Puzzling Asked by user35295 on October 29, 2020
Create all numbers from 0-100 only using 1,2,3,4 and 5. No repeats and you have to use each number. Also, you can use any operation. I’ve only gotten to 50 by pure brute force. I think that this might be fun for you puzzlers!
Also, could someone please help with tags and wording of this puzzle. I know this is similar Expressing numbers using 0, 1, 2, 3, and 4 but I’m still posting this.
Note: You may not use concatenation to combine digits. Ex 1 and 2 to get 21 or 12
Also, you can use any operation.
Ok then.
$begin{array}{c|c} 0 & log_{frac1 2} left( log_{4!!-3} 5 right) 1 & log_{frac1 2} left( log_{4!!-3} sqrt 5 right) 2 & log_{frac1 2} left( log_{4!!-3} sqrt{sqrt 5,} right) 3 & log_{frac1 2} left( log_{4!!-3} sqrt{sqrt{sqrt 5,},} right) 4 & log_{frac1 2} left( log_{4!!-3} sqrt{sqrt{sqrt{sqrt 5,},},} right) 5 & log_{frac1 2} left( log_{4!!-3} sqrt{sqrt{sqrt{sqrt{sqrt 5,},},},} right) 6 & log_{frac1 2} left( log_{4!!-3} sqrt{sqrt{sqrt{sqrt{sqrt{sqrt 5,},},},},} right) 7 & log_{frac1 2} left( log_{4!!-3} sqrt{sqrt{sqrt{sqrt{sqrt{sqrt{sqrt 5,},},},},},} right) 8 & log_{frac1 2} left( log_{4!!-3} sqrt{sqrt{sqrt{sqrt{sqrt{sqrt{sqrt{sqrt 5,},},},},},},} right) 9 & log_{frac1 2} left( log_{4!!-3} sqrt{sqrt{sqrt{sqrt{sqrt{sqrt{sqrt{sqrt{sqrt 5,},},},},},},},} right) vdots & vdots end{array}$
would you mind running me through this solution?
This is because for any number $x$ (and in my examples, $4!!-3=5$)
$$log_frac12left[log_xunderbrace{sqrt{sqrt{dotssqrt{x,},},}}_text{n square roots}right]equiv n$$
And the reason this is true
$$ begin{align} & a^b=cimplies log_a c = b & sqrt x = x^{frac12} & sqrt{sqrt x} = x^{frac14} & sqrt{sqrt{sqrt x}} = x^{frac18} vdots & log_x sqrt{sqrt x} = frac14 & log_frac12 left[ log_x sqrt{sqrt x} right] = log_frac12 left(frac14right) = 2 impliedby left(frac12right)^2=frac14 end{align} $$
See what happens when you add another square root.
Correct answer by theonlygusti on October 29, 2020
$begin{align} 0 & = (1 + 2 - 3) times (4 + 5) 1 & = 1 + (2+3-5) times 4 2 & = 2 + (1+3-4) times 5 3 & = 1 -2+3-4+5 4 & = 1 times (2+3-5) + 4 5 & = 1-2-3+4+5 6 & = 5+1 times (2+3-4) 7 & = 5+2 times (4-3) times 1 8 & = 5+3 times (4-2-1) 9 & = 5+3 + (4-2-1) 10 & = 5+4 + (3-2) times 1 11 & = 5+4 + (3-2) + 1 12 & = 5+4+3 times (2-1) 13 & = 5+4+3 + 2-1 14 & = 5+4+3 + 2 times 1 15 & = 5+4+3 + 2 + 1 16 & = 5+3 + 4 times 2 times 1 17 & = 5+3 + 4 times 2 + 1 18 & = 5 + 4 + 3 ^ 2 times 1 19 & = 5 + 4 + 3 ^ 2 + 1 20 & = 5 times 4 times (3 - 2) times 1 21 & = 