + sqrt(4))! + 4 + sqrt(4)
727 4 (sqrt(sqrt(sqrt(4/.4')))^(4!)) - sqrt(4)
728 4 (4 + sqrt(4))! + 4 + 4
729 4 (4 + sqrt(4))! + 4 / .4`
3 sqrt(sqrt(sqrt((4/.4')^4!)))
730 4 (4 + sqrt(4))! + 4 / .4
731 4 (sqrt(sqrt(sqrt(4/.4')))^(4!)) + sqrt(4)
732 4 (4 + sqrt(4))! + 4! / sqrt(4)
733 4 (sqrt(sqrt(sqrt(4/.4')))^(4!)) + 4
734 4 ((.4' + (4%)') / sqrt(.4' % ) % ) + sqrt(.4')
4 (sqrt(4) - .4!) / (.4!)% + sqrt(.4')
735 4 (sqrt(.4') / 4' % ) + (4! / 4)!
736 4 (4 + sqrt(4))! + 4 * 4
737 4 (.4' + .(sqrt(4))' % ) / (.(4!)' %o ) / .4)
4 root (. (sqrt(4)) ', 4) + sqrt(.4'%) ^ (-sqrt(4))
738 4 (4 / .(sqrt(4))') + (4! / 4)!
4 (root(-sqrt(4), .4`%) - 4!%) / sqrt(4)%
739 4 ((.(4!) - sqrt(.4' % )) / .(4!) %o ) + 4!
4 (.(sqrt(4)) '+ sqrt(.4'%)) / (4%)'% + 4!
740 4 (4 + sqrt(4))! + 4! - 4
741 4 (4 - sqrt(.4') - 4 % ) / .4' %
742 4 (4 + sqrt(4))! + 4! - sqrt(4)
743 4 (.(sqrt(4))' + (4!) %o / .(sqrt(4))') / (.4') %o
4 (sqrt(4 /.4'%) + (sqrt(4(%)') / (4%)'
744 3 (4 + sqrt(4))! + 4!
745 4 .(sqrt(4))^(-4) + (sqrt(4) / .4)!
4 (sqrt(4 / .4`) - sqrt(4)%) / .4%
746 4 (4 + sqrt(4))! + 4! + sqrt(4)
747 4 ((sqrt(4) / .4 %) - sqrt(4)) / sqrt(.4')
748 4 (4 + sqrt(4))! + 4! + 4
749 4 ((sqrt(4) / .4 %) - sqrt(.4')) / sqrt(.4')
750 4 (sqrt(4) / .4)! / .4 / .4
3 sqrt(4 / .4`) / .4%
3 (root(-.sqrt(4), .sqrt(4)))*.4!
751 4 ((sqrt(4) / .4 %) + sqrt(.4')) / sqrt(.4')
752 4 (sqrt(4) + 4)! + root.4(4)
753 4 (sqrt(sqrt(sqrt(4/.4')))^(4!)) + 4!
754 4 (sqrt(4) / .4 %) / sqrt(.4')) + 4
4 root (-.sqrt (4), .sqrt (4) ) * .4! + 4
755 4 (4 - .(sqrt(4)) - .4') / .4' %
4 (4 - (sqrt(4%) + .4`)) / .4`%
756 4 (4! + 4)! / (4! + sqrt(4))!
757 4 (.(sqrt(4))' - ((4!) %o / .4')) / .(sqrt(4))' %o
4 (.4! + sqrt(.4'%)) / (4%)'% - sqrt(4)
758 4 (root(.(sqrt(4))',4) % - sqrt(.4' % )) / sqrt(.4') %
759 4 (4- sqrt(.4') + 4 % ) / .4' %
760 4 (4! + 4)^sqrt(4) - 4!
761 4 (sqrt(4) / .(4!)' % ) - sqrt(sqrt(sqrt(4 ^ (4!))))
762 4 (root(.(sqrt(4))' ,4) - 4) / sqrt(.4')
4 (root(-sqrt(4), .4`%) + 4!%) / sqrt(4)%
763 4 (.4! + sqrt(.4'%)) / (4%)'% + 4
4 (.4! '+ sqrt(.4'%)) / (4%)'% - sqrt(4)
764 4 (4 + sqrt(4))! + 44
765 4 (root(.(sqrt(4))' ,4) - sqrt(4)) / sqrt(.4')
4 (4 - (4! / .4)%) / .4`%
766 4 root.4(4)*4! - sqrt(4)
767 4 (root(.(sqrt(4))' ,4) - sqrt(.4')) / sqrt(.4')
768 4 (4 + 4) * 4! * 4
3 root.4(4) * 4!
769 4 (root(.(sqrt(4))' ,4) + sqrt(.4')) / sqrt(.4')
770 4 root.4(4)*4! + sqrt(4)
771 4 (root(.(sqrt(4))' ,4) + sqrt(4)) / sqrt(.4')
772 4 root.4(4)*4! + 4
773 4 ((sqrt(4) - .4') / (.(sqrt(4)) % )') - 4
774 4 (4 + sqrt(4))! + 4! / .4`
775 4 (sqrt(.4') / .4' % ) + .(sqrt(4)) ^ (- 4)
4 (4 - (.4 / .4`)) / .4%
776 4 ((4 - .4') / .4' % ) - 4!
777 4 (sqrt(4) / .(4!)' % ) - (4! + 4!)
3 (sqrt(4) - .4') / (sqrt(4%)%)'
778 4 ((sqrt(4) - .4') / .(sqrt(4)) % ) + .(sqrt(4))'
779 4 (.(4!) - sqrt(.4'%) - .(sqrt(4))'%o) / .(sqrt(4))'%o
4 (sqrt(4) - .4') / (.sqrt (4)%)' + sqrt (4)
780 4 (4! + 4)^sqrt(4) - 4
781 4 (sqrt(4) / .(4!)' % ) - 44
782 4 (4! + 4)^sqrt(4) - sqrt(4)
783 4 ((sqrt(.4') / .4' % ) + 4!) / .(sqrt(4))'
4 (4 + sqrt(4%)%) / (.4` + sqrt(.4`%))%
784 3 (4! + 4)^sqrt(4)
785 4 (4 - .4' - sqrt(.4' %)) / .4' %
786 4 (4! + 4)^sqrt(4) + sqrt(4)
787 4 (sqrt(.4') / .(4!)' % ) + root(.(sqrt(4))',4)
788 4 (4! + 4)^sqrt(4) + 4
789 4 (sqrt(4) - .(4!) - sqrt(.4') % ) / .(sqrt(4))' %
790 4 (4 - .4' - 4' % ) / .4' %
791 4 (4 - .4' - 4 % ) / .4' %
792 4 (4! - sqrt(4)) * 4! / sqrt(.4`)
3 (sqrt(4) - (4!)%) / (.(sqrt(4))')%
793 4 (sqrt(4) - .(4!) + .(sqrt(4))' % ) / .(sqrt(4))' %
4 (sqrt(4) / .4!'%) - root (.4, 4)
794 4 (sqrt(4) - .(4!)) / .(sqrt(4))' % ) + sqrt(4)
4 (root(.4, 4) - 4!%) / 4%
795 4 (4 - sqrt(.4') - .4) / .4' %
796 4 ((4 - .4') / .4' % ) - 4
797 4 (sqrt(4) - .(sqrt(4))' - sqrt(.4') % / .(sqrt(4))' %
798 4 ((4 - .4') / .4' % ) - sqrt(4)
799 4 (4 - .4' - .4' % ) / .4' %
800 4 sqrt(4) * (4! - 4)^sqrt(4)
3 root(.4, 4) / 4%
801 4 (4 - .4' + .4' % ) / .4' %
802 4 ((4 - .4') / .4' % ) + sqrt(4)
803 4 (sqrt(4) - .(sqrt(4))' + sqrt(.4') % / .(sqrt(4))' %
804 4 ((4 - .4') / .4' % ) + 4
805 4 (root .4,(4) + .(sqrt(4)) / 4 %
4 (sqrt(4%) + root(.4, 4)) / 4%
806 4 ((4 - .4) / .4' % ) - 4
807 4 ((4! / 4' %) - sqrt(4)) / sqrt(.4')
808 4 (4! + 4)^sqrt(4) + 4!
809 4 ((4! / 4' %) - sqrt(.4')) / sqrt(.4')
810 4 4! / sqrt(.4`) / (.4` - .4)
3 (4 - .4) / .4`%
811 4 ((4! / 4' %) + sqrt(.4')) / sqrt(.4')
812 4 ((4! / 4' %) / sqrt(.4')) + sqrt(4)
813 4 ((4! / 4'%) + sqrt(4)) / sqrt(.4')
814 4 ((4! / 4' %) / sqrt(.4')) + 4
815 4 (4! / sqrt(.4') + .(sqrt(4))') / 4' %
4 (4 - .4` + sqrt(.4`%)) / .4`%
816 4 4! * (4! + 4 / .4)
817 4 (sqrt(4) / .(4!)' % ) - (4 + 4)
818 4 (sqrt(4) - .(sqrt(4))' + 4 % ) / .(sqrt(4))' %
819 4 (4! / .(4!)' + (4!/4)!
4 (4 / sqrt(.4'))! + 4! / .(4!)'
4 (4 + 4% - .4) / .4`%
820 4 (4! / .(4!)) + (4!/4)!
4 ((4 * 4) + .4) / sqrt(4)%
821 4 (.4' / .(sqrt(4))' % / .(4!)') - 4
3 sqrt(4)/.(4!)'% - 4
822 4 ((4 - .(4!)) / .4' % ) - 4!
4 ((4 - 4!%) / .4`%) - 4!
823 4 (.4' / .(sqrt(4))' % / .(4!)') - sqrt(4)
3 sqrt(4)/.(4!)'% - sqrt(4)
824 4 ((4 - .4') / .4' % ) + 4!
3 (sqrt(4) - .(4!)'%) / .(4!)'%
825 4 ((4!/.(4!)' / .(4!)) * sqrt(4)
3 sqrt(4) / (.(4!)' - .(4!))
2 sqrt(4) / .(4!)'%
2 sqrt(4) / .(4!)' %
4 ((4 / .4`) + 4!) / 4%
826 4 ((4 - .(sqrt(4))' / .4' % ) - 4!
4 (4! * 4!) + sqrt(.4% ^ -sqrt(4))
3 (sqrt(4) + .(4!)'%) / .(4!)'%
827 4 (.4' / .(sqrt(4))' % / .(4!)') + sqrt(4)
3 sqrt(4)/.(4!)'% + sqrt(4)
828 4 (4! * 4! - 4!) / sqrt(.4`)
829 4 (.4' / .(sqrt(4))' % / .(4!)') + 4
3 sqrt(4)/.(4!)'% + 4
830 4 (sqrt(4) + sqrt(.4' % ) - .(sqrt(4))') / .(sqrt(4))' %
4 ((4 / 4!%) - sqrt(.4`%)) / sqrt(4)%
831 4 ((4 - .(sqrt(4)) / .4' % ) - 4!
4 ((4 - sqrt(4%)) / .4`%) - 4!
832 4 4! * 4! + 4^4
833 4 ((4 / 4!%) - sqrt(.4`)%) / sqrt(4)%
834 4 (4! / 4' % / sqrt(.4')) + 4!
3 sqrt(4)/.(4!)% + sqrt(.4')
835 4 ((.4' / .(sqrt(4))' % ) + .4) / .(4!)
4 ((4 / sqrt(4)%) + .4) / 4!%
3 (sqrt(4) + .4%) / .(4!)%
836 4 ((.4' + (sqrt(4))' % ) / .(sqrt(4))' % ) * 4
837 4 (4 - .(4!) - 4 %) / .4' %
4 (4 - (4 + 4!)%) / .4`%
838 4 sqrt(.4') + 4 + (sqrt(4) / .(4!) % )
839 4 ((sqrt(4) + .4 % ) / .(4!) % ) + 4
840 4 (4 + 4)! / (4! + 4!)
841 4 (4! + sqrt(4) / .4)^sqrt(4)
842 4 ((4 - .(4!)) / .4' % ) - 4
4 ((4 - 4!%) / .4`%) - 4
843 4 (sqrt(4) / .(4!)' % ) + (4 / .(sqrt(4))')
844 4 ((4 - .(4!)) / .4' % ) - sqrt(4)
4 ((4 - 4!%) / .4`%) - sqrt(4)
845 4 sqrt(sqrt(sqrt(.(sqrt(4))))^(-4!)) + (4 / sqrt(.4'))!
4 (4 - (4! + .4`)%) / .4`%
846 4 (4! + (4! / 4' %)) / sqrt(.4')
3 (4 - 4!%) / .4`%
847 4 (4 - .(4!) + .4' % ) / .4' %
4 (4 - (4! - .4`)%) / .4`%
848 4 4! * (4! - .4`) / sqrt(.4`)
849 4 (4 - .(sqrt(4))' - .4' % ) / .4' %
3 sqrt(4)/.(4!)'% + 4!
850 4 ((4 - .(4!)) / .4' % ) + 4
4 ((4 / .4) + 4!) / 4%
3 (4 - .(sqrt(4))') / .4'%
851 4 (4 - .(sqrt(4))' + .4' % ) / .4' %
4 ((4 - sqrt(4%)) / .4`%) - 4
852 4 ((4 - .(sqrt(4))') / .4' % ) + sqrt(4)
4 (4 / .4`%) - (sqrt(4) * 4!)
853 4 ((4 - .(sqrt(4))) / .4' % ) - sqrt(4)
4 ((4 - sqrt(4%)) / .4`%) - sqrt(4)
854 4 ((4 - .(sqrt(4)) - .4' % ) / .4' %
4 (4 + 4!% - .4`) / .4`%
855 3 (4 - .(sqrt(4)) / .4' %
3 (4 - sqrt(4%)) / .4`%
856 4 4! * (4! - .(sqrt(4))') / sqrt(.4')
4 (4 / .4`%) - 44
857 4 (4 - .(sqrt(4)) / .4' % ) + sqrt(4)
4 ((4 - sqrt(4%)) / .4`%) + sqrt(4)
858 4 (4! * 4! - 4) / sqrt(.4`)
859 4 (4 - .(sqrt(4))' + 4 % ) / .4' %
4 4 + ((4 - sqrt(4%)) / .4`%)
860 4 4! * 4! / sqrt(.4`) - 4
861 4 (4! * 4! - sqrt(4)) / sqrt(.4`)
862 4 4! * 4! / sqrt(.4`) - sqrt(4)
863 4 (4! * 4! - sqrt(.4`)) / sqrt(.4`)
864 3 4! * 4! / sqrt(.4`)
865 4 (4! * 4! + sqrt(.4`)) / sqrt(.4`)
866 4 4! * 4! / sqrt(.4`) + sqrt(4)
867 4 (4! * 4! + sqrt(4)) / sqrt(.4`)
868 4 4! * 4! / sqrt(.4`) + 4
869 4 (sqrt(4) - sqrt(.4' % ) - .(sqrt(4))' % ) / .(sqrt(4))' %
870 4 (4! * 4! + 4) / sqrt(.4`)
3 (sqrt(4) - sqrt(.4'%)) / .sqrt(4)'%
871 4 (sqrt(4) - sqrt(.4' % ) + .(sqrt(4))' % ) / .(sqrt(4))' %
872 4 (4 / .4' % ) - (4 + 4!)
873 4 (sqrt(4) - sqrt(.4' % ) + sqrt(.4') % ) / .(sqrt(4))' %
4 (4 - (4! / sqrt(4))%) / .4`%
874 4 ((4 - .(sqrt(4))') / .4' % ) + 4!
4 (4 / .4`%) - (sqrt(4) + 4!)
875 4 (4 - sqrt(.4' % ) - 4' % ) / .4' %
876 4 (4 - sqrt(.4' % ) - 4 % ) / .4' %
3 (4 / .4`%) - 4!
877 4 ((4 + .4' % ) / .4' %) - 4!
878 4 (4 / .4' % ) - (4! - sqrt(4))
879 4 ((4 - .(sqrt(4))) / .4' % ) + 4!
4 ((4 - sqrt(4%)) / .4`%) + 4!
880 4 44 * (4! - 4)
3 (sqrt(4) - 4!%) / sqrt(4%)%
881 4 .(sqrt(4))^(-4) + (4 ^ 4)
4 4 ^ 4 + 4% ^ -sqrt(4)
882 4 (4 / .4' %) - (4 / .(sqrt(4))')
4 (4 - (4 + 4)%) / .4`%
3 (sqrt(4) - 4%) / .sqrt(4)'%
883 4 ((4 - sqrt(.4' %)) / .4' % ) - sqrt(4)
884 4 (4 - sqrt(.4' % ) - .4' % ) / .4' %
885 3 (4 - sqrt(.4' % )) / .4' %
886 4 ((4 + 4'%) / .4'%) - 4!
887 4 ((4 - sqrt(.4' % ) / .4' % ) + sqrt(4)
888 4 444 * sqrt(4)
889 4 ((4 - sqrt(.4' % )) / .4' % ) + 4
890 4 (4 - .4' % - 4 % ) / .4' %
3 (4 - 4'%) / .4'%
4 (4 - (4 + .4')%) / .sqrt(4)'%
891 4 ((4! / .(4!)') / .4') * 4
3 (4 - 4%) / .4`%
892 4 (4 - 4 % + .4' % ) / .4' %
893 4 ((4 - 4 % ) / .4' ) + sqrt(4)
894 4 ((4 - 4' % ) / .4' % ) + 4
895 4 ((4 - 4 % ) / .4' % ) + 4
896 4 4! * 4! * (sqrt(4) - .4`)
3 (4 / .4`%) - 4
897 4 ((4 - .4' % ) / .4' % ) - sqrt(4)
898 4 (4 - .4' % - .4' % ) / .4' %
3 (4 / .4`%) - sqrt(4)
899 4 root(.(sqrt(4)),4) - sqrt(sqrt(sqrt(.(sqrt(4)))))^(-4!)
3 (4 - .4`%) / .4`%
900 4 (4! + 4! / 4)^sqrt(4)
2 4 / .4' %
901 3 (4 + .4' % ) / .4' %
902 4 (4 + .4' % + .4' % ) / .4' %
3 (4 / .4`%) + sqrt(4)
903 4 ((4 + .4' % ) / .4' % ) + sqrt(4)
904 4 root(.(sqrt(4)),4) - (sqrt(4) / .4)!
3 4 + (4 / .4`%)
905 4 (4 / .4' %) + (sqrt(4) / .4)
906 4 (4 / .4' %) + (4! / 4)
907 4 ((4 + 4 %) / .4' % ) - sqrt(4)
908 4 (4 / .4' %) + 4 + 4
909 4 (4 / .4' %) + (4 / .4')
3 (4 + 4%) / .4`%
910 4 sqrt(4)^(4!) * .(sqrt(4)' - .(sqrt(4)'
4 (4 / .4) + (4 / .4`%)
3 (4 + 4'%) / .4'%
4 (4 + (4 + .4')%) / .4'%
911 4 ((4 + 4' %) + .4' %) / .4' %
912 4 4! * (4! / sqrt(.4`) + sqrt(4))
913 4 ((4 + 4 % ) / .4' % ) + 4
914 4 ((4 + 4' %) / .4' %) + 4
915 3 (4 + sqrt(.4' %)) / .4' %
916 4 root(.(sqrt(4)),4) - (4! / .(sqrt(4))'
4 (4 * 4) + (4 / .4`%)
917 4 ((4 + sqrt(.4' % )) / .4' % ) + sqrt(4)
918 4 (4 / .4' % ) + (4 / .(sqrt(4))')
4 (4 + (4 + 4)%) / .4`%
3 (sqrt(4) + 4%) / (.sqrt(4)')%
919 4 ((4 + sqrt(.4' % )) / .4' % ) + 4
920 4 (4 / .4' %) + 4! - 4
921 4 (4 + .(sqrt(4)) / .4' %) - 4!
4 ((4 + sqrt(4%)) / .4`%) - 4!
922 4 (4 / .4' %) + 4! - sqrt(4)
923 4 ((4 - .4' % ) / .4' % ) + 4!
924 4 root(.(sqrt(4)),4) - (4! / .(4!))
3 (4 / .4`%) + 4!
925 4 root(.(sqrt(4)),4) - (4! / .(4!)')
4 (4 + (.4` / 4)) / .4`%
926 4 (4 / .4' %) + 4! + sqrt(4)
927 4 (sqrt(4) + sqrt(.4' % ) - (sqrt(.4')) % / .(sqrt(4))' %
4 (4 + (4! / sqrt(4))%) / .4`%
928 4 4 * (4^4 - 4!)
929 4 (sqrt(4) + sqrt(.4' % ) - .(sqrt(4))' % ) / .(sqrt(4))' %
930 4 ((4 + .(4!)) / .4' %) - 4!
4 (4 - (4 + 4!)%) / .4%
3 (sqrt(4) + sqrt(.4'%)) / (.sqrt(4)')%
931 4 (sqrt(4) + sqrt(.4' % ) + .(sqrt(4))' % ) / .(sqrt(4))' %
932 4 (4 / .4' %) + root(.4,4)
933 4 ((4 + 4 % ) / .4' % ) + 4!
934 4 ((4 + 4' %) / .4' % ) + 4!
935 4 (4 + .(sqrt(4)) - 4' % ) / .4' %
4 (4 - (sqrt(4) + 4!)%) / .4%
936 4 (4! + sqrt(4)) * 4! / sqrt(.4`)
937 4 (sqrt(.4') - 4 % - .(sqrt(4)) % / sqrt(.4' % ) %
4 (sqrt(.4`) - (4 + sqrt(4%))%) / sqrt(.4`%)%
938 4 ((4 - .(4!)) / .4 % ) - sqrt(4)
4 ((4 - 4!%) / .4%) - sqrt(4)
939 4 (4 - .(4!) - .4 % ) / .4 %
4 (4 - (4! + .4)%) / .4%
940 4 (4 / .4%) - (4! / .4)
3 (4 - 4!%) / .4%
941 4 ((4 + 4'%) / .4'%) - 4!
942 4 (4 - .(4!)) / .4 % ) + sqrt(4)
4 ((4 - 4!%) / .4%) + sqrt(4)
943 4 ((4 + .(sqrt(4))) / .4' %) - sqrt(4)
4 ((4 + sqrt(4%)) / .4`%) - sqrt(4)
944 4 (4 / .4' %) + 44
945 4 (4 / .4' %) + (sqrt(4) / 4' %)
3 (4 + sqrt(4%)) / .4`%
946 4 (4 / .4 %) - (4! / .4')
947 4 (4 + .(sqrt(4)) / .4' %) + sqrt(4)
4 ((4 + sqrt(4%)) / .4`%) + sqrt(4)
948 4 (4 / .4' %) + 4! + 4!
949 4 (4 + .(sqrt(4)) / .4' %) + 4
4 4 + ((4 + sqrt(4%)) / .4`%)
950 3 (4 + .(sqrt(4))') / .4' %
3 (4 - sqrt(4%)) / .4%
951 4 ((4!) + (sqrt(sqrt(sqrt(.4))))^(-4!)) * (4!)
952 4 (4 / .4 %) - (4! + 4!)
953 4 (4 + .(4!) - .4' % ) / .4' %
4 (4 + (4! - .4`)%) / .4`%
954 3 (4 + .(4!)) / .4' %
3 (4 + 4!%) / .4`%
955 4 (4 / .4 %) - (sqrt(4)/ 4' %)
956 4 (4 / .4 %) - 44
957 4 ((4^4) - 4!) / .(4!)'
4 ((4! - sqrt(4%))% + .4) / sqrt(.4`%)%
958 4 ((4 + .(4!)) / .4' %) + 4
4 4 + ((4 + 4!%) / .4`%)
959 4 (sqrt(sqrt(sqrt(4 ^ 4!)))) - sqrt(.4' %)) / sqrt(.4' %)
960 4 (4 * 4!) * 4 / .4
3 4! / sqrt(.4 ^ -sqrt(4))%
961 4 (sqrt(sqrt(sqrt(4 ^ 4!)))) + sqrt(.4' %)) / sqrt(.4' %)
962 4 (sqrt(4) / .4' %) + root(.(sqrt(4))' ,4)
4 sqrt(4) + (4! / sqrt(.4 ^ -sqrt(4))%)
963 4 (sqrt(sqrt(sqrt(4 ^ 4!)))) + .(sqrt(4)) / sqrt(.4' %)
4 (4 + (4 + 4!)%) / .4`%
964 4 root(.(sqrt(4)),4) - 4! / .4
4 root(sqrt(4%), 4) - (4! / .4)
965 4 (4 + sqrt(.4' % ) + .(sqrt(4))') / .4' %
966 4 (4.4 / .4' %) - 4!
967 4 (sqrt(4) - sqrt(.4'%) + (sqrt(.4'%))%) / .(sqrt(4)%)
4 (sqrt(.4`) - (sqrt(4) + sqrt(4%))%) / sqrt(.4`%)%
968 4 44 * (4! - sqrt(4))
969 4 ((4 + 4'%) / .4'%) - 4!
970 4 root(.(sqrt(4)),4) - 4! / .4'
3 (sqrt(.4`) - sqrt(4)%) / sqrt(.4`%)%
971 4 sqrt(sqrt(4^4!)) - (root(-(.(sqrt(4)),.(sqrt(4))
4 ((4 - sqrt(4)%) / .4%) - 4!
972 4 4 * (root.4(4/.4'))
4 (4 / .4 %) - (4 + 4!)
973 4 ((sqrt(.4') - .(sqrt(4)) % ) / sqrt(.4' % ) % ) - 4!
4 ((sqrt(4%) - sqrt(4))% + sqrt(.4`)) / sqrt(.4`%)%
974 4 ((4 + .(sqrt(4))') / .4' % ) + 4!
4 (4 / .4%) - (sqrt(4) + 4!)
975 4 (4! + sqrt(4))! / sqrt(.4') * (4!)!
976 4 (4! / 4)! + 4 ^ 4
3 (4 / .4%) - 4!
977 4 ((4 + .4 % ) / .4 %) - 4!
978 4 (4 / .4 %) - (4! - sqrt(4))
979 4 root(.(sqrt(4))' ,4) - (sqrt(4) / 4' %
4 root(sqrt(4%), 4) - (sqrt(4%) / .4`%)
980 4 root(.(sqrt(4)),4) - 44
3 (sqrt(4) - 4%) / sqrt(4%)%
981 4 (4.4 - 4 % ) / .4' %
982 4 (4 / .4 % ) - (4 / .(sqrt(4))')
4 (4 - (4 + sqrt(4))!%%) / .4%
983 4 (sqrt(4 ^ 4!) * .(4!)) - 4 %
984 4 sqrt(((4 + 4)! + 4!) * 4!)
985 4 (4 / .4 %) - (sqrt(.4') / 4' %)
986 4 (4.4 / .4' %) - 4
987 4 (4! - sqrt(4) - sqrt(.4' % )) / (sqrt(4) % )'
4 (sqrt(.4`) - (sqrt(4%) + sqrt(.4`))%) / sqrt(.4`%)%
988 4 root(.(sqrt(4)),4) - (4! / sqrt(.4'))
4 ((4 - 4%) / .4%) - sqrt(4)
989 4 (4.4 - .4' % ) / .4' %
990 4 44 / (.4` - .4)
2 4! / (4!)' %o
3 (4 - 4%) / .4%
991 4 (4 / .4 %) - (4 / .4')
992 4 root(.(sqrt(4)),4) - root(.4,4)
4 (4 / .4%) - (4 + 4)
993 4 (4! - sqrt(4) + sqrt(.4' % )) / sqrt(4) % )'
4 ((4 - sqrt(4)%) / .4%) - sqrt(4)
994 4 (4 / .4 %) - (4! / 4)
3 (sqrt(.4`) - .4%) / sqrt(.4`%)%
995 4 (4 / .4 %) - (sqrt(4) / .4)
3 (4 - sqrt(4)%) / .4%
996 4 sqrt(sqrt(sqrt((4 / .4)^4!))) - 4
3 (4 / .4%) - 4
997 4 (4 / .4 %) - sqrt(4 / .4')
3 (sqrt(.4`) - sqrt(4%)%) / sqrt(.4`%)%
998 4 sqrt(sqrt(sqrt((4 / .4)^4!))) - sqrt(4)
3 (4 / .4%) - sqrt(4)
999 4 444 / .4`
3 (4 - .4%) / .4%
2 4/(.4%)'
1000 4 4 * 4^4 - 4!
3 sqrt(sqrt(sqrt((4 / .4)^4!)))
2 4 / .4 %
1001 4 4/.4 % + 4/4
3 (4 + .4%) / .4%
1002 3 4/.4 % + sqrt(4)
1003 4 4/.4 % + sqrt(4/.4')
3 (sqrt(4%)% + sqrt(.4`)) / sqrt(.4`%)%
1004 3 4/.4 % + 4
1005 4 4/.4 % + sqrt(4)/.4
3 (4 + sqrt(4)%) / .4%
1006 4 4/.4 % + sqrt(4) + 4
3 (.4% + sqrt(.4`)) / sqrt(.4`%)%
1007 4 (4 + 4! %o + .4 %) / .4 %
4 ((4 + 4)!% - .4) / .4
1008 4 4/.4 % + 4 + 4
3 ((4 + 4)! / .4)%
1009 4 4/.4 % + 4/.4'
1010 4 4/.4 % + 4/.4
3 (4 + 4%) / .4%
1011 4 ((sqrt(4)/.4' %) - sqrt(.4')) / .4'
1012 4 4/.4 % + 4!/sqrt(4)
1013 4 ((sqrt(4)/.4' %) + .(sqrt(4))' / .4'
4 ((4 + 4)!% + sqrt(4)) / .4
1014 3 (4!/(4!)' %o + 4!
4 4 + ((4 + 4%) / .4%)
1015 4 4/.4 % + sqrt(.4')/(4)' %
4 root(sqrt(4%), 4) - (4 / .4`)
1016 4 4/.4 % + (4 * 4)
1017 4 ((sqrt(4)/,4' %) + sqrt(4)) / .4'
1018 4 4/.4 % + 4/.(sqrt(4))'
4 (4 + (4 + 4)!%) / .4
4 (sqrt(sqrt(4^4!)) - 4!)/4
1019 4 root(.(sqrt(4)),4) - (sqrt(4)/.4)
4 root(sqrt(4%), 4) - (sqrt(4) / .4)
1020 4 4/.4 % + (4! - 4)
3 root(sqrt(4%), 4) - 4
1021 4 root(.(sqrt(4)),4) - sqrt(4/.4')
4 root(sqrt(4%), 4) - sqrt(4 / .4`)
1022 4 4/.4 % + (4! - sqrt(4))
3 root(sqrt(4%), 4) - sqrt(4)
1023 4 root(.(sqrt(4)),4) - 4/4
4 root(sqrt(4%), 4) - (4 / 4)
4 (sqrt(sqrt(4^4!)) - 4)/4
3 4/(.4%)' + 4!
1024 2 root(.(sqrt(4)),4)
2 root(sqrt(4%), 4)
1025 4 root(.(sqrt(4)),4) + 4/4
4 (4 + (.4 / 4)) / .4%
4 (sqrt(sqrt(4^4!)) + 4)/4
1026 3 root(.(sqrt(4)),4) + sqrt(4)
3 sqrt(4) + root(sqrt(4%), 4)
1027 4 root(.(sqrt(4)),4) + sqrt(4/.4')
4 sqrt(4 / .4`) + root(sqrt(4%), 4)
1028 3 root(.(sqrt(4)),4) + 4
3 4 + root(sqrt(4%), 4)
1029 4 root(.(sqrt(4)),4) + sqrt(4)/.4
4 (sqrt(4) / .4) + root(sqrt(4%), 4)
1030 4 root(.(sqrt(4)),4) + sqrt(4) + 4
4 (sqrt(sqrt(4^4!)) + 4!)/4
3 (sqrt(4)% + sqrt(.4`)) / sqrt(.4`%)%
1031 4 (sqrt(.4') + sqrt(4) % + sqrt(.4' %)%) / sqrt(.4' %)%
1032 4 root(.(sqrt(4)),4) + 4 + 4
4 (4! * 44) - 4!