5 times 4 times (3 - 2) + 1 22 & = 5 times 4 + 3 - 2 + 1 23 & = 5 times 4 + 3 times (2 - 1) 24 & = 5 times 4 + 3 + (2 - 1) 25 & = 5^{4-3+2-1} 26 & = (5 + 4 + 3 + 1) times 2 27 & = 3 times (4-1) times (5-2) 28 & = (5times 3 - 1) times frac{4}{2} 29 & = 5 times 3 times frac{4}{2} - 1 30 & = 5 times 3 times frac{4}{2} times 1 31 & = 5 times 3 times frac{4}{2} + 1 32 & = 2^5 + 4 -3 - 1 33 & = 2^5 + 4 - 3 times 1 34 & = 2^5 + 4 - 3 + 1 35 & = (3 + 4) times 5 times (2-1) 36 & = (3 + 4) times 5 + (2-1) 37 & = 2 times 4 times 5 - 3 times 1 38 & = 2 times 4 times 5 - 3 + 1 39 & = (5 + 4 times 2 ) times 3 times 1 40 & = (5 + 4 times 2 ) times 3 + 1 41 & = (4 + 5 times 2 ) times 3 - 1 42 & = (4 + 5 times 2 ) times 3 times 1 43 & = (4 + 5 times 2 ) times 3 + 1 44 & = (1+2+3+5) times 4 45 & = 3 times 5 times (4 - 2 +1) 46 & = (5 times 4 + 3 ) times 2 times 1 47 & = (5 times 4 + 3 ) times 2 + 1 48 & = 2^4 times (5-3+1) 49 & = (5+2) times (4+3) times 1 50 & = (5+2) times (4+3) + 1 51 & = (5 times 4 - 3) times (2+1) 52 & = (3 times 5 - 2) times 4 times 1 53 & = (3 times 5 - 2) times 4 + 1 54 & = (5 times 4 - 2) times 3 times 1 55 & = (5 times 4 - 2) times 3 + 1 56 & = (5+3 -1) times 4^2 57 & = (5 times 4 times 3) -2 -1 58 & = (5 times 4 times 3) -2 times 1 59 & = (5 times 4 times 3) -2 +1 60 & = (5 times 4 times 3) times (2 -1) 61 & = (5 times 4 times 3) + 2 - 1 62 & = (5 times 4 times 3) + 2 times 1 63 & = (5 times 4 times 3) + 2 + 1 64 & = 2^5 times (4-3) times 1 65 & = 2^5 times (4-3) + 1 66 & = 2^5 + 4-3+1 67 & = 4! times 3 - 5 times (2-1) 68 & = 4! times 3 - 5 + (2-1) 69 & = (4+3) times 5 times 2 -1 70 & = (4+3) times 5 times 2 times 1 71 & = (4+3) times 5 times 2 + 1 72 & = 4! times (5-2) times 1^3 73 & = 4! times (5-2) + 1^3 74 & = 5^2 times 3 - 1^4 75 & = 5^2 times 3 times 1^4 76 & = 5^2 times 3 + 1^4 77 & = 4! times 3 + 5 times 1^2 78 & = 4! times 3 + 5 + 1^2 79 & = 4! times 3 + 5 + 2 times 1 80 & = 4! times 3 + 5 + 2 + 1 81 & = 3^{4-1} times (5-2) 82 & = 4! times 3 + 5 times 2 times 1 83 & = 4! times 3 + 5 times 2 + 1 84 & = 3^4 + 5 - 2 times 1 85 & = 3^4 + 5 - 2 + 1 86 & = 3^4 + 5 times 1^2 87 & = 3^4 + 5 + 1^2 88 & = 3^4 + 5 +2^1 89 & = 3^4 + 5 + 2 + 1 90 & = 3^2 times 5 times 2^1 91 & = 3^2 times 5 times 2 + 1 92 & = 3^4 + 5 times 2 + 1 93 & = 2^5 times 3 +1 - 4 94 & = 5^2 times 4 - 3! times 1 95 & = 5^2 times 4 - 3! + 1 96 & = 5^2 times 4 - 3 - 1 97 & = 5^2 times 4 - 3 times 1 98 & = 5^2 times 4 - 3 + 1 99 & = 5^2 times 4 -1^3 100 & = 5^2 times 4 times 1^3 end{align}$
Someone please double check it.