1033 4 root(.(sqrt(4)),4) + 4/.4'
4 (4 / .4`) + root(sqrt(4%), 4)
1034 4 root(.(sqrt(4)),4) + 4/.4
4 (4 / .4) + root(sqrt(4%), 4)
1035 4 (4!/sqrt(4) %) - (.4/.(4!)' %)
4 ((sqrt(4) / .4) - .4) / .4`%
1036 4 (4!/sqrt(4)' %) - 44
4 (4! / sqrt(4)) + root(sqrt(4%), 4)
1037 4 (sqrt(.4') + 4! %o + sqrt(.4' %) %) / (sqrt.4' %) %)
1038 4 (4!/(4!)' %o) + 4! + 4!
1039 4 root(.(sqrt(4)),4) + sqrt(.4')/4' %
4 root(-sqrt(4), .4`%) + root(sqrt(4%), 4)
1040 4 root(.(sqrt(4)),4) + (4 * 4)
4 4 * (4 + 4 ^ 4)
1041 4 ((.(sqrt(4) ^ -(sqrt(4)) / 4! %o) - sqrt(.4')
4 (4 - 4% + sqrt(.4`)) / .4`%
1042 4 root(.(sqrt(4)),4) + (4/.(sqrt(4))')
1043 5 ((4!/4)! - 4! - sqrt(.4')) / sqrt(.4')
4 44 + (sqrt(4) / (.(sqrt(4)) % )')
1044 4 (4/.4 %) + 44
1045 4 (4/.4 %) + (sqrt(4)/4' %)
1046 4 (4! - sqrt(4)) + root(.(sqrt(4)),4)
4 ((4 + sqrt(4%)) / .4%) - 4
1047 4 (4! - sqrt(.4') - sqrt(.4' %)) / sqrt(4)' %
1048 3 4! + root(.(sqrt(4)),4)
3 4! + root(sqrt(4%), 4)
1049 4 .(sqrt(4)) ^ -(sqrt(4)) + root(.(sqrt(4)),4)
4 (4 + sqrt(4%) - .4%) / .4%
1050 4 (4/.4 %) + sqrt(4) / 4 %
3 (4 + sqrt(4%)) / .4%
1051 4 (.4' - 4! %o - .4' % %) / 4 % %
4 (4 + sqrt(4%) + .4%) / .4%
1052 4 (4! * 44) - 4
1053 4 (.4' + 4! %o - 4 % %) / 4' % %
1054 4 (4/.4 %) + (4!/.4')
4 44*4! - sqrt(4)
1055 4 (4!/sqrt(4)' %) - (.(sqrt(4)) ^ -(sqrt(4))
4 (4 - (sqrt(4) - 4!)%) / .4%
1056 4 (4!+4!)*(4! - sqrt(4))
3 (4!/sqrt(4)' %) - 4!
3 4! * 44
1057 4 ((4 ^ 4) + .(4!)') / .(4!)'
4 ((4 - sqrt(4%))% + sqrt(.4`)) / sqrt(.4`%)%
1058 4 (4!/sqrt(4)' %) - (4! - sqrt(4))
4 sqrt(4) + (4! * 44)
1059 4 (4! - .4 - (sqrt(.4' % )) / sqrt(4)' %
4 (4 + (4! - .4)%) / .4%
1060 4 (4! / sqrt(4)' %) - (4! - 4)
4 44*4! + 4
3 (4 + 4!%) / .4%
1061 4 (4! - (.4 + sqrt(4)' % )) / sqrt(4)' %
4 (4 + (4! + .4)%) / .4%
1062 4 (4! / sqrt(4)' %) - 4 / .(sqrt(4))'
4 ((4 + 4!%) / .4%) + sqrt(4)
3 (4! - .4) / (sqrt(4))'%
4 (4! - .4) / (sqrt(4) + sqrt(4%)')%
1063 4 (4! - .4 + sqrt(4)' % ) / sqrt(4)' %
4 ((4 + sqrt(4%))% + sqrt(.4`)) / sqrt(.4`%)%
1064 4 (4! / sqrt(4)' %) - (4 * 4)
4 4 + ((4 + 4!%) / .4%)
1065 4 (4! / sqrt(4)' %) - sqrt(.4') / 4' %
4 (4 ^ 4 - .4) / 4!%
1066 4 ((4 ^ 4) / .(4!)) - sqrt(.4')
4 (4 ^ 4 / 4!%) - sqrt(.4`)
1067 4 ((4! - .(sqrt(4)) / sqrt(4)' % ) - 4
1068 4 (4! / sqrt(4)' %) - 4!/sqrt(4)
4 root(sqrt(4%), 4) + 44
1069 4 ((4! - .(sqrt(4)) / sqrt(4)' % ) - sqrt(4)
4 root(sqrt(4%), 4) + (sqrt(4%) / .4`%)
1070 4 (4! / sqrt(4)' %) - 4/.4
4 (4 + (4 + 4!)%) / .4%
3 (4! - .sqrt(4)') / (sqrt(4))'%
4 (4! - .sqrt(4)') / (sqrt(4) + sqrt(4%)')%
1071 4 (4! / sqrt(4)' %) - 4/.4'
4 ((sqrt(4) / .4%) - 4!) / .4`
1072 4 (4! / sqrt(4)' %) - (4 + 4)
4 4! * (44 + sqrt(.4`))
1073 4 (4! - .(sqrt(4)) + 4' % ) / sqrt(4)' %
1074 4 (4! / sqrt(4)' %) - (4 + sqrt(4))
4 ((4 + sqrt(4))! - 4) / sqrt(.4`)
1075 4 (4! / sqrt(4)' %) - sqrt(4)/.4
4 (4 ^ 4 + sqrt(4)) / 4!%
1076 3 (4! / sqrt(4)' %) - 4
4 (44 / 4%) - 4!
1077 4 (4! / sqrt(4)' %) - sqrt(4/.4')
4 ((4 + sqrt(4))! - sqrt(4)) / sqrt(.4`)
3 (4! - sqrt(.4'%)) / (sqrt(4))'%
4 (4! - sqrt(.4'%)) / (sqrt(4) + sqrt(4%)')%
1078 3 (4! / sqrt(4)' %) - sqrt(4)
4 (4! / .4`) + root(sqrt(4%), 4)
1079 4 (4! / sqrt(4)' %) - 4/4
4 ((4 + sqrt(4))! - sqrt(.4`)) / sqrt(.4`)
1080 2 4! / sqrt(4)' %
3 (4 + sqrt(4))! / sqrt(.4`)
4 44*4! + 4!
1081 3 (4! + sqrt(4)' % ) / sqrt(4)' %
4 ((4 + sqrt(4))! + sqrt(.4`)) / sqrt(.4`)
1082 3 (4! / sqrt(4)' % ) + sqrt(4)
4 ((4 + sqrt(4))! / sqrt(.4`)) + sqrt(4)
1083 4 (4! / sqrt(4)' % ) + sqrt(4/.4')
4 ((4 + sqrt(4))! + sqrt(4)) / sqrt(.4`)
1084 3 (4! / sqrt(4)' % ) + 4
4 (4! / .4) + root(sqrt(4%), 4)
1085 4 (4! / sqrt(4)' % ) + sqrt(4)/.4
1086 4 (4! / sqrt(4)' % ) + sqrt(4) + 4
4 (4 + (4 + sqrt(4))!) / sqrt(.4`)
1087 4 ((.(4!) + 4! %o) / 4! % %o) - sqrt(4)
1088 4 (4! / sqrt(4)' % ) + 4 + 4
4 (4! - (sqrt(4) + 4!%)) / sqrt(4)%
1089 4 (4! / sqrt(4)' % ) + 4/.4'
4 ((4 / .4`) + 4!) ^ sqrt(4)
3 (4! + sqrt(4%)) / (sqrt(4))'%
4 (4! + sqrt(4%)) / (sqrt(4) + sqrt(4%)')%
1090 4 (4! / sqrt(4)' % ) + 4/.4
4 (44 - .4) / 4%
1091 3 ((.(4!) + 4! % %o) + sqrt(4)
4 (4! + sqrt(4%)%) / (sqrt(4) + sqrt(4%))%
1092 4 (4! / sqrt(4)' % ) + 4! / sqrt(4)
1093 4 ((.(4!) + 4! %o) / (4!)' % %o) + 4
1094 4 (44 - .(4!)) / 4 %
4 (44 - 4!%) / 4%
1095 4 (4! / sqrt(4)' % ) + (sqrt(.4') / 4' % )
4 (44 - sqrt(4%)) / 4%
1096 4 (4! / sqrt(4)' % ) + (4 * 4)
4 (44 / 4%) - 4
1097 4 (4! + .4 - sqrt(4)' % ) / sqrt(4)' %
4 (sqrt(.4`) - sqrt(4%)% + sqrt(.4`%)) / sqrt(.4`%)%
1098 3 (4! + .4) / sqrt(4)' %
4 (44 / 4%) - sqrt(4)
1099 4 (4! + .4 + sqrt(4)' % ) / sqrt(4)' %
4 (44 - 4%) / 4%
1100 4 (4! / sqrt(4)' % ) + (4! - 4)
3 44 / 4%
1101 4 (4.4 + .4 % ) / .4 %
1102 4 (4! / sqrt(4)' % ) + (4! - sqrt(4))
4 sqrt(4) + (44 / 4%)
1103 4 ((4! - sqrt(4)' %) / sqrt(4)' % ) + 4!
4 (sqrt(4%)% + sqrt(.4`) + sqrt(.4`%)) / sqrt(.4`%)%
1104 4 (4! / sqrt(4)' % ) + 4!
4 (44 + sqrt(4))*4!
4 4 + (44 / 4%)
3 4!/(sqrt(4))'% + 4!
4 4! / (sqrt(4) + sqrt(4%)')% + 4!
1105 4 (4! / sqrt(4)' % ) + .(sqrt(4)) ^ - (sqrt(4))
4 (sqrt(4%) + 44) / 4%
1106 4 (4! / sqrt(4)' % ) + 4! + sqrt(4)
4 (4!% + 44) / 4%
1107 4 (4! + .4 + .(sqrt(4))) / (sqrt(4))' %
1108 4 (4! / sqrt(4)' % ) + 4! + 4
4 ((4 + 4)!%% + .4) / .4%
1109 4 (4! + .4' + .(sqrt(4)) / (sqrt(4))' %
1110 4 (4! / sqrt(4)' % ) + (sqrt(4) / sqrt(.4' % )
4 444 / .4
3 (4! + sqrt(.4')) / (sqrt(4))'%
4 (4! + sqrt(.4')) / (sqrt(4) + sqrt(4%)')%
1111 4 (4! + sqrt(.4') + sqrt(4)' % ) / (sqrt(4))' %
2 .4' / (4%%)'
1112 4 (4! / sqrt(4)' % ) + root.4,(4)
4 (4! - sqrt(4) + 4!%) / sqrt(4)%
1113 4 (4! + sqrt(.4') + sqrt(.4' % )) / sqrt(4)' %
4 (sqrt((.4`% ^ -sqrt(4))%) - 4!%) / sqrt(4)%
3 .4'/(4%%)' + sqrt(4)
1114 4 ((4! + sqrt(.4')) / sqrt(4)' % ) + 4
4 root(sqrt(4%), 4) + (.4 / .4`%)
1115 4 ((.(sqrt(4)) ^ -(sqrt(4)) - (.(sqrt(4))) / (sqrt(4))' %
4 ((sqrt(4) / .4`%) - 4) / .4
3 .4'/(4%%)' + 4
1116 4 (4! / sqrt(4)' % ) + (4! / sqrt(.4'))
4 ((sqrt(4) / .4%) - 4) / .4`
1117 4 ((.4' + .(4!) % - .4' % % ) / 4 % %
1118 4 (sqrt(4) + (4! - .4)%) / sqrt(4%)%
1119 4 ((sqrt(4%) / .4`%) - 4!%) / 4%
1120 3 (sqrt(4) + 4!%) / sqrt(4%)%
1121 4 (sqrt(4) / (.4 * .4`)%) - 4
1122 4 (sqrt(4) + (4! + .4)%) / sqrt(4%)%
1123 4 (sqrt(4) / (.4 * .4`)%) - sqrt(4)
1124 4 4! + (44 / 4%)
1125 3 sqrt(4) / (.4 * .4`)%
1126 4 ((sqrt(4) / .4`%) + .4) / .4
1127 4 sqrt(4) + (sqrt(4) / (.4 * .4`)%)
1128 4 (sqrt(4) * 4! * 4!) - 4!
4 (4!+4!)*4! - 4!
1129 4 4 + (sqrt(4) / (.4 * .4`)%)
1130 4 (sqrt(4) + (sqrt(4) / .4`%)) / .4
1131 4 (4!% + (sqrt(4%) / .4`%)) / 4%
1132 4 (4! / .(sqrt(4))') + root(.(sqrt(4)), 4)
1133 4 (.(sqrt(4))' + .4' % - sqrt(.4') % % ) / sqrt(4) % %
1134 4 (4 + (sqrt(4) / .4%)) / .4`
1135 4 (4 + (sqrt(4) / .4`%)) / .4
3 .4'/(4%%)' + 4!
1136 4 ((sqrt(4) * 4!) - sqrt(.4`)) * 4!
1137 4 (4!% + sqrt((.4`% ^ -sqrt(4))%)) / sqrt(4)%
1138 4 (4 / .(4!)' % ) - root(.(sqrt(4))', 4)
1139 4 (4 + 4!) + (.(sqrt(4))' / sqrt(4) % % )'
1140 4 (4 + 4 - .4) / sqrt(.4`)%
1141 4 sqrt(4 / .4' % ) + (.(sqrt(4))' / sqrt(4) % % )'
1142 4 ((.4 ^ 4) - sqrt4)' % % ) / .(sqrt(4)) % %
1143 4 (root(.(sqrt(4))', 4)) - 4) / .4'
1144 4 (sqrt(4) + 4!) * 44
1145 4 (4 + sqrt(.4`% ^ -sqrt(4))) / sqrt(4%)
1146 4 (4! / sqrt(4)%) - (4! / .4`)
1147 4 (4! / sqrt(.4')) + (.(sqrt(4))' / sqrt(4) % % )'
1148 4 (sqrt(4) * 4! * 4!) - 4
4 (4!+4!)*4! - 4
1149 4 (sqrt(4) / (.4 * .4`)%) + 4!
1150 4 (sqrt(4) + 44) / 4%
4 4!*4! * sqrt(4) - sqrt(4)
1151 4 (root(.(sqrt(4))', 4) - .4') / .4'
1152 3 sqrt(4) * 4! * 4!
1153 4 root(.(sqrt(4))' 4) + .4') / .4'
1154 4 sqrt(4) + (sqrt(4) * 4! * 4!)
1155 4 (4! - (.4 / .4`)) / sqrt(4)%
3 (4! - sqrt(.4')) / (sqrt(4)%)'
1156 4 (4! / sqrt(4)%) - 44
4 4!*4! * sqrt(4) + 4
1157 4 ((4 + 4!) / (4!)' %o ) + sqrt(4)
1158 4 (4! / (sqrt(4) % )') - sqrt(4 / .4' % )
1159 4 ((4 + 4!) / (4!)' %o ) + 4
1160 4 (4 + (4! * 4!)) * sqrt(4)
1161 4 ((4 ^ 4) + sqrt(4)) / .(sqrt(4))'
1162 4 (.(sqrt(4))' + ((4! / sqrt(.4')) %o ) / .(sqrt(4))' %o
1163 4 (4! / (sqrt(4) % )') - .(sqrt(4)) ^ -(sqrt(4))
1164 4 (4 + 4 - 4!%) / sqrt(.4`)%
1165 4 (4 + sqrt(.4`) - sqrt(.4`)%) / .4%
1166 4 ((4 + sqrt(.4`)) / .4%) - sqrt(.4`)
3 (4! - .4') / (sqrt(4)%)'
1167 4 (4! - sqrt(.4`) + sqrt(.4`)%) / sqrt(4)%
1168 4 (4! / sqrt(4)%) - root(.4, 4)
1169 4 (sqrt(4) + 4! - sqrt(4)' % ) / sqrt(4)' %
1170 4 (4 + 4 - sqrt(4%)) / sqrt(.4`)%
3 (4! + sqrt(4)) / (sqrt(4))'%
4 (4! + sqrt(4)) / (sqrt(4) + sqrt(4%)')%
1171 4 (sqrt(4) + 4! + sqrt(4)' % ) / sqrt(4)' %
1172 4 (4! / sqrt(4)%) - (4 + 4!)
1173 4 (4! - (4! / .4`)%) / sqrt(4)%
1174 4 (4! / sqrt(4)%) - (sqrt(4) + 4!)
1175 4 (4! - (sqrt(4) / 4)) / sqrt(4)%
1176 3 (4! / sqrt(4)%) - 4!
4 4!*4! * sqrt(4) + 4!
1177 4 ((sqrt(4)% + 4!) / sqrt(4)%) - 4!
3 (4! - .(sqrt(4))') / (sqrt(4)%)'
1178 4 (4! - 44%) / sqrt(4)%
1179 4 ((sqrt(4) / .4%) + 4!) / .4`
1180 3 (4! - .4) / sqrt(4)%
1181 4 (sqrt(4)% + 4! - .4) / sqrt(4)%
1182 4 sqrt(4) + ((4! - .4) / sqrt(4)%)
1183 4 (4! / (sqrt(4) % )') - (sqrt(4) / .4)
1184 4 (4! / sqrt(4)%) - (4 * 4)
3 4!/(sqrt(4)%)' - 4
1185 4 ((sqrt(4) / .4`%) + 4!) / .4
1186 4 (4! - (4 + 4!)%) / sqrt(4)%
3 (4! - (4%)') / (sqrt(4)%)'
3 4!/(sqrt(4)%)' - sqrt(4)
1187 4 (4! - (sqrt(4) + 4!)%) / sqrt(4)%
3 (4! - (sqrt(4)%)') / (sqrt(4)%)'
1188 3 (4! - 4!%) / sqrt(4)%
3 4! / (.4!' - (.sqrt(4))')
1189 4 ((sqrt(4) - 4!)% + 4!) / sqrt(4)%
3 (4! + (sqrt(4)%)') / (sqrt(4)%)'
1190 4 4! /(.4!' - (.sqrt(4))' ) + sqrt(4)
3 (4! - sqrt(4%)) / sqrt(4)%
1191 4 (4! / sqrt(4)%) - (4 / .4`)
1192 4 sqrt(4) * ((4! / 4%) - 4)
3 4!/(sqrt(4)%)' + 4
1193 4 (4! / (sqrt(4) % )') + (sqrt(4) / .4)
1194 4 (4! / sqrt(4)%) - (4 + sqrt(4))
1195 4 (4! - (.4 / 4)) / sqrt(4)%
1196 3 (4! / sqrt(4)%) - 4
1197 4 ((sqrt(4)% + 4!) / sqrt(4)%) - 4
1198 3 (4! / sqrt(4)%) - sqrt(4)
1199 4 (4! + (.sqrt(4))' )/(.4!' - (.sqrt(4))' )
3 (4! - sqrt(4)%) / sqrt(4)%
1200 2 4! / sqrt(4) %
1201 3 (sqrt(4)% + 4!) / sqrt(4)%
1202 3 sqrt(4) + (4! / sqrt(4)%)
1203 4 4!/(sqrt(4))% + sqrt(4/.4')
1204 3 4 + (4! / sqrt(4)%)
1205 4 4!/(sqrt(4))% + sqrt(4)/.4
1206 4 4+sqrt(4)+(4!/sqrt(4)%)
1207 4 .4'/(4%%)' + (4! x 4)
1208 4 4!/(sqrt(4))% + (4 x sqrt(4))
1209 4 4!/(sqrt(4))% + 4/.4'
1210 4 (4! + .4')/(.4!' - (.sqrt(4))' )
3 (4! + sqrt(4%)) / sqrt(4)%
1211 4 .4'/(4%%)' + 4/4%
1212 4 4! /(.4!' - (.sqrt(4))' ) + 4!
3 (4! + 4!%) / sqrt(4)%
1215 4 4!/(.4' - .4) /.4'
1220 3 (4! + .4) / sqrt(4)%
1221 4 (4! + sqrt(.4'))/(.4!' - (.sqrt(4))' )
1224 3 (4! / sqrt(4)%) + 4!
1225 4 sqrt((4! - sqrt(.4'))/sqrt(.4'))^4
1226 4 (.sqrt(4) ^ (- 4) )*sqrt(4) - 4!
1232 4 (4! + 4)*44
1242 4 (4!*4! - 4!)/.4'
1246 4 (.sqrt(4) ^ (- 4) )*sqrt(4) - 4
1248 4 (.sqrt(4) ^ (- 4) )*sqrt(4) - sqrt(4)
1250 3 sqrt(4) / 4 % / 4 %
1252 4 (.sqrt(4) ^ (- 4) )*sqrt(4) + sqrt(4)
1254 4 (.sqrt(4) ^ (- 4) )*sqrt(4) + 4
1256 4 4^4 /.sqrt(4) - 4!
1258 4 ((.sqrt(4) ^ (- 4) ) + 4) * sqrt(4)
1260 4 ((4!+4)/4)! /4
1270 4 (4^4 - sqrt(4))/.sqrt(4)
1272 4 4!*4!/.4' - 4!
1274 4 (.sqrt(4) ^ (- 4) )*sqrt(4) + 4!
1275 4 (root(.(sqrt(4))' , 4) - sqrt(4))/.4
1276 4 4^4 /.sqrt(4) - 4
1278 4 (4^4 - .4) /.sqrt(4)
1279 4 (root(.(sqrt(4))' , 4) - .4)/.4
1280 3 4 ^ 4 / sqrt(4%)
1281 4 (root(.(sqrt(4))' , 4) + .4)/.4
1282 4 (4^4 + .4) /.sqrt(4)
1284 4 4^4 /.sqrt(4) + 4
1285 4 (root(.(sqrt(4))' , 4) + sqrt(4))/.4
1287 4 (4!*4! - 4)/.4'
1290 4 (4^4 + sqrt(4))/.sqrt(4)
1292 4 4!*4!/.4' - 4
1294 4 4!*4!/.4' - sqrt(4)
1295 4 (4!*4! - .4')/.4'
1296 3 (4!/4)^4
1297 4 (4!*4! + .4')/.4'
1298 4 4!*4!/.4' + sqrt(4)
1300 4 4!*4!/.4' + 4
3 (sqrt(4) + 4!) / sqrt(4) %
1304 4 4^4 /.sqrt(4) + 4!
1305 4 (4!*4! + 4)/.4'
1308 4 (4! + .(sqrt(4))' )*4!/.4'
1311 4 sqrt(sqrt(sqrt(44/4)^4!))
1312 4 (4!/.4' + sqrt(.4'))*4!
1320 4 4!*4!/.4' + 4!
1325 4 (4! - .4')/(.4! - (.sqrt(4))' )
1326 4 4! /(.4! - (.sqrt(4))' ) - 4!
1331 4 sqrt(sqrt(sqrt(44/4)^4!))
1332 4 (4! + sqrt(.4'))*4!/.4'
1340 4 (root(.(sqrt(4))' , 4) + 4!)/.4
1344 4 (4!/.4 - 4)*4!
1346 4 4! /(.4! - (.sqrt(4))' ) - 4
1348 4 4! /(.4! - (.sqrt(4))' ) - sqrt(4)
1350 4 (4!*4! + 4!)/.4'
3 (4 + sqrt(4)) / .4`%
3 4! / (.4! - (.sqrt(4))')
1352 4 4! /(.4! - (.sqrt(4))' ) + sqrt(4)
1354 4 4! /(.4! - (.sqrt(4))' ) + 4
1360 3 (4!% + sqrt(.4`)) / sqrt(.4`%)%
1369 4 sqrt((4! + sqrt(.4'))/sqrt(.4'))^4
1374 4 4! /(.4! - (.sqrt(4))' ) + 4!
1375 4 (4 - sqrt(.4') )/(.4!' - .4!)
1380 4 (4!*4! - 4!)/.4
1386 4 (4! + 4)/(.4!' - (.sqrt(4))' )
1388 4 (root(-.sqrt(4), .sqrt(4)) - sqrt(4)) * .4'
1392 4 ((4!/4)! - 4!)*sqrt(4)
1400 4 (4! - sqrt(.4'))*4!/.4
3 (4 + 4!) / sqrt(4)%
1404 4 (4! + sqrt(4))*(4!/.4')
1408 4 (4! - sqrt(4))*sqrt(sqrt(sqrt(4^4!)))
1416 4 4!*4!/.4 - 4!
1424 4 (4!/.4 - sqrt(.4'))*4!
1428 4 (4! - .sqrt(4))*4!/.4
1430 4 (4!*4! - 4)/.4
1432 4 ((4!/4)! - 4)*sqrt(4)
1435 4 (4!*4! - sqrt(4))/.4
1436 4 4!*4!/.4 - 4
1438 4 4!*4!/.4 - sqrt(4)
1439 4 (4!*4! - .4)/.4
1440 3 (4!/4)! * sqrt(4)
1441 4 (4!*4! + .4)/.4
1442 4 4!*4!/.4 + sqrt(4)
1444 4 4!*4!/.4 + 4
1445 4 (4!*4! + sqrt(4))/.4
1448 4 ((4!/4)! + 4)*sqrt(4)
1450 4 (4!*4! + 4)/.4
1452 4 (4! + .sqrt(4))*4!/.4
1456 4 (4!/.4 + sqrt(.4'))*4!
1458 4 4*4/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!))))
1464 4 4!*4!/.4 + 4!
1480 4 (4! + sqrt(.4'))*4!/.4
1485 4 (4 - .4)/(.4!' - .4!)
1488 4 (4!/.4 + sqrt(4))*4!
1500 4 sqrt(.4') / 4'% * 4 / 4%
4 (4!*4! + 4!)/.4
3 (4 + sqrt(4)) / .4%
2 sqrt(.4') / .4'%
1512 4 sqrt(sqrt(sqrt(4^4!)))*4! - 4!
1520 4 (sqrt(sqrt(sqrt(4^4!))) - sqrt(.4'))*4!
1521 4 (sqrt(4! + sqrt(4))^4)/.4'
1530 4 (root(.sqrt(4) , 4) - 4)/sqrt(.4')
1532 4 sqrt(sqrt(sqrt(4^4!)))*4! - 4
1533 4 (root(.sqrt(4) , 4) - sqrt(4))/sqrt(.4')
1534 4 sqrt(sqrt(sqrt(4^4!)))*4! - sqrt(4)
1535 4 (root(.sqrt(4) , 4) - sqrt(.4'))/sqrt(.4')
1536 3 root(sqrt(4%), 4) / sqrt(.4`)
1537 4 (root(.sqrt(4) , 4) + sqrt(.4'))/sqrt(.4')
1538 4 sqrt(sqrt(sqrt(4^4!)))*4! + sqrt(4)
1539 4 (root(.sqrt(4) , 4) - sqrt(4))/sqrt(.4')
1540 4 sqrt(sqrt(sqrt(4^4!)))*4! + 4
1542 4 (root(.sqrt(4) , 4) + 4)/sqrt(.4')
1550 4 (4 - .4!')/(.4!' - .4!)
1551 4 (4 - .4!)/(.4!' - .4!)
1552 4 (sqrt(sqrt(sqrt(4^4!))) + sqrt(.4'))*4!
1560 4 (4! + sqrt(4))/.4 * 4!
1562 4 ((.sqrt(4) ^ (- 4)) - .sqrt(4))/.4
1563 4 ((.sqrt(4) ^ (- 4)) + .sqrt(4))/.4
1566 4 ((4!/4)! - 4!)/.4'
1568 4 sqrt(4*(4! + 4)^4)
1572 4 (root(.sqrt(4) , 4) + 4!)/sqrt(.4')
1575 4 (4! + 4)/(.4! - (.sqrt(4))' )
1577 4 (((4%)' - .(sqrt(4))') / .(4!)' % % ) + sqrt(4)
4 (4!‰)' /(.4!%%)' + 4!*4!
4 ((4%)'‰ + (sqrt(.4')% /.4!' )'% )/(.sqrt(4)‰)'‰
1584 4 (root(.4 , 4))/(.4!' - (.sqrt(4))' )
1596 4 (4!/4)! /.4' - 4!
1600 4 (4*4+4!)^sqrt(4)
3 ((4! - 4) ^ 4)%
1611 4 ((4!/4)! - 4)/.4'
1616 4 (4!/4)! /.4' - 4
1618 4 (4!/4)! /.4' - sqrt(4)
1619 4 ((4!/4)! - .4')/.4'
1620 3 (4 + sqrt(4))! / .4`
1621 4 ((4!/4)! + .4')/.4'
1622 4 (4!/4)! /.4' + sqrt(4)
1624 4 (4!/4)! /.4' + 4
1625 4 (4! + sqrt(4))!/(4!)! /.4
1626 4 4/(.4!' - .4!) - 4!
1629 4 ((4!/4)! + 4)/.4'
1632 4 (44 + 4!)*4!
1638 4 sqrt(sqrt(4^4!)) * .4 - .4
1640 4 (sqrt(sqrt(4^4!)) + 4) * .4
1644 4 (4!/4)! /.4' + 4!
1646 4 4/(.4!' - .4!) - 4
1648 4 (sqrt(sqrt(4^4!)) + 4!) * .4
4 4/(.4!' - .4!) - sqrt(4)
1650 2 4 / .(4!)' %
3 4/(.4!' - .4!)
1652 4 4/(.4!' - .4!) + sqrt(4)
1654 4 4/(.4!' - .4!) + 4
1656 4 (4+4)! /4! - 4!
1664 4 sqrt(sqrt(sqrt(4^4!))) * (4! + sqrt(4))
1674 4 ((4!/4)! + 4!)/.4'
4 4/(.4!' - .4!) + 4!
1676 4 (4+4)! /4! - 4
1678 4 (4+4)! /4! - sqrt(4)
1679 4 ((4+4)! - 4!)/4!
1680 3 (4 + 4)! / 4!
1681 4 ((4+4)! + 4!)/4!
1682 4 (4+4)! /4! + sqrt(4)
1684 4 (4+4)! /4! + 4
1690 4 (sqrt(4! + sqrt(4))^4)/.4
1700 4 (root.4(4) + sqrt(4)) / sqrt(4) %
1704 4 (4+4)! /4! + 4!
1724 4 sqrt(sqrt(sqrt(4!/sqrt(4))^4!)) - 4
1726 4 sqrt(sqrt(sqrt(4!/sqrt(4))^4!)) - sqrt(4)
1728 4 4!*4!*sqrt(4/.4')
1730 4 sqrt(sqrt(sqrt(4!/sqrt(4))^4!)) + sqrt(4)
1732 4 sqrt(sqrt(sqrt(4!/sqrt(4))^4!)) + 4
1736 4 .4' + .4' + (4!%o ^ -sqrt(4))
1740 4 ((4!/4)! - 4!)/.4
1749 4 (4 + .4!)/(.4!' - .4!)
1750 4 (4 + .4!')/(.4!' - .4!)
1752 4 sqrt(sqrt(sqrt(4!/sqrt(4))^4!)) + 4!
1764 4 sqrt(44 - sqrt(4))^4
1776 4 4 (444)
1782 4 (4!/sqrt(.4'))/(.4!' - (.sqrt(4))' )
1790 4 ((4!/4)! - 4)/.4
1792 4 sqrt(sqrt(sqrt(4^4!))) * (4! + 4)
1795 4 ((4!/4)! - sqrt(4))/.4
1796 4 (4!/4)! /.4 - 4
1798 4 (4!/4)! /.4 - sqrt(4)
1799 4 ((4!/4)! - .4)/.4
1800 4 4 / .(sqrt(4))' * 4 / 4%
3 (4!/4)! /.4
2 4 / .(sqrt(4))' %
1801 4 ((4!/4)! + .4)/.4
1802 4 (4!/4)! /.4 + sqrt(4)
1804 4 (4!/4)! /.4 + 4
1805 4 ((4!/4)! + sqrt(4))/.4
1810 4 ((4!/4)! + 4)/.4
1815 4 (4 + .4)/(.4!' - .4!)
1820 4 sqrt(sqrt(4^4!)) * .4' - .4'
1824 4 (4!/4)! /.4 + 4!