Answered by Marius on October 29, 2020
$ 0 = 3^2 times 1 - 4 - 5 $
$ 1 = 3^2 + 1 - 4 - 5 $
$ 2 = (4 - 5 + 3)/ 1^2 $
$ 3 = (5 + 4) times 1 - 2 times 3 $
$ 4 = (5 + 3) times 1^2 - 4 $
$ 5 = 5 times 2 - 4 - 1^3 $
$ 6 = 3 times 2 + 5 - 1 - 4 $
$ 7 = 5 times 2 - 3 times 1^4 $
$ 8 = 4 + 5 - 3 + 2^1 $
$ 9 = 3^2 - 4 - 1 + 5 $
$ 10 = 5 times 2 - 4 + 1 + 3 $
$ 11 = 5 + 3 + 4 - 1^2 $
$ 12 = 4 times 5 times 1 - 2^3 $
$ 13 = 4 times 5 - 1 - 3 times 2 $
$ 14 = 4 times 5 - 3 times 2 times 1 $
$ 15 = 1 + 2 + 3 + 4 + 5 $
$ 16 = 4 + 5 + 2 times 3 + 1 $
$ 17 = 5 + 3 + 2 times 4 + 1 $
$ 18 = 5 + 4 + 1 + 2^3 $
$ 19 = 5 + 4 + 1 + 3^2 $
$ 20 = 5 times 4 - 3 + 2 + 1 $
$ 21 = 5 times 4 + 3 - 2 times 1 $
$ 22 = 5 times 4 + 3 - 2 + 1 $
$ 23 = 4 times 3 + 5 times 2 + 1 $
$ 24 = 5 times 4 + 2 times (3 - 1) $
$ 25 = 5 times 4 + 3 + 2 times 1 $
$ 26 = 5 times 4 + 3 + 2 + 1 $
$ 27 = 5 times 4 + 3 times 2 + 1 $
$ 28 = 5 times 4 times 1 + 2^3 $
$ 29 = 5 times 4 times 1 + 3^2 $
$ 30 = 5 times 4 + 3^2 + 1 $
$ 31 = 5 times (4 + 2) + 1^3 $
$ 32 = 5 times (4+2) + 3 - 1 $
$ 33 = 5 times (4+2) + 3 times 1 $
$ 34 = 5 times (4+2) + 3 + 1 $
$ 35 = 5 times 3 times 2 + 4 + 1 $
$ 36 = 5 times (4+2) times 1 + 3! $
$ 37 = 5 times (4+2) + 3! + 1 $
$ 38 = 4! + 2 times 5 + 3 + 1 $
$ 39 = 2^5 + 4 + 3 times 1 $
$ 40 = 2^5 + 4 + 3 + 1 $
$ 41 = 5 times 2^3 + 1^4 $
$ 42 = 5 times 3^2 + 4 - 1 $
$ 43 = 5 times 2^3 + 4 - 1 $
$ 44 = 5 times 2^3 + 4 times 1 $
$ 45 = 5 times 2^3 + 4 + 1 $
$ 46 = 5 times 4 times 2 times 1 + 3! $
$ 47 = 5 times 3(4 - 1) + 2 $ or $ 5 times 4 times 2 + 1 + 3! $
$ 48 = 4! times 2 times 1^3 $
$ 49 = 4! times 2 + 1^{3+5} $
$ 50 = 4! times 2 + 3 - 1^5 $ or $ 5 times (4+3+2+1) $
$ 51 = 4! times 2 times 1^5 + 3 $
$ 52 = 4! times 2 + 3 + 1^5 $
$ 53 = 4! times 2 + 5 times 1^3 $
$ 54 = 4! times 2 + 5 + 1^3 $
$ 55 = 4! times 2 + 5 + 3 - 1 $
$ 56 = 4! times 2 + 5 + 3 times 1 $
$ 57 = 5 times 4 times 3 - 1 - 2 $ or $ 4! times 2 + 5 + 3 + 1 $
$ 58 = 5 times 4 times 3 - 2 times 1 $
$ 59 = 5 times 4 times 3 - 2 + 1 $
$ 60 = 5 times 4 times 3 times 1^2 $
$ 61 = 5 times 4 times 3 - 1 + 2 $
$ 62 = 5 times 4 times 3 + 2 times 1 $
$ 63 = 5 times 4 times 3 + 1 + 2 $
$ 64 = 2^5 times (4 - 3 + 1) $
$ 65 = 4! times 3 - 5 - 2 times 1 $
$ 66 = 4! times 3 - 5 - 2 + 1 $
$ 67 = 4! times 3 - 5 times 1^2 $
$ 68 = 4! times 3 - 5 - 1 + 2 $
$ 69 = 4! times 3 - 5 + 2 times 1 $
$ 70 = 4! times 3 - 5 + 2 + 1 $
$ 71 = 4! times 3 - 1^{5+2} $
$ 72 = 4! times 3 times 1^{5+2} $
$ 73 = 4! times 3 + 1^{5+2} $
$ 74 = 4! times 3 + 2 times 1^5 $
$ 75 = 4! times 3 times 1 + 5 - 2 $
$ 76 = 4! times 3 + 5 - 2 + 1 $
$ 77 = 4! times 3 + 5 times 1^2 $
$ 78 = 4! times 3 + 5 + 1^2 $
$ 79 = 4! times 3 + 5 + 2 times 1 $
$ 80 = 4! times 3 + 5 + 2 + 1 $
$ 81 = 4! times 3 + 5 times 2 - 1 $
$ 82 = 4! times 3 + 5 times 2 times 1 $
$ 83 = 4! times 3 + 5 times 2 + 1 $
$ 84 = 3^4 + 5 - 2 times 1 $
$ 85 = 3^4 + 5 - 1^2 $
$ 86 = 3^4 + 5 times 1^2 $
$ 87 = 3^4 + 5 + 1^2 $
$ 88 = 3^4 + 5 + 2 times 1 $
$ 89 = 3^4 + 5 + 2 + 1 $
$ 90 = 3^4 + 5 times 2 - 1 $
$ 91 = 3^4 + 5 times 2 times 1 $
$ 92 = 3^4 + 5 times 2 + 1 $
$ 93 = 4! times (3 + 1) - 5 + 2 $
$ 94 = 4! times (5 - 1^3) - 2 $
$ 95 = 4! times (5 + 3)/2 - 1 $
$ 96 = 4! times 1 times (5+3)/2 $
$ 97 = 4! times (5+3)/2 + 1 $
$ 98 = 4! times (5-1^3) + 2 $
$ 99 = 4! times (5-1^2) + 3 $
$ 100 = 5 times 4 times (3+2) times 1 $
$ 101 = 5 times 4 times (3+2) + 1 $
Answered by Maria Deleva on October 29, 2020
I wrote a program in Python 3:
from collections import defaultdict
from functools import lru_cache
from itertools import combinations, chain, product
from operator import add, sub, mul, truediv, pow
import random
@lru_cache(maxsize=None)
def powerset(s):
return chain.from_iterable(combinations(s, r) for r in range(1, len(s)))
operations = [
('+', add),
('-', sub),
('*', mul),
('/', truediv),
('**', pow),
]
def bracket(s):
if len(s) > 1:
return '(' + s + ')'
return s
def sample(s):
return random.sample(s, min(len(s), 5))
@lru_cache(maxsize=None)
def calculate(nums):
if len(nums) == 1:
num = nums[0]
return {num: str(num)}
answer = defaultdict(set)
for left_parts in powerset(nums):
right_parts = tuple(x for x in nums if x not in left_parts)