1860 4 ((4!/4)! + 4!)/.4
1872 4 (4!/.4' + 4!)*4!
1875 4 (sqrt(4) /.4)! /(sqrt(sqrt(sqrt( .4^4! ))))
1880 3 (4 - 4!%) / sqrt(4%)%
1900 4 (4! / sqrt(.4') + sqrt(4)) / sqrt(4) %
3 (4 - sqrt(4%)) / sqrt(4%)%
1905 4 sqrt((4/.4)! + sqrt(.4'%) ^ (- sqrt(4)))
1912 4 sqrt(44^4) - 4!
1920 4 4!*4*(4! - 4)
1925 4 (4 + sqrt(.4') )/(.4!' - .4!)
1932 4 sqrt(44^4) - 4
1934 4 sqrt(44^4) - sqrt(4)
1936 4 (44) * (44)
3 44^sqrt(4)
1938 4 sqrt(44^4) + sqrt(4)
1940 4 sqrt(44^4) + 4
1944 4 4!/(.sqrt(4))' * 4/(.sqrt(4))'
1960 4 sqrt(44^4) + 4!
1976 3 (4 / sqrt(4%)%) - 4!
1980 4 (4!*4)/(.4!' * .sqrt(4))
3 (4 - 4%) / sqrt(4%)%
1990 3 (4 - sqrt(4)%) / sqrt(4%)%
1996 3 (4 / sqrt(4%)%) - 4
1998 3 (4 / sqrt(4%)%) - sqrt(4)
1999 3 (4 - sqrt(4%)%) / sqrt(4%)%
2000 4 (4! - 4) * 4 / 4%
2 .4' / .(sqrt(4))' %o
2 4 / sqrt(4%)%
2001 3 (4 + sqrt(4%)%) / sqrt(4%)%
2002 3 (4 / sqrt(4%)%) + sqrt(4)
2004 3 4 + (4 / sqrt(4%)%)
2010 3 (4 + sqrt(4)%) / sqrt(4%)%
2013 4 (root(.(sqrt(4))' , 4) - 4!)/.4!'
2016 4 ((4!+4)/4)!*.4
3 ((4 + 4)! / sqrt(4%))%
2020 3 (4 + 4%) / sqrt(4%)%
2024 4 sqrt(sqrt(4^4!)) /sqrt(4) - 4!
3 (4 / sqrt(4%)%) + 4!
2025 3 (4 * .4`% ^ -sqrt(4))%
2036 4 (sqrt(sqrt(4^4!)) - 4!) /sqrt(4)
2044 4 sqrt(sqrt(4^4!)) /sqrt(4) - 4
2046 4 (sqrt(sqrt(4^4!)) - 4) /sqrt(4)
2047 4 (sqrt(sqrt(4^4!)) - sqrt(4)) /sqrt(4)
2048 3 sqrt(4) * root(sqrt(4%), 4)
2049 4 (sqrt(sqrt(4^4!)) + sqrt(4)) /sqrt(4)
2050 4 (sqrt(sqrt(4^4!)) + 4) /sqrt(4)
2052 4 sqrt(sqrt(4^4!)) /sqrt(4) + 4
2060 4 (sqrt(sqrt(4^4!)) + 4!) /sqrt(4)
2072 4 sqrt(sqrt(4^4!)) /sqrt(4) + 4!
2082 4 (root(-.sqrt(4), .sqrt(4)) - sqrt(4) )*sqrt(.4')
2084 4 (root(-.sqrt(4), .sqrt(4))*sqrt(.4') + sqrt(.4')
2086 4 (root(-.sqrt(4), .sqrt(4)) + 4)*sqrt(.4')
2088 4 (root(.(sqrt(4))' , 4))/.4!' - 4!
2091 4 (sqrt(sqrt(sqrt( .(sqrt(4))' ^ (- 4!) ))) - 4)*4!
2100 4 (44 - sqrt(4)) / sqrt(4) %
3 (4 + sqrt(4%)) / sqrt(4%)%
2108 4 (root(.(sqrt(4))' , 4))/.4!' - 4
2110 4 (root(.(sqrt(4))' , 4))/.4!' - sqrt(4)
2113 4 (root(.(sqrt(4))' , 4) + .4!')/.4!'
2114 4 (root(.(sqrt(4))' , 4))/.4!' + sqrt(4)
2116 4 (root(.(sqrt(4))' , 4))/.4!' + 4
2111 4 (root(.(sqrt(4))' , 4) - .4!')/.4!'
2112 3 (root(.(sqrt(4))' , 4))/.4!'
2120 3 (4 + 4!%) / sqrt(4%)%
2125 4 (root(.(sqrt(4))' , 4) - sqrt(4))/.4!
2134 4 (root(.(sqrt(4))' , 4))/.4! + sqrt(.4')
2136 4 (root(.(sqrt(4))' , 4))/.4!' + 4!
2139 4 (sqrt(sqrt(sqrt( .(sqrt(4))' ^ (- 4!) ))) - sqrt(4))*4!
2150 4 (root(.(sqrt(4))' , 4) + 4)/.4!
2160 4 4!*4/(.4' - .4)
3 4! * .4 / .4`%
2163 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) - 4!
2178 4 44 /(.4!' - (.sqrt(4))' )
2183 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) - 4
2185 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) - sqrt(4)
2187 3 sqrt(sqrt(sqrt( .(sqrt(4))' ^ (- 4!) )))*4!
2189 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) + sqrt(4)
2191 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) + 4
2196 4 (root(.(sqrt(4))' , 4) - 4!)/.(sqrt(4))'
2197 4 sqrt(sqrt(sqrt( (4! + sqrt(4))/sqrt(4) )^4!))
2200 4 (4! - sqrt(4)) * 4 / 4%
3 44 / sqrt(4)%
2208 4 4 * (4!)! / (4! - sqrt(4))
2211 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) + 4!
2235 4 (sqrt(sqrt(sqrt( .(sqrt(4))' ^ (- 4!) ))) + sqrt(4))*4!
2240 4 ((4!+4)/4)!*.4'
2250 3 4 / (.4 * .4`)%
2256 4 (4!*4 - sqrt(4))*4!
2277 4 (4!*4! - 4!)/.4!'
2280 4 4!*4!*4 - 4!
2283 4 (sqrt(sqrt(sqrt( .(sqrt(4))' ^ (- 4!) ))) + 4)*4!
2286 4 (root(.(sqrt(4))' , 4) - 4)/.(sqrt(4))'
2288 4 (4!*4! - 4)*4
2295 4 (root(.sqrt(4) , 4) - 4)/.4'
2296 4 (4!*4! - sqrt(4))*4
2300 4 (44 + sqrt(4)) / sqrt(4) %
4 4!*4!*4 - 4
2301 4 (root(.(sqrt(4))' , 4) - sqrt(.4'))/.(sqrt(4))'
2302 4 4!*4!*4 - sqrt(4)
2303 4 (root(.sqrt(4) , 4) - .4' )/.4'
2304 4 (4!+4!) * sqrt(4) * 4!
3 4*4!^sqrt(4)
2305 4 (root(.sqrt(4) , 4) + .4' )/.4'
2306 4 4!*4!*4 + sqrt(4)
2307 4 (root(.(sqrt(4))' , 4) + sqrt(.4'))/.(sqrt(4))'
2308 4 4!*4!*4 + 4
2312 4 (4!*4! + sqrt(4))*4
2313 4 (root(.sqrt(4) , 4) + 4)/.4'
2320 4 (4!*4! + 4)*4
2322 4 (root(.(sqrt(4))' , 4) + 4)/.(sqrt(4))'
2328 4 4!*4!*4 + 4!
2332 4 (4! - .4')*4!/.4!'
2376 3 4!*4!/.4!'
2352 4 4!*4!/.4!' - 4!
2354 4 (4! - .(sqrt(4))')*4!/.4!'
2358 4 (root(.sqrt(4) , 4) + 4!)/.4'
2360 4 (4! - .4)*4!/.4!
2368 4 (4! + sqrt(.4'))*4!*4
2372 4 4!*4!/.4!' - 4
2374 4 4!*4!/.4!' - sqrt(4)
2375 4 (4!*4! - .4!')/.4!'
2376 4 44/.4' * 4!
2377 4 (4!*4! + .4!')/.4!'
2378 4 4!*4!/.4!' + sqrt(4)
2380 4 4!*4!/.4!' + 4
2396 4 4!*4!/.4! - 4
2398 4 (4! + .(sqrt(4))')*4!/.4!'
2399 4 (4!*4! - .4!)/.4!
2400 3 4!*4!/.4!
2401 4 ((4! + 4)/4)^4
2402 4 4!*4!/.4! + sqrt(4)
2404 4 ((.sqrt(4) ^ (- 4) ) - 4!) * 4
2412 4 (root(.(sqrt(4))' , 4) + 4!)/.(sqrt(4))'
2420 4 (4! + .sqrt(4))*4!/.4!
2424 4 (4! + .4!)*4!/.4!
2430 4 4!/(.4' - .4) /.(sqrt(4))'
2440 4 (4! + .4)*4!/.4!
2442 4 (4! + sqrt(.4'))*4!/.4!'
2448 4 (4!/.4! + sqrt(4))*4!
2472 4 (4!/.4!' + 4)*4!
2475 4 (4!*4! + 4!)/.4!'
2476 3 sqrt(4)% ^ -sqrt(4) - 4!
2484 4 ((.sqrt(4) ^ (- 4) ) - 4)*4
2492 4 ((.sqrt(4) ^ (- 4) ) - sqrt(4))*4
2496 4 (4!/.4! + 4)*4!
3 sqrt(4)% ^ -sqrt(4) - 4
2498 3 sqrt(4)% ^ -sqrt(4) - sqrt(4)
2500 4 qrt(sqrt(sqrt((4/.4)^4!)))/.4
2 sqrt(4)% ^ -sqrt(4)
2502 3 sqrt(4) + sqrt(4)% ^ -sqrt(4)
2504 3 4 + sqrt(4)% ^ -sqrt(4)
2508 4 ((.sqrt(4) ^ (- 4) ) + sqrt(4))*4
2516 4 ((.sqrt(4) ^ (- 4) ) + 4)*4
2517 4 (.4'% + (4!‰/(4%)')'‰)/(.sqrt(4)%)'‰
2520 4 ((4!+4)/4)!)/sqrt(4)
2524 3 sqrt(4)% ^ -sqrt(4) + 4!
2536 4 (root(.(sqrt(4) , 4))/.4 - 4!
2540 4 (root(.(sqrt(4))' , 4) - 4)/.sqrt(4)
2544 4 (4!/(.sqrt(4))' - sqrt(4))*4!
2550 4 (root(.sqrt(4) , 4) - 4 )/.4
2555 4 (root(.sqrt(4) , 4) - sqrt(4) )/.4
2556 4 (root(.sqrt(4), 4))/.4 - 4
2556 4 (root(.sqrt(4), 4))/.4 - 4
2558 4 (root(.sqrt(4) , 4))/.4 - sqrt(4)
2559 4 (root(.sqrt(4) , 4) - .4)/.4
2560 4 4^4 * 4 / .4
3 root(sqrt(4%), 4) / .4
2561 4 (root(.sqrt(4) , 4) + .4)/.4
2562 4 (root(.sqrt(4) , 4))/.4 + sqrt(4)
2564 4 (root(.sqrt(4) , 4))/.4 + 4
2565 4 (root(.sqrt(4) , 4) + sqrt(4) )/.4
2568 4 4!*4!/(.sqrt(4))' - 4!
2570 4 (root(.sqrt(4) , 4) + 4)/.4
2574 4 (4!*4! - 4)/(.sqrt(4))'
2580 4 (root((.sqrt(4))' , 4) + 4)/.sqrt(4)
2583 4 (4!*4! - sqrt(4))/(.sqrt(4))'
2584 4 (root(.sqrt(4) , 4))/.4 + 4!
2588 4 4!*4!/(.sqrt(4))' - 4
2589 4 (4!*4! - sqrt(.4'))/(.sqrt(4))'
2590 4 4!*4!/(.sqrt(4))' - sqrt(4)
2591 4 (4!*4! - (.sqrt(4))' )/(.sqrt(4))'
2592 4 sqrt(4) * (4! / 4)^4
3 4!*4!/.(sqrt(4))'
2593 4 (4!*4! + (.sqrt(4))' )/(.sqrt(4))'
2594 4 4!*4!/(.sqrt(4))' + sqrt(4)
2595 4 (4!*4! + sqrt(.4'))/(.sqrt(4))'
2596 4 ((.sqrt(4) ^ (- 4) ) + 4!) * 4
2600 4 (4! + sqrt(4)) * 4 / 4%
2601 4 (4!*4! + sqrt(4))/(.sqrt(4))'
2610 4 (4!*4! + 4)/(.sqrt(4))'
2616 4 4!*4!/(.sqrt(4))' + 4!
2620 4 (root(.sqrt(4) , 4) + 4!)/.4
2640 4 (sqrt(4) /.4)! * (4! - sqrt(4))
3 (sqrt(4) - 4!%) / sqrt(.4`%)%
2664 4 (4! + sqrt(.4'))*4! /.(sqrt(4))'
2673 4 (4!/.4')/(.4!' - (.sqrt(4))' )
2680 4 (root(.(sqrt(4))' , 4) + 4!)/.sqrt(4)
2688 4 (4! + 4)*4!*4
3 (4 + 4)! * sqrt(.4`%)
2700 4 (sqrt(4) /.4)! /(.4' - .4)
3 4! / (sqrt(4) * .4`)%
2704 4 sqrt(4!+4!+4)^4
2728 4 (sqrt(sqrt(4^4!) - 4)*sqrt(.4')
2730 4 (sqrt(sqrt(4^4!))*sqrt(.4') - sqrt(.4')
2732 4 (sqrt(sqrt(4^4!) + sqrt(4))*sqrt(.4')
2744 4 sqrt(sqrt(sqrt(4! - 4/.4)^4!))
2750 4 (sqrt(sqrt(sqrt(.sqrt(4) ^ (- 4!)))))*(4! - sqrt(4))
2 sqrt(.4') / (4!) %o
2760 4 (sqrt(sqrt(sqrt(4!^4!))) - 4!) * .sqrt(4)
2763 4 (sqrt(sqrt(sqrt( (.sqrt(4))' ^ (- 4!) ))) + 4!)*4!
2764 4 (sqrt(sqrt(sqrt(4!^4!))) - 4)*.sqrt(4)
2765 4 sqrt(sqrt(sqrt(4!^4!))) * .sqrt(4) + .sqrt(4)
2784 4 ((sqrt(4) /.4)! - 4)*4!
2800 4 (4! + 4) * 4 / 4%
2808 4 4!/(.sqrt(4))' * (4! + sqrt(4))
2809 4 sqrt((4! + .4')/.4')^4
2816 4 sqrt(sqrt(sqrt(4^4!)))*44
2832 4 ((sqrt(4) /.4)! - sqrt(4))*4!
2856 4 (sqrt(4) /.4)! *4! - 4!
2860 4 (4!*4! - 4)/.sqrt(4)
2864 4 ((4!/4)! - 4)*4
2870 4 (4!*4! - sqrt(4) )/.sqrt(4)
2871 4 ((4!/4)! - 4!)/.4!'
2872 4 ((4!/4)! - sqrt(4))*4
2876 4 (sqrt(4) /.4)! *4! - 4
2878 4 (sqrt(4) /.4)! *4! - sqrt(4)
2879 4 (4!*4! - .sqrt(4) )/.sqrt(4)
2880 4 (4!*4 + 4!)*4!
3 (sqrt(4) /4)! * 4!
2881 4 (4!*4! + .sqrt(4) )/.sqrt(4)
2882 4 (sqrt(4) /.4)! *4! + sqrt(4)
2884 4 (sqrt(4) /.4)! *4! + 4
2888 4 ((4!/4)! + sqrt(4))*4
2890 4 (4!*4! + sqrt(4))/.sqrt(4)
2892 4 sqrt(4!/.4')^4 - 4!
2896 4 ((4!/4)! + 4)*4
2900 4 ((4! / .4') + 4) / sqrt(4) %
3 (sqrt(4) - sqrt(.4`%)) / sqrt(.4`%)%
2904 4 (sqrt(4) /.4)! *4! + 4!