for (left_num, left_strings), (right_num, right_strings) in product(
calculate(left_parts).items(),
calculate(right_parts).items()):
for op_str, op_func in operations:
orders = [list]
if op_str not in '+*':
orders += [reversed]
for order in orders:
try:
result_num = op_func(*order([left_num, right_num]))
except (ZeroDivisionError, OverflowError):
continue
if isinstance(result_num, complex) or abs(result_num) > 1000:
continue
for left_string, right_string in product(sample(left_strings),
sample(right_strings)):
result_string = '{1} {0} {2}'.format(op_str,
*order([bracket(left_string),
bracket(right_string)]))
assert eval(result_string) == result_num
answer[result_num].add(result_string)
return answer
def main():
answer = calculate((1, 2, 3, 4, 5))
nums = sorted(num for num in answer if int(num) == num and num >= 0)
for i, num in enumerate(nums):
if num != i:
break
print(int(num), '=',
' or '.join(sample(answer[num]))
.replace('**', '^')
.replace('*', '×'))
main()
It uses addition, subtraction, multiplication, division, exponentiation (x to the power of y), and parentheses. It gives up to 5 solutions for each number from 1 up to 177. It could give solutions for many more numbers but you'd start to see gaps, since apparently you can't make 178. Unfortunately it's not smart enough to tell when two solutions are essentially the same, so there's often lots of very similar looking solutions for a particular number, although I tried to mix them up. You can also get more solutions per number, but when I tried with 7 I hit the character limit in my answer.
0 = (2 + 3) - (5 ^ (1 ^ 4)) or (3 ^ 2) - (4 + (5 × 1)) or (((5 + 3) / 4) / 2) - 1 or ((1 + 2) / 3) + (4 - 5) or (3 - (1 + 2)) ^ (4 / 5)
1 = 1 ^ (4 ^ (3 - (2 × 5))) or 1 ^ (4 × (2 × (3 / 5))) or (1 - 2) ^ ((5 ^ 3) × 4) or 1 ^ (5 + (4 + (2 - 3))) or (3 × 1) / (2 - (4 - 5))
2 = (1 + (3 - 2)) ^ (5 - 4) or 2 - (5 ^ ((1 - 4) ^ 3)) or ((1 ^ 5) ^ 3) × (4 - 2) or (3 - 1) / (4 + (2 - 5)) or (3 - 4) - ((2 × 1) - 5)
3 = 3 ^ ((5 - 4) ^ (2 ^ 1)) or (5 - 4) + ((1 + 3) / 2) or 2 × (3 / ((5 - 4) + 1)) or ((1 + 3) + 5) - (2 + 4) or (4 + 3) + ((2 - 5) - 1)
4 = (1 / 2) ^ (5 - (4 + 3)) or (3 / 1) + (2 - (5 - 4)) or (3 - (4 - 5)) / (2 - 1) or (4 + 3) - (2 + (1 ^ 5)) or (2 - (5 - 3)) + (1 × 4)
5 = (4 + 5) - (3 - (1 - 2)) or (3 - (1 + 5)) + (2 × 4) or (5 × 3) / ((4 + 1) - 2) or (5 + 3) - (1 - (2 - 4)) or ((4 / 2) + 3) / (1 ^ 5)
6 = (4 × 3) + (1 - (5 + 2)) or (3 × 4) + (1 - (5 + 2)) or (4 × 3) - ((1 ^ 2) + 5) or (3 / (1 - 4)) + (2 + 5) or (2 - 5) × ((1 ^ 4) - 3)
7 = ((5 + 2) / (3 + 1)) × 4 or (5 + 4) - (2 / (1 ^ 3)) or (5 + (4 - 2)) × (1 ^ 3) or ((5 × 2) / (1 ^ 4)) - 3 or (1 × 5) - (4 - (3 × 2))
8 = 3 + (5 ^ (4 - (2 + 1))) or ((2 × 3) - 4) × (5 - 1) or (1 × 5) + ((2 - 3) + 4) or 2 + ((5 + (4 - 3)) × 1) or ((5 + 1) + 2) × (4 - 3)
9 = (3 ^ 2) - (4 - (5 - 1)) or (4 × 1) - (5 / (2 - 3)) or (5 + 2) - (4 / (1 - 3)) or (1 ^ (3 / 5)) + (4 × 2) or 3 - (((2 - 5) + 1) - 4)
10 = 2 + ((4 × (1 + 5)) / 3) or (5 × (1 ^ 3)) × (4 - 2) or (5 + (3 - 2)) + (4 ^ 1) or (5 - 4) + (3 ^ (2 / 1)) or (3 + 1) / ((4 - 2) / 5)
11 = (4 - (2 - 1)) + (5 + 3) or ((3 × 5) - 4) × (1 ^ 2) or (3 ^ 2) - ((4 - 5) - 1) or (5 + 4) - ((2 - 1) - 3) or (3 + (2 × 4)) ^ (1 ^ 5)
12 = (1 × 2) × (5 + (4 - 3)) or (5 × 4) - ((1 × 2) ^ 3) or ((5 + 1) × 2) × (4 - 3) or ((1 + 5) × (2 ^ 3)) / 4 or (3 × ((5 - 1) ^ 2)) / 4
13 = (3 + ((4 + 2) - 1)) + 5 or (3 + 1) × (2 + (5 / 4)) or (2 + (4 + 3)) - (1 - 5) or (5 + (2 + 3)) + (4 - 1) or ((5 - (1 + 2)) ^ 4) - 3
14 = (5 - (2 - (3 × 4))) - 1 or (2 ^ 4) + ((1 ^ 5) - 3) or (3 - 1) × ((4 + 5) - 2) or ((4 + (3 + 5)) + 2) / 1 or (2 × (4 + 3)) ^ (1 ^ 5)
15 = (3 × 2) + ((4 + 5) ^ 1) or (1 × (5 + 4)) + (3 × 2) or ((4 + 5) × 2) - (3 ^ 1) or 1 - ((5 - (4 ^ 2)) - 3) or (2 ^ 4) + (3 - (5 - 1))
16 = ((5 × 3) + 4) - (1 + 2) or ((4 × 3) + 1) + (5 - 2) or (3 + 5) / (2 × (1 / 4)) or (5 + (4 × 2)) + (1 × 3) or (4 + (5 - 1)) + (2 ^ 3)
17 = 1 - (((3 - 5) × 4) × 2) or (3 ^ 4) - (2 ^ (5 + 1)) or (5 × 3) - ((2 - 4) / 1) or 2 - (5 × ((1 ^ 3) - 4)) or ((2 + 5) × 3) - (4 / 1)
18 = (4 × 3) × ((5 / 2) - 1) or ((5 × 3) + 1) + (4 - 2) or (5 × 4) - ((1 + 3) - 2) or (5 × 3) + (1 - (2 - 4)) or (2 + 4) + ((5 - 1) × 3)