2912 4 sqrt(4!/.4')^4 - 4
2914 4 sqrt(4!/.4')^4 - sqrt(4)
2916 3 (4! / .4')^sqrt(4)
2918 4 sqrt(4!/.4')^4 + sqrt(4)
2920 4 sqrt(4!/.4')^4 + 4
2928 4 (4! + .4)*(sqrt(4) /.4)!
2940 3 (sqrt(4) - 4%) / sqrt(.4`%)%
2940 4 sqrt(4!/.4')^4 + 4!
2946 4 (4!/4)!/.4!' - 4!
2950 4 (4! - .4)*(sqrt(sqrt(sqrt( .sqrt(4) ^(- 4!)))))
2952 4 (4!/.4!' + 4!)*4!
2960 4 (4! + sqrt(.4'))*(sqrt(4) /.4)!
2966 4 (4!/4)!/.4!' - 4
2968 4 (4!/4)!/.4!' - sqrt(4)
2969 4 ((4!/4)! - .4!')/.4!'
2970 3 (sqrt(4) - sqrt(4)%) / sqrt(.4`%)%
3 (4!/4)! /.4!'
2971 4 ((4!/4)! + .4!')/.4!'
2972 4 (4!/4)!/.4!' + sqrt(4)
2974 4 (4!/4)!/.4!' + 4
2975 4 (4! - .sqrt(4))*(sqrt(sqrt(sqrt( (.sqrt(4))^( - 4!)))))
2976 4 ((sqrt(4) /.4)! + 4)*4!
3 (sqrt(4) / sqrt(.4`%)%) - 4!
2990 3 (sqrt(4) - sqrt(.4`)%) / sqrt(.4`%)%
2994 4 (4!/4)!/.4!' + 4!
3 (sqrt(4) - .4%) / sqrt(.4`%)%
2996 4 (4!/4)!/.4! - 4
3 (sqrt(4) / sqrt(.4`%)%) - 4
2997 3 (sqrt(4) - sqrt(4%)%) / sqrt(.4`%)%
2998 4 (4!/4)!/.4! - sqrt(4)
4 ((4!/4)! - .4!)/.4!
3 (sqrt(4) / sqrt(.4`%)%) - sqrt(4)
2999 3 (sqrt(4) - sqrt(.4`%)%) / sqrt(.4`%)%
3000 4 sqrt(sqrt(sqrt(sqrt(4) /.4)^4!)) * 4!
3 (4!/4)! /.4!
2 sqrt(.4') / .(sqrt(4))' %o
2 sqrt(4) / sqrt(.4`%)%
3001 4 ((4!/4)! + .4!)/.4!
3 (sqrt(4) + sqrt(.4`%)%) / sqrt(.4`%)%
3002 4 (4!/4)!/.4! + sqrt(4)
3 sqrt(4) + (sqrt(4) / sqrt(.4`%)%)
3003 3 (sqrt(4) + sqrt(4%)%) / sqrt(.4`%)%
3004 4 (4!/4)!/.4! + 4
3 4 + (sqrt(4) / sqrt(.4`%)%)
3005 4 ((.sqrt(4) ^ (- 4) ) - 4!)/.sqrt(4)
3006 3 (sqrt(4) + .4%) / sqrt(.4`%)%
3010 3 (sqrt(4) + sqrt(.4`)%) / sqrt(.4`%)%
3024 4 (4!/4)!/.4! + 4!
3 (sqrt(4) / sqrt(.4`%)%) + 4!
3025 4 sqrt((4! - sqrt(4))/.4)^4
3030 4 (4! + .4!)*(sqrt(sqrt(sqrt( (.sqrt(4))^( - 4!)))))
3 (sqrt(4) + sqrt(4)%) / sqrt(.4`%)%
3048 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' - 4!
3050 4 (4! + .4)*(sqrt(sqrt(sqrt( .sqrt(4)^( - 4!)))))
3060 3 (sqrt(4) + 4%) / sqrt(.4`%)%
3068 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' - 4
3069 4 ((4!/4)! + 4!)/.4!'
3070 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' - sqrt(4)
3072 3 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))'
3074 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' + sqrt(4)
3076 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' + 4
3096 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' + 4!
3100 4 ((4!/4)! + 4!)/.4!
3 (sqrt(4) + sqrt(.4`%)) / sqrt(.4`%)%
3101 4 (.sqrt(4) ^ (- 4) )/.sqrt(4) - 4!
3105 4 ((.sqrt(4) ^ (- 4) ) - 4)/.sqrt(4)
3115 4 ((.sqrt(4) ^ (- 4) ) - sqrt(4))/.sqrt(4)
3120 4 (sqrt(4) /.4)! * (4! + sqrt(4))
3121 4 (.sqrt(4) ^ (- 4) )/.sqrt(4) - 4
3123 4 ((.sqrt(4) ^ (- 4) ) - .4)/.sqrt(4)
3124 4 ((.sqrt(4) ^ (- 4) ) - .sqrt(4))/.sqrt(4)
3125 2 root(-.(sqrt(4), .(sqrt(4))
3 4% ^ -sqrt(4) / sqrt(4%)
3126 4 ((.sqrt(4) ^ (- 4) ) + .sqrt(4))/.sqrt(4)
3127 4 ((.sqrt(4) ^ (- 4) ) + .4)/.sqrt(4)
3129 4 (.sqrt(4) ^ (- 4) )/.sqrt(4) + 4
3132 4 ((4!/4)! - 4!)/(.sqrt(4))'
3135 4 ((.sqrt(4) ^ (- 4) ) + sqrt(4))/.sqrt(4)
3136 4 sqrt(4!/.4 - 4)^4
3145 4 ((.sqrt(4) ^ (- 4) ) + 4)/.sqrt(4)
3149 4 (.sqrt(4) ^ (- 4) )/.sqrt(4) + 4!
3168 4 (4!/(.sqrt(4))' + 4!)*4!
3200 3 sqrt(sqrt(sqrt(4 ^ (4!))) / sqrt(4) %
3216 4 (4!/4)! /(.sqrt(4))' - 4!
3222 4 ((4!/4)! - 4)/(.sqrt(4))'
3231 4 ((4!/4)! - sqrt(4))/(.sqrt(4))'
3236 4 (4!/4)! /(.sqrt(4))' - 4
3237 4 ((4!/4)! - sqrt(.4'))/(.sqrt(4))'
3238 4 (4!/4)! /(.sqrt(4))' - sqrt(4)
3239 4 ((4!/4)! - (.sqrt(4))' )/(.sqrt(4))'
3240 4 (4! / 4)^4 / .4
3 (4!/4)! /.(sqrt(4))'
3241 4 ((4!/4)! + (.sqrt(4))' )/(.sqrt(4))'
3242 4 (4!/4)! /(.sqrt(4))' + sqrt(4)
3243 4 ((4!/4)! + sqrt(.4'))/(.sqrt(4))'
3244 4 (4!/4)! /(.sqrt(4))' + 4
3245 4 ((.sqrt(4) ^ (- 4) ) + 4!)/.sqrt(4)
3249 4 ((4!/4)! + sqrt(4))/(.sqrt(4))'
3250 4 (sqrt(sqrt(sqrt(.sqrt(4) ^ (- 4!)))))*(4! + sqrt(4))
3258 4 ((4!/4)! + 4)/(.sqrt(4))'
3264 4 (4!/4)! /(.sqrt(4))' + 4!
3300 4 (sqrt(sqrt(sqrt(4 ^ (4!))) + sqrt(4)) / sqrt(4) %
3 (4! - sqrt(4)) / sqrt(.4`)%
3312 4 (sqrt(sqrt(sqrt(4!^4!))) - 4!)*.4!
3318 3 (4!^4)% + .4!
3348 4 ((4!/4)! + 4!)/(.sqrt(4))'
3360 4 (sqrt(4) /.4)! * (4! + 4)
3 (sqrt(4) + 4!%) / sqrt(.4`%)%
3364 4 sqrt(4!/.4 - sqrt(4))^4
3375 4 sqrt(sqrt(sqrt((4 + sqrt(4))/.4)^4!))
3 root(-sqrt(4), .4`%) / .4`%
3376 4 sqrt(sqrt(4^4!)) - (4!/4)!
3400 4 (sqrt(sqrt(sqrt(4 ^ (4!))) + 4) / sqrt(4) %
3432 4 sqrt(sqrt(sqrt(4!^4!)))/4 - 4!
3450 4 (sqrt(sqrt(sqrt(4!^4!))) - 4!)/4
3452 4 sqrt(sqrt(sqrt(4!^4!)))/4 - 4
3454 4 sqrt(sqrt(sqrt(4!^4!)))/4 - sqrt(4)
3455 4 (sqrt(sqrt(sqrt(4!^4!))) - 4)/4
3456 3 sqrt(sqrt(sqrt(4!^4!))) /4
3457 4 (sqrt(sqrt(sqrt(4!^4!))) + 4)/4
3458 4 sqrt(sqrt(sqrt(4!^4!)))/4 + sqrt(4)
3460 4 sqrt(sqrt(sqrt(4!^4!)))/4 + 4
3462 4 (sqrt(sqrt(sqrt(4!^4!))) + 4!)/4
3472 4 ((sqrt(sqrt(.(sqrt(4) ^ -4!) * .(sqrt(4))') - .(sqrt(4))'
3480 4 sqrt(sqrt(sqrt(4!^4!)))/4 + 4!
3481 4 sqrt((4! - .4)/.4)^4
3500 4 (4! / sqrt(.4') % ) - (4! / .(4!))
3 (4! - sqrt(.4`)) / sqrt(.4`)%
3520 4 sqrt(sqrt(4^4!) - 4!*4!
3540 3 (4! - .4) / sqrt(.4`)%
3564 3 (4! - 4!%) / sqrt(.4`)%
3570 3 (4! - sqrt(4%)) / sqrt(.4`)%
3576 3 (4! / sqrt(.4`)%) - 4!
3580 4 ((4!/4)! - 4)/.sqrt(4)
3590 3 (4! - sqrt(.4`%)) / sqrt(.4`)%
3594 3 (4! - 4%) / sqrt(.4`)%
3596 3 (4! / sqrt(.4`)%) - 4
3597 3 (4! - sqrt(4)%) / sqrt(.4`)%
3598 3 (4! / sqrt(.4`)%) - sqrt(4)
3599 4 ((4!/4)! - .sqrt(4))/.sqrt(4)
3 (4! - sqrt(.4`)%) / sqrt(.4`)%
3600 3 (4! / .4)^sqrt(4)
2 4! / sqrt(.4') %
3601 4 ((4!/4)! + .sqrt(4))/.sqrt(4)
3 (4! + sqrt(.4`)%) / sqrt(.4`)%
3602 4 sqrt(4!/.4)^4 + sqrt(4)
3 sqrt(4) + (4! / sqrt(.4`)%)
3603 3 (sqrt(4)% + 4!) / sqrt(.4`)%
3604 4 sqrt(4!/.4)^4 + 4
3 4 + (4! / sqrt(.4`)%)
3606 3 (4! + 4%) / sqrt(.4`)%
3610 4 ((4!/4)! + sqrt(4))/.sqrt(4)
3 (4! + sqrt(.4`%)) / sqrt(.4`)%
3620 4 ((4!/4)! + 4)/.sqrt(4)
3624 4 sqrt(4!/.4)^4 + 4!
3 4! + (4! / sqrt(.4`)%)
3629 3 (4/.4')!% + .sqrt(4)
3630 3 (4! + sqrt(4%)) / sqrt(.4`)%
3636 3 (4! + 4!%) / sqrt(.4`)%
3645 4 (4!/4)! /(.4' * .4')
3660 3 (4! + .4) / sqrt(.4`)%
3700 4 (4! / .(4!)) + (4! / sqrt(.4') % )
3 (4! + sqrt(.4`)) / sqrt(.4`)%
3720 4 ((4!/4)! + 4!)/.sqrt(4)
3750 3 root(-sqrt(4), .4`%) / .4%
3780 4 (4+4)! /4! /.4'
3800 4 (sqrt(.4') / (.4') % + sqrt(4)) / 4 %
3840 4 sqrt(sqrt(4^4!)) - 4^4
3 4 ^ 4 / sqrt(.4`%)
3844 4 sqrt(4!/.4 + sqrt(4))^4
3872 4 sqrt(44*4)^4
3888 4 sqrt(sqrt(sqrt(4!^4!)))/(4 - .4')
3900 4 ((4 * 4) - .4) / .4 %
3 (sqrt(4) + 4!) / sqrt(.4`)%
3969 4 sqrt((4! + 4)/.4')^4
3971 4 sqrt(sqrt(4^4!)) - sqrt(sqrt(sqrt(.sqrt(4) ^ (- 4!) )))
3976 4 sqrt(sqrt(4^4!)) - (sqrt(4) /.4)!
3988 4 sqrt(sqrt(4^4!)) - 4!/(.sqrt(4))'
3996 4 sqrt(sqrt(4^4!)) - 4!/.4!
3997 4 sqrt(sqrt(4^4!)) - 4!/.4!'
4000 4 sqrt(sqrt(4^4!)) - 4!*4
3 4 * 4 / .4%
4032 4 (4+4)! /4 * .4
4036 4 sqrt(sqrt(4^4!)) - 4!/.4
4042 4 sqrt(sqrt(4^4!)) - 4!/.4'
4048 4 sqrt(sqrt(4^4!)) - 4! - 4!
4052 4 sqrt(sqrt(4^4!)) - 44
4060 4 sqrt(sqrt(4^4!)) - 4!/sqrt(.4')
4064 4 sqrt(sqrt(4^4!)) - root(.4 , 4)
4068 4 sqrt(sqrt(4^4!)) - 4! - 4
4070 4 sqrt(sqrt(4^4!)) - 4! - sqrt(4)
4071 4 sqrt(sqrt(4^4!)) - (.sqrt(4))^(- sqrt(4))
4072 3 sqrt(sqrt(4^4!)) - 4!
4074 4 sqrt(sqrt(4^4!)) - 4! + sqrt(4)
4076 4 sqrt(sqrt(4^4!)) - 4! + 4
4078 4 sqrt(sqrt(4^4!)) - 4/(.sqrt(4))'
4080 4 sqrt(sqrt(4^4!)) - 4*4
4084 4 sqrt(sqrt(4^4!)) - 4!/sqrt(4)
4086 4 sqrt(sqrt(4^4!)) - 4/.4
4087 4 sqrt(sqrt(4^4!)) - 4/.4'
4088 4 sqrt(sqrt(4^4!)) - (4+4)
4090 4 sqrt(sqrt(4^4!)) - 4!/4
4091 4 sqrt(sqrt(4^4!)) - sqrt(4) /.4
4092 3 sqrt(sqrt(4^4!)) - 4
4093 4 sqrt(sqrt(4^4!)) - sqrt(4/.4')
4094 3 sqrt(sqrt(4^4!)) - sqrt(4)
4095 4 sqrt(sqrt(4^4!)) - 4/4
4096 3 (4 + 4)^4
2 sqrt(sqrt(4 ^ 4!))
4097 4 sqrt(sqrt(4^4!)) + 4/4
4098 3 sqrt(sqrt(4^4!)) + sqrt(4)
4099 4 sqrt(sqrt(4^4!)) + sqrt(4/.4')
4100 3 sqrt(sqrt(4 ^ (4!)) + 4
4101 4 sqrt(sqrt(4^4!)) + sqrt(4) /.4
4102 4 sqrt(sqrt(4^4!)) + 4!/4
4104 4 sqrt(sqrt(4^4!)) + 4 + 4
4105 4 sqrt(sqrt(4^4!)) + 4/.4'
4106 4 sqrt(sqrt(4^4!)) + 4/.4
4108 4 sqrt(sqrt(4^4!)) + 4!/sqrt(4)
4112 4 sqrt(sqrt(4^4!)) + 4*4
4114 4 sqrt(sqrt(4^4!)) + 4/(.sqrt(4))'
4116 4 sqrt(sqrt(4^4!)) + 4! - 4
4118 4 sqrt(sqrt(4^4!)) + 4! - sqrt(4)
4120 3 sqrt(sqrt(4^4!)) + 4!