19 = ((5 ^ (3 - 1)) - 2) - 4 or (2 × 5) - (3 × (1 - 4)) or (2 - 3) + ((1 × 5) × 4) or ((4 × 3) + 2) + (5 ^ 1) or (4 / (2 - 1)) + (5 × 3)
20 = (1 + 5) × (2 + (4 / 3)) or ((5 × 4) + 3) - (2 + 1) or (4 × 2) / (1 - (3 / 5)) or (2 ^ 4) / ((3 + 1) / 5) or (3 - 1) + (2 × (5 + 4))
21 = 3 - ((2 / 1) - (4 × 5)) or ((5 × 1) - 2) × (4 + 3) or (3 ^ 1) × (5 - (2 - 4)) or (5 × 4) - ((1 ^ 3) - 2) or ((5 × 4) + 3) - (1 × 2)
22 = ((5 × (2 + 1)) + 3) + 4 or (2 + 5) + (3 × (4 + 1)) or ((5 × 3) - (4 / 1)) × 2 or (3 + (5 + (4 - 1))) × 2 or ((3 × 1) × 4) + (2 × 5)
23 = (4 ^ 2) + (3 + (5 - 1)) or ((2 × 4) + (5 × 3)) / 1 or (2 × 5) + ((4 × 3) + 1) or (3 - 1) - (4 - (5 ^ 2)) or 1 - (3 - (5 ^ (4 / 2)))
24 = ((2 ^ 4) + (3 × 1)) + 5 or (2 ^ 1) × ((5 + 4) + 3) or (5 ^ 2) - (4 - (3 ^ 1)) or (3 × 1) + ((4 ^ 2) + 5) or ((2 × 4) × 3) / (1 ^ 5)
25 = ((2 + 3) × 5) × (1 ^ 4) or (3 + (5 × 4)) + (2 × 1) or ((3 × (2 ^ 5)) / 4) + 1 or ((2 × 5) ^ (3 - 1)) / 4 or 5 + ((3 + (2 ^ 4)) + 1)
26 = (1 × 4) + ((5 ^ 2) - 3) or (4 + 1) + (3 × (5 + 2)) or (2 × 3) + (4 × (5 × 1)) or (3 ^ (1 + 2)) + (4 - 5) or ((2 × 3) × (5 / 1)) - 4
27 = 1 / (3 ^ ((4 - 5) - 2)) or (3 × 1) ^ ((4 × 2) - 5) or (2 × (3 ^ 4)) / (5 + 1) or ((5 - 2) ^ 4) / (3 ^ 1) or (2 - (4 - 5)) ^ (1 × 3)
28 = (4 × (5 + 2)) × (1 ^ 3) or (5 + 2) × ((1 ^ 3) × 4) or ((4 × 5) ^ 1) + (2 ^ 3) or (5 × (3 + 2)) - (1 - 4) or (4 + (5 ^ 2)) - (1 ^ 3)
29 = (2 + 3) + (4 × (1 + 5)) or (2 × (4 × 3)) + (1 × 5) or ((4 / 2) ^ 5) - (3 ^ 1) or (1 × 5) + ((2 × 3) × 4) or (1 ^ 4) + (3 + (5 ^ 2))
30 = ((1 + 4) × (3 + 2)) + 5 or (4 × 3) × ((5 ^ 1) / 2) or ((4 / 2) + 3) × (1 + 5) or ((5 + 2) + 3) × (4 - 1) or (1 - ((2 - 4) ^ 5)) - 3
31 = (2 × 3) + ((1 + 4) × 5) or (4 ^ (5 / 2)) - (1 ^ 3) or 1 × (4 - ((2 - 5) ^ 3)) or ((4 × (2 + 1)) × 3) - 5 or ((4 + 1) × 5) + (3 × 2)
32 = (4 × (5 + 3)) ^ (2 - 1) or (2 ^ 5) × (4 - (3 / 1)) or (2 × 4) × (3 + (1 ^ 5)) or (2 / 1) × ((3 - 5) ^ 4) or 2 / (1 × (4 ^ (3 - 5)))
33 = 1 - ((2 / (3 - 4)) ^ 5) or (4 / 1) + ((2 ^ 5) - 3) or (2 ^ 5) - (3 - (1 × 4)) or (4 + (5 + 2)) × (3 × 1) or ((2 ^ 5) - (3 - 4)) / 1
34 = (3 - 1) - ((2 - 4) ^ 5) or ((1 - 3) + 4) + (2 ^ 5) or ((4 / 2) ^ 5) + (3 - 1) or ((4 + 1) × 5) + (3 ^ 2) or 2 - (((3 - 4) - 1) ^ 5)
35 = (2 × ((3 × 4) + 5)) + 1 or (1 × 3) - ((2 - 4) ^ 5) or 5 / ((1 ^ 2) / (4 + 3)) or (1 + ((4 ^ 3) + 5)) / 2 or ((4 / 2) ^ 5) + (1 × 3)
36 = 4 × ((3 + 5) + (1 ^ 2)) or (5 × 4) + ((3 + 1) ^ 2) or ((5 + 4) + 3) × (2 + 1) or (4 + 2) × ((1 ^ 3) + 5) or (3 × (5 - 2)) × (1 × 4)
37 = ((3 + 1) × (2 × 4)) + 5 or ((5 × 2) × 4) - (3 × 1) or ((2 × 5) × 4) - (3 ^ 1) or (((2 × 5) ^ 1) × 4) - 3 or (5 / (1 / (4 + 3))) + 2
38 = (3 × (5 + (4 × 2))) - 1 or (2 ^ 1) × (4 + (5 × 3)) or (2 / 1) × (4 + (3 × 5)) or ((4 + (3 × 5)) × 2) × 1 or ((3 - 1) ^ 5) + (2 + 4)
39 = (1 + (3 × 4)) × (5 - 2) or (5 × (2 × 4)) - (1 ^ 3) or 3 / (1 / (5 + (2 × 4))) or (((2 ^ 5) + 3) + 4) ^ 1 or 1 - ((5 - (3 ^ 4)) / 2)
40 = (2 / ((1 ^ 3) / 4)) × 5 or ((5 / 1) + (2 + 3)) × 4 or 5 / ((2 / (4 × 1)) ^ 3) or (3 + 2) × ((4 - 1) + 5) or ((3 + 5) + 2) × (1 × 4)
41 = ((5 ^ 3) - 2) / (4 - 1) or 1 × (((3 ^ 2) × 4) + 5) or (4 × (3 ^ 2)) + (5 ^ 1) or (1 ^ 3) + (5 × (4 × 2)) or (2 × ((4 × 5) - 1)) + 3
42 = (3 × ((5 × 2) + 4)) × 1 or (2 + 4) × (5 - (1 - 3)) or 2 × ((5 ^ (3 - 1)) - 4) or (2 + 5) × ((4 + 3) - 1) or 1 + ((4 × (3 ^ 2)) + 5)
43 = (((2 ^ 4) × 3) / 1) - 5 or (3 + ((5 × 2) × 4)) ^ 1 or ((3 × (4 ^ 2)) - 5) × 1 or 1 / (2 / (5 + (3 ^ 4))) or (3 × 1) + ((5 × 2) × 4)
44 = (2 ^ 5) + (3 × (4 / 1)) or (4 ^ 1) × (5 + (2 × 3)) or (3 + ((5 × 4) × 2)) + 1 or 4 / (1 / (5 + (2 × 3))) or (2 ^ 5) + ((3 / 1) × 4)
45 = (4 + 5) × ((2 / 1) + 3) or (4 + 5) / (1 / (2 + 3)) or (3 × 4) + (1 + (2 ^ 5)) or (1 + (4 - 2)) × (5 × 3) or (3 + 2) × (4 + (1 × 5))
46 = (2 / 1) × (3 + (4 × 5)) or (3 × (1 + (4 ^ 2))) - 5 or ((2 + 3) × (5 + 4)) + 1 or (2 × (3 + (4 × 5))) × 1 or (2 / 1) × (3 + (5 × 4))
47 = (5 × 4) + (3 ^ (2 + 1)) or 3 + ((1 + (2 × 5)) × 4) or 2 + (((4 - 1) × 3) × 5) or (2 × ((5 × 4) + 3)) + 1 or ((1 + 4) × 3) + (2 ^ 5)
48 = (3 + 1) × (4 × (5 - 2)) or ((2 + 4) × (3 + 5)) × 1 or ((5 + 4) - 1) × (2 × 3) or ((5 - 3) ^ 4) × (1 + 2) or (4 + 2) × ((3 + 5) ^ 1)
49 = ((2 + 