4200 4 (sqrt(4) / .4' %o ) - (sqrt(.4') / .(sqrt(4))' % )
3 (4 + 4!) / sqrt(.4`)%
4121 4 sqrt(sqrt(4^4!)) + (.sqrt(4))^(- sqrt(4))
4122 4 sqrt(sqrt(4^4!)) + 4! + sqrt(4)
4124 4 sqrt(sqrt(4^4!)) + 4! + 4
4125 4 sqrt(sqrt(sqrt((4/.4)^4!)))/.4!'
4128 4 sqrt(sqrt(4^4!)) + root(.4 , 4)
4132 4 sqrt(sqrt(4^4!)) + 4!/sqrt(.4')
4140 4 sqrt(sqrt(4^4!)) + 44
4144 4 sqrt(sqrt(4^4!)) + 4! + 4!
4150 4 sqrt(sqrt(4^4!)) + 4!/.4'
4156 4 sqrt(sqrt(4^4!)) + 4!/.4
4160 4 sqrt(sqrt(4^4!)) + sqrt(sqrt(sqrt(4^4!)))
4192 4 sqrt(sqrt(4^4!)) + 4! * 4
4195 4 sqrt(sqrt(4^4!)) + 4!/.4!'
4196 4 sqrt(sqrt(4^4!)) + 4!/.4!
4200 4 (4+4)! /(4! *.4)
4204 4 sqrt(sqrt(4^4!)) + 4!/(.sqrt(4))'
4216 4 sqrt(sqrt(4^4!)) + (sqrt(4) /.4)!
4220 4 (root(.sqrt(4) , 4))/.4!' - 4
4221 4 sqrt(sqrt(4^4!)) + sqrt(sqrt(sqrt(.sqrt(4) ^ (- 4!) )))
4224 3 (root(.sqrt(4) , 4))/.4!'
4225 4 sqrt((sqrt(4) + 4!)/.4)^4
4228 4 (root(.sqrt(4) , 4))/.4!' + 4
4248 4 (root(.sqrt(4) , 4))/.4!' + 4!
4250 4 (root(.sqrt(4) , 4) - 4)/.4!
4266 4 (root(.sqrt(4) , 4))/.4! - sqrt(.4')
4275 4 (root(.sqrt(4) , 4) + sqrt(4))/.4!
4300 4 ((4 / (4)' % ) - 4) / sqrt(4)
4320 4 (4!/4)!*4!/4
4323 4 (root(.sqrt(4) , 4) + 4!)/.4!'
4336 4 ((4! / sqrt(4)'%) + 4) * 4
4352 4 sqrt(sqrt(4^4!)) + 4^4
4356 4 sqrt((sqrt(sqrt(sqrt(4^4!))) + sqrt(4) )^4
4374 4 sqrt(.4') * (4/.4')^4
4392 4 (4! + .4) / sqrt(4)'% * 4
4394 4 (sqrt(sqrt(sqrt(4! + sqrt(4))))^4! )/ 4
4400 4 44 * 4 / 4%
4444 4 4444
4500 2 sqrt(4) / .4' %o
3 (4! - 4) / .4`%
4600 4 (sqrt(4) / .4' %o ) + (4! / .(4!))
4700 4 (sqrt(4) / .4' %o ) + (.4' / .(sqrt(4))' % )
4800 4 (4! + 4!) * 4 / 4%
3 (4 / sqrt(4)%) * 4!
4900 4 (4! / 4' %o ) - (sqrt(4) / .4 %)
4950 3 (4! - sqrt(4)) / .4`%
5000 4 sqrt(4) / .4% * 4 / .4
3 (4! - 4) / .4%
5040 3 ((4 + 4!) / 4)!
5100 4 (4! / 4' %o ) - (sqrt(.4') / .(sqrt(4))' % )
5120 3 root(sqrt(4%), 4) / sqrt(4%)
5184 4 4 * (4! / 4)^4
5200 4 (4! / 4' %o ) - (.4' / (sqrt(4))' % )
5250 3 (4! - sqrt(.4`)) / .4`%
5300 4 (4! / 4' %o ) - (4! / .(4!))
3 (4! - .4`) / .4`%
5310 3 (4! - .4) / .4`%
5346 3 (4! - 4!%) / .4`%
5355 3 (4! - sqrt(4%)) / .4`%
5376 3 (4! / .4`%) - 4!
5385 3 (4! - sqrt(.4`%)) / .4`%
5391 3 (4! - 4%) / .4`%
5396 3 (4! / .4`%) - 4
5398 3 (4! / .4`%) - sqrt(4)
5399 3 (4! - .4`%) / .4`%
5400 4 4! / 4'% * 4 / .4
2 4! / (4)' %o
2 4! / .4`%
5401 3 (4! + .4`%) / .4`%
5402 3 sqrt(4) + (4! / .4`%)
5404 3 4 + (4! / .4`%)
5409 3 (4! + 4%) / .4`%
5415 3 (4! + sqrt(.4`%)) / .4`%
5424 3 4! + (4! / .4`%)
5445 3 (4! + sqrt(4%)) / .4`%
5454 3 (4! + 4!%) / .4`%
5490 3 (4! + .4) / .4`%
5500 4 (4! / 4' %o ) + (4! / .(4!))
3 (4! - sqrt(4)) / .4%
5550 3 (4! + sqrt(.4`)) / .4`%
5600 4 (4! / 4' %o ) + (.4' / .(sqrt(4))' % )
5625 3 sqrt(4)% ^ -sqrt(4) / .4`
5640 3 (4 - 4!%) / sqrt(.4`%)%
5700 4 (4! / 4' %o ) + (sqrt(.4') / .(sqrt(4))' % )
3 (4 - sqrt(4%)) / sqrt(.4`%)%
5760 3 (4!^sqrt(4)) * 4
5800 4 (4! / 4 %o ) - (.4' / .(sqrt(4))' % )
5850 3 (sqrt(4) + 4!) / .4`%
5900 4 (4! / 4 %o ) - (4! / .(4!))
3 (4! - .4) / .4%
5940 3 (4! - 4!%) / .4%
5950 3 (4! - sqrt(4%)) / .4%
5970 3 (4 - sqrt(4)%) / sqrt(.4`%)%
5976 3 (4! / .4%) - 4!
5990 3 (4! - 4%) / .4%
5994 3 (4 - .4%) / sqrt(.4`%)%
5995 3 (4! - sqrt(4)%) / .4%
5996 3 (4! / .4%) - 4
5997 3 (4 - sqrt(4%)%) / sqrt(.4`%)%
5998 3 (4! / .4%) - sqrt(4)
5999 3 (4! - .4%) / .4%
6000 4 4! / 4% * 4 / .4
2 4! / 4 %o
6001 3 (4! + .4%) / .4%
6002 3 sqrt(4) + (4! / .4%)
6003 3 (4 + sqrt(4%)%) / sqrt(.4`%)%
6004 3 4 + (4! / .4%)
6005 3 (sqrt(4)% + 4!) / .4%
6006 3 (4 + .4%) / sqrt(.4`%)%
6010 3 (4! + 4%) / .4%
6024 3 4! + (4! / .4%)
6030 3 (4 + sqrt(4)%) / sqrt(.4`%)%
6050 3 (4! + sqrt(4%)) / .4%
6060 3 (4! + 4!%) / .4%
6100 4 (4! / 4 %o ) + (4! / .(4!))
3 (4! + .4) / .4%
6120 4 4^4*4!-4!
6144 3 4!*4^4
6200 4 (4! / 4 %o ) + (.4' / .(sqrt(4))' % )
6250 3 sqrt(4)% ^ -sqrt(4) / .4
6300 4 (4! / 4 %o ) + (sqrt(.4') / .(sqrt(4))' % )
3 (4 + 4!) / .4`%
6360 3 (4 + 4!%) / sqrt(.4`%)%
6400 4 sqrt(sqrt(sqrt(4^(4!)))) * 4 / 4%
3 4 ^ 4 / 4%
6500 4 (4! / 4 %o ) + (sqrt(4) / .4 % )
3 (sqrt(4) + 4!) / .4%
6561 3 (4 / .4')^4
6600 4 ((4 * 4) + .(4!)') / .(4!)' %
3 44 / sqrt(.4`)%
6700 4 ((4 * 4) + .(4!)') / .(4!)' %
6750 3 sqrt(4 / .4`%) / .4`%
6800 4 (4 / .(sqrt(4))' % ) + (sqrt(4) / 4 % % )
6900 4 (4! / 4 %o ) + (4 / .4' % )
7000 4 (4! / 4 %o ) + (4 / .4 % )
3 (4 + 4!) / .4%
7100 4 ((4 * 4) - .(sqrt(4))') / .(sqrt(4))' %
7200 4 (4! / 4 %o ) + (4! / sqrt(4) % )
3 root(.4, 4) / .4`%
7300 4 ((4 * 4) + .(sqrt(4))') / .(sqrt(4))' %
7400 4 (.4' / .(sqrt(4))' %o ) + (4! / 4' %o )
7500 4 (4! / 4 %o ) + (sqrt(.4') / .4' %o )
3 sqrt(4 / .4`%) / .4%
7600 4 ((sqrt(4) / 4 % ) + sqrt(.4')) / sqrt(.4') %
7700 4 ((sqrt(.4') / 4' % ) + .4) / .(sqrt(4)) %
7776 3 root(-sqrt(4%), 4 / 4!)
7800 4 (4! / 4 %o ) + (4 / .(sqrt(4))' % )
7744 4 44^sqrt(4) * 4
7800 4 (4! / 4 %o ) + (4 / .(sqrt(4))' % )
7900 4 ((4 * 4) - .(sqrt(4))) / .(sqrt4)) %
8000 4 (4 + 4) * 4 / .4%
3 root(.4, 4) / .4%
8064 3 (4 + 4)! * sqrt(4%)
8100 3 (.4 / .4`%) ^ sqrt(4)
8192 4 sqrt(4) * (4 + 4)^4
3 root(sqrt(.4`%), sqrt(4)) / 4
8250 2 sqrt(4) / .(4!)' %o
8640 3 4! * 4! / sqrt(.4`%)
9000 4 4 / .4'% * 4 / .4
2 4 / .4' %o
3 4 / (.4` - .4)%
9216 3 (4*4!)^sqrt(4)
9375 3 4% ^ -sqrt(4) / sqrt(.4`%)
9600 4 4 * 4! * 4 / 4%
9900 2 4! / .(4!)'
10000 3 (4/.4)^4
2 4 / 4 %%
10626 4 (4!)! / (4! - 4) / 4!
10800 2 4! / sqrt(4)' %o
11100 4 444 / 4%
12000 4 (sqrt(4) / .4)! * 4 / 4%
2 4! / sqrt(4) %o
12144 4 (4!)! / (4! - sqrt(4) / sqrt(.4`))
12288 4 sqrt(4) * 4! * 4^4
13122 4 sqrt(4) * (4/.4')^4
13248 4 4! * (4!)! / (4! - sqrt(4))
13824 3 4! * 4! * 4!
2 4! ^ sqrt(sqrt(sqrt(4!)))
14400 4 (4!^sqrt(4)) * 4 / .4%
14641 4 (44 / 4)^4
15000 4 sqrt(.4') / 4'% * 4 / .4%
2 sqrt(.4') / .4' %%
16000 4 4 * 4 * 4 / .4%
16384 4 ((4^4)^sqrt(4))/4
16500 2 4 / .(4!)' %o
18000 4 4 / .(sqrt(4))' * 4 / .4%
2 4 / .(sqrt(4))' %%
18432 4 (4*4!)^sqrt(4) * sqrt(4)
20000 4 (4! - 4) * 4 / .4%
2 .4' / .(sqrt(4))' %%
20736 3 (4! / sqrt(4))^4
21984 4 (4! / .4')^sqrt(4) * 4!
22000 4 (4! - sqrt(4)) * 4 / .4%
24000 3 4! * 4 / .4%
24576 4 4 * 4! * 4^4
25600 4 4^4 * 4 / 4%
26000 4 (4! + sqrt(4)) * 4 / .4%
26016 4 ((4! / sqrt(4)' % ) + 4) * 4!
26244 4 4 * (4/.4')^4
26352 4 (4! + .4) / sqrt(4)'% * 4!
27500 2 sqrt(.4') / (4!) %%
28000 4 (4! + 4) * 4 / .4%
30000 4 sqrt(4) / sqrt(.4'%) * 4 / .4%
2 sqrt(.4') / .(sqrt(4))' %%
31104 4 4! * (4! / 4)^4
32400 4 (4!/4)^4 / 4%
34560 3 (4!^sqrt(4)) * 4!
36000 4 4! / sqrt(.4`) * 4 / .4%
2 4! / sqrt(.4') %o
36864 4 (4*4!)^sqrt(4) * 4
40000 4 (4/.4)^4 * 4
40320 2 (4 + 4)!
41472 4 (4!)^4 / (4 * sqrt(4))
44000 4 44 * 4 / .4%
45000 2 sqrt(4) / .4' %%
48000 4 (4! + 4!) * 4 / .4%
50000 4 sqrt(4) / .4% * 4 / 4%
54000 4 4! / 4'% * 4 / 4%
2 4! / (4)' %%
55296 4 4*4!^sqrt(4) * 4!
57600 4 4!^sqrt(4) * 4 / 4%
60000 4 4! / 4% * 4 / 4%
2 4! / 4 %%
64000 4 sqrt(sqrt(sqrt(4^(4!)))) * 4 / .4%
65536 3 (4 * 4)^4
63756 4 (4!)! / (4! - 4) / 4
69120 4 (4!^sqrt(4)) * 4! * sqrt(4)
72000 4 (4 + sqrt(4))! * 4 / 4%
82944 3 (4!)^4 / 4
85184 3 sqrt(sqrt(sqrt(44^4!)))
86400 4 (4! / .4)^sqrt(4) * 4!
90000 4 4 / .4'% * 4 / 4%
90720 4 (4 + sqrt(4)/.4)! / 4
95040 4 (4! / sqrt(4))! / (4 * sqrt(4))
96000 4 4 * 4! * 4 / .4%
98304 4 (4 + 4)^4 * 4!
100000 4 4! / .(4!) * 4 / .4%
111000 4 444 / .4%
120000 4 (sqrt(4) / .4)! * 4 / .4%
127512 4 (4!)! / (4! - 4) / sqrt(4)
131072 4 sqrt(4) 4^(4 * sqrt(4))
138240 4 (4!^sqrt(4)) * 4! * 4
144000 4 (4!^sqrt(4)) * 4 / 4%
147456 4 4^(4 * sqrt(4)) / .4'
157464 4 (4 / .4')^4 * 4!
163840 4 4^(4 * sqrt(4)) / .4
165888 3 4!^4 / sqrt(4)
197136 4 444^sqrt(4)
221184 4 (4*4!)^sqrt(4) * 4!
234256 3 (4! - sqrt(4))^4
255024 3 (4!)! / (4! - 4)
256000 4 4^4 * 4 / .4%
262144 4 4 * 4^(4 * sqrt(4))
324000 4 (4! / 4)^4 / .4%
331776 2 4!^4
362880 3 (4 + sqrt(4)/.4)!
2 (4 / .4')!
390625 4 (4! + 4/4)^4
409600 4 (4^4 / .4) ^ sqrt(4)
422500 4 ((4! + sqrt(4))! / (4!)!) ^ sqrt(4)
451584 4 (4! * (4! + 4)) ^ sqrt(4)
456976 3 (4! + sqrt(4))^4
483025 4 ((4 + sqrt(4))! - 4!) ^ sqrt(4)
500000 4 sqrt(4) / .4% * 4 / .4%
512656 4 ((4 + sqrt(4))! - 4) ^ sqrt(4)
515524 4 ((4 + sqrt(4))! - sqrt(4)) ^ sqrt(4)
518400 3 ((4 + sqrt(4))!) ^ sqrt(4)
521284 4 ((4 + sqrt(4))! + sqrt(4)) ^ sqrt(4)
524176 4 ((4 + sqrt(4))! + 4) ^ sqrt(4)
540000 4 4! / 4'% * 4 / .4%
553536 4 ((4 + sqrt(4))! + 4!) ^ sqrt(4)
576000 4 4!^sqrt(4) * 4 / .4%
600000 4 4! / 4% * 4 / .4%
614652 4 (((4!)+4)^4)-4
614656 3 (4! + 4)^4
614660 4 (4! + 4)^4 + 4
663552 3 sqrt(4) * 4!^4
720000 4 (4 + sqrt(4))! * 4 / .4%
731025 4 ((4 - .(sqrt(4)) / .4'%) ^ sqrt(4)
746496 4 (4! * 4! / sqrt(.4`)) ^ sqrt(4)
810000 3 (sqrt(4) / sqrt(.4'%))^4
811801 4 ((4 + .4' % ) / .4'%) ^ sqrt(4)
883225 4 ((4 - sqrt(.4' % )) / .4' %) ^ sqrt(4)
900000 4 4 / .4'% * 4 / .4%
907200 4 (4 + sqrt(4)/.4)! / .4
937024 4 44^4 / 4
990000 2 4! / .(4!)'%%
1000000 4 (4 / .4) ^ (4 + sqrt(4))
1048576 4 sqrt(sqrt(4^44)) / 4
4 (4! + 4 + 4)^4
1098304 4 (4! + root(.(sqrt(4)),4)) ^ sqrt(4)
1106704 4 (sqrt(4)*4!^sqrt(4)) ^ sqrt(4)
1327104 3 4 * 4!^4
1440000 4 (4!^sqrt(4)) * 4 / .4%
1451520 4 4(4+(sqrt4)/.4)!
1572864 4 4! 4^(4 * sqrt(4))
1600000 3 (4! - 4)^4
1679616 3 (4! / sqrt(.4`))^4
1874048 4 44^4 / sqrt(4)
2097152 4 sqrt(sqrt(4^44)) / sqrt(4)
2654208 4 4 * 4!^4 * sqrt(4)
2916000 4 (4! / 4)^4 / .4'%
3628800 2 (4 / .4)!
3748096 3 44^4
4194304 3 sqrt(sqrt(4^44))
5308416 4 4 * 4!^4 * 4
7496192 4 sqrt(4) * 44^4
7962624 3 4!^(sqrt(4)/.4)
9370240 4 44^4 / .4
Infinity 3 4 / (4-4)
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Contributors
The first contributors to the solutions I didn't find are listed
below, note that in many cases the solution may have subsequently
been replaced by simpler solutions.
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Matthew Cordone
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1451520
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Rizvan Dadaev
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167, 187, 283, 340, 350, 415, 421, 427, 438, 447, 470, 553, 583, 588, 626, 683, 687,
701, 707, 713, 734, 737, 739, 743, 750, 754, 757, 763, 779, 793,
971,
1018, 1023, 1025, 1030, 1054, 1060, 1080, 1104, 1150, 1156, 1176, 1188, 1190, 1199,
1210, 1212, 1215, 1221, 1225, 1226, 1232, 1242, 1246, 1248,
1252, 1254, 1256, 1258, 1260, 1270, 1272, 1274, 1275, 1276,
1278, 1279, 1281, 1282, 1284, 1285, 1287, 1290, 1292, 1294, 1295, 1297, 1298,
1300, 1304, 1305, 1308, 1311, 1312, 1320, 1325, 1326, 1331, 1332, 1340, 1344, 1346,
1348, 1350, 1352, 1354, 1369, 1374, 1375, 1380, 1386, 1388, 1392,
1400, 1404, 1408, 1416, 1424, 1428, 1430, 1432, 1435, 1436, 1438, 1439, 1441, 1442, 1444, 1445, 1448,
1450, 1452, 1456, 1458, 1464, 1480, 1485, 1488,
1500, 1512, 1520, 1521, 1530, 1532, 1533, 1534, 1535, 1537, 1538, 1539, 1540, 1542,
1550, 1551, 1552, 1560, 1562, 1563, 1566, 1568, 1572, 1575, 1577, 1584, 1596,
1611, 1616, 1618, 1619, 1621, 1622, 1624, 1625, 1626, 1629, 1632, 1638, 1640, 1644, 1646, 1648,
1650, 1652, 1654, 1656, 1664, 1674, 1676, 1678, 1679, 1681, 1682, 1684, 1690,
1704, 1724, 1726, 1728, 1730, 1732, 1740, 1749, 1750, 1752, 1764, 1782,
1790, 1792, 1795, 1796, 1798, 1799,
1800, 1801, 1802, 1804, 1805, 1810, 1815, 1820, 1824, 1860, 1872, 1875,
1905, 1912, 1920, 1925, 1932, 1934, 1938, 1940, 1944, 1960, 1980,
2012, 2013, 2016, 2024, 2036, 2044, 2046, 2047, 2049,
2050, 2052, 2060, 2072, 2082, 2084, 2086, 2088, 2091,
2108, 2110, 2111, 2112, 2113, 2114, 2116, 2125, 2134, 2136, 2139,
2150, 2160, 2163, 2178, 2183, 2185, 2187, 2189, 2191, 2196, 2197,
2211, 2235, 2240, 2256, 2277, 2280, 2283, 2286, 2288, 2295, 2296,
2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2312, 2313, 2320, 2322, 2328, 2332,
2352, 2354, 2358, 2360, 2368, 2372, 2374, 2375, 2376, 2377, 2378, 2380, 2396, 2398, 2399,
2400, 2401, 2402, 2404, 2412, 2420, 2424, 2430, 2440, 2442, 2448,
2472, 2475, 2484, 2492, 2496,
2500, 2508, 2516, 2520, 2536, 2540, 2544, 2550, 2555, 2556, 2558, 2559,
2561, 2562, 2564, 2565, 2568, 2570, 2574, 2580, 2583, 2584, 2588, 2589, 2590, 2591,
2592, 2593, 2594, 2595, 2596,
2601, 2610, 2616, 2620, 2640, 2664, 2673, 2680, 2688,
2700, 2704, 2728, 2730, 2732, 2744, 2750, 2760, 2763, 2764, 2765, 2784,
2808, 2809, 2816, 2832, 2856, 2860, 2864, 2870, 2871, 2872, 2876, 2878, 2879, 2880,
2881, 2882, 2884, 2888, 2890, 2892, 2896,
2904, 2912, 2914, 2918, 2920, 2928, 2940, 2946, 2950, 2952, 2960, 2966, 2968, 2969,
2970, 2971, 2972, 2974, 2975, 2976, 2994, 2996, 2998, 2999,
3000, 3001, 3002, 3004, 3005, 3024, 3025, 3030, 3048, 3050, 3068, 3069, 3070, 3072,
3074, 3076, 3096, 3100, 3101, 3105, 3115, 3120, 3121, 3123, 3124, 3126, 3127, 3129, 3132,
3135, 3136, 3145, 3149, 3168, 3216, 3222, 3231, 3236, 3237, 3238, 3239,
3240, 3241, 3242, 3243, 3244, 3245, 3249, 3250, 3258, 3264,
3312, 3318, 3348, 3360, 3364,
3375, 3376, 3432, 3450, 3452, 3454, 3455, 3456, 3457, 3458, 3460, 3462, 3480,
3481, 3520, 3580, 3599,
3601, 3602, 3604, 3610, 3620, 3624, 3629,
3645, 3720, 3780, 3840, 3844, 3872, 3888, 3969, 3971, 3976, 3988, 3996, 3997,
4000, 4032, 4036, 4042, 4048, 4052, 4060, 4064, 4068, 4070, 4071,
4072, 4074, 4076, 4078, 4080, 4084, 4086, 4087, 4088, 4090, 4091, 4092, 4093, 4094, 4095,
4097, 4098, 4099, 4100, 4101, 4102, 4104, 4105, 4106, 4108, 4112, 4114, 4116, 4118,
4120, 4121, 4122, 4124, 4125, 4128,
4132, 4140, 4144, 4150, 4156, 4160, 4192, 4195, 4196, 4200, 4204, 4216, 4220, 4221, 4224,
4225, 4228, 4248, 4250, 4266, 4275, 4320, 4323, 4352, 4356, 4374 4394
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Contributed the following solutions
using just two "4"s.
π and e were also contributed, although the solution for e requires 5 fours.
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Ewart Shaw
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219, 267, 351, 371, 373, 377, 379, 705, 727, 731, 733, 753, 972, 975
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Richard Schorn
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First to uncover a solution for 113 but it uses rather "non-standard"
combination of decimal place (.) and repeated digit (`), see
2/9.
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Ewald R. de Wit
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103, 121, 125, 142, 146
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Martin Olivella
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181, 186, 188, 190, 194, 286, 290, 292, 362, 380,
384, 386, 388, 408, 488, 514, 536, 832, 900, 976, 1000
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Heiner Marxen
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154, 164, 169, 179, 182, 184, 204, 238, 242, 251, 275, 287,
289, 295, 296, 298, 299, 301, 302, 305, 310, 316,325,338, 348, 356, 358,
359, 361, 364, 372, 375, 426, 450, 472, 476, 478, 482, 496, 510, 520, 524,
526, 530, 601, 621, 622, 623, 626, 627, 628, 629, 635, 636, 638, 639, 641,
642, 644, 645, 646, 649, 654, 660, 664, 660, 670, 750, 841
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Scott Forschler
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The solutions for 90, 100, 113, 165 using
"%"
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Wayne Goode
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202, 214, 218, and a simpler solution to 66
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Jörg Wiegels
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165, 177, 183, 195, 269, 270, 271, 274,
279, 294, 318, 322, 344, 378, 381,
383, 385, 387, 390, 405, 441, 495, 522, 525, 531, 538,
542, 544, 549, 555, 608, 612, 656, 666, 675, 684, 688, 768, 774, 810,
828, 848, 856, 860, 861, 862, 863, 865, 867,
868, 870, 896, 990, 1008, 1014, 1016
Simpler solutions for
13, 39, 41, 47, 57, 58, 78, 90, 116, 118, 120, 122, 124, 180, 288,
300, 320, 360, 484, 640, 540, 560, 567, 585, 592, 864
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Charles Dillingham
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Pointed out that there are simpler
solutions for some numbers than those listed above. For example
"4 * 4 * 4" for 64 instead of "sqrt(sqrt(sqrt(4^(4!))))". The definition
of the simplest was determined by the number of 4's needed, consideration
of the operator complexity was only used when there was the same number of
4's. This has been partially resolved by giving double solutions for some
numbers where the solution with the minimum number of 4's is particularly
clumsy.
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Peter Karsanow
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Donated some solutions which have five 4's,
(See the
comment above regarding the use of 2 instead of sqrt(4))
for example, 157, 167, 193, 197, 203, 223, 231, 281, 337, 406, 551, 657
836, 856, and 881.
Also some three 4 solutions for numbers
over 1000, namely 1440, 1936, 2304, 2916, 3600, 4096, 6144, 6561, 9216, 10000,
>3824, and 16384. Some simpler solutions for 81, 567, and 650.
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Brad McInnes
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Provided solution for 984, 996, 998, and a three 4's solution for 1000.
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Frank Mrazik
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73, 167, 171, 173, 185, 187, 191, 193, 197, 198, 199,
201, 203, 205, 206, 209, 211, 213, 217, 221, 223, 226, 227, 229,
231, 233, 237, 249, 263, 273, 277, 283, 285, 291, 293, 297,
303, 306 - 309, 311, 313, 314, 315, 317, 319, 321, 323,
326 - 335, 337,
339 - 342, 345, 346, 347, 349, 353, 354, 355, 357, 363, 365 - 370,
374, 391, 393 - 397, 399,
401, 403, 406, 407, 409, 411, 412, 413, 415, 417, 419, 421, 423, 425, 429,
435, 437, 439, 414, 418,
428, 422, 430, 431, 432, 433, 434, 436, 438, 443, 445, 447, 449,
451 - 455, 457 - 461, 463, 465, 466, 467, 469,
470, 471, 473, 474, 475, 477, 479, 481, 483, 485, 487,
489 - 495, 497, 498, 499,
501, 502, 503, 505, 506, 507, 509, 511, 513, 515, 517, 518, 519,
521, 523, 527, 533, 534, 535, 537, 539, 541, 543, 545, 547, 553,
557, 559, 561, 563, 565, 583, 587, 589,
593 - 597, 599, 603, 606, 607, 609 - 611, 613 - 615, 617, 619,
630 - 634, 637, 643, 647, 651, 653, 655, 657 - 659,
661 - 663, 665, 667, 669,
671, 673, 677, 679, 681, 682, 683, 685 - 687, 689 - 691, 693, 695, 697, 699,
701, 702, 703, 706, 709, 713,
734, 735, 737, 738, 739, 741, 743, 745, 747, 749, 751, 752, 754,
755, 757 - 759, 761, 762, 765, 767, 771, 773, 775 - 779,
781, 783, 785, 787, 789 - 791, 793 - 799,
801 - 807, 809, 811 - 815, 817 - 827, 829 - 831,
834 - 839, 842 - 847, 849 - 857, 859, 869,
871 - 879, 881 - 887, 889 - 895, 897, 898, 899,
901 - 911, 913 - 927, 929 - 935, 937 - 952, 954 - 959,
961 - 967, 969, 970, 971, 973, 974,
977 - 983, 985 - 989, 991 - 995, 997, 1001 - 1117, 1132, 1133,
1138, 1139, 1141, 1142, 1143, 1147, 1151, 1153, 1157 - 1163, 1169,
1171, 1183, 1193, 1250, 1577, 2517.
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Rick Hevener
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Provided solution for 18, 157 and 163 using the very
imaginative 24/99.
Contributed more elegant solutions for 31, 49, 76, 89, 125, 146, 159
and interesting alternatives for
17, 21, 36, 100, 102, 107, 109, 126, 140, 141, 162, 279.
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David Bevan
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Provided lots of solutions based upon a computer search, this includes
lots of more elegant solutions. In particular he pointed out a third
solution for 17 and noted the following cleaner notations,
.(4!) is the same as 4!% and
.(sqrt(4)) is the same as sqrt(4%).
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Vijay Kailas
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Came up with 1206.
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Guido Roach
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An alternative 4 four solution for 113, namely ( sqrt(4) / .4' + sqrt(4)% ) / 4%
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Joe Martin
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An improved solution for 533 = (4! * .4' - sqrt(.4)%) / sqrt(4)%
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Toufic Batouli
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Toufic proposed the use of degrees, minutes, and seconds as standard notation.
Using these symbols provides some additional solutions to numbers using only two 4s.
Since each degree is 60 minutes, or 3600 seconds, we have
[(4!) Deg / 4 Sec] = 21,600
[(4!) Deg / 4 Sec]% = 216
[(4!) Deg / 2 Sec] = 43,200
[(4!) Deg / 2 Sec]% = 432
We also have additional results for both 0 and 1 using only one 4 because 24!
is an integer (N) multiple of 360:
Sin((4!)! Deg) = Sin(N * 360 Deg) = 0
Cos((4!)! Deg) = Cos(N * 360 Deg) = 1
Also, since one degree is equal to pi/180 radians we can get many additional
numbers using only two 4s. The additional solutions come from the relationship
arccos(x) = 90 Deg - x. So only two 4's are needed for:
Arccos(Sin(4 Deg))/(Sqrt(4) Deg) = 86 Deg / 2 Deg = 43
Further examples are given here.
And of course the well known problem of 113 without using the double factorial:
129 - 16 = [Arccos(Sin(4 Deg))/(4! Sec)]% - 4*4 = 113
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Nikkol Bauer
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New or alternative answers for the following:
729, 777, 792, 821, 823, 824, 825, 826, 827, 829, 834, 835, 849, 850, 870,
882, 890, 910, 918, 930, 999, 1023, 1062, 1062, 1070, 1070, 1077,
1089, 1089, 1104, 1104, 1110, 1111, 1113, 1115, 1135, 1155, 1166,
1170, 1177, 1184, 1186, 1187, 1189, 1192, 1203, 1205, 1207, 1208, 1209, 1211
largely based upon the following relationships and observations.
.(4!)'% = .002424242424...
.sqrt(4)'% = .002222222...
.4'% = .0044444....
4'% = .04444444.... (this is really stretching it because
four repeating divided by 100 is infinity)
(4 + .4')% = same as above with two fours
(sqrt(4))'% = .022222222 ... (also pushing it)
(4%%)' = 0.000400040004 ...
(sqrt(4) + sqrt(4%)')% = same as above with two fours
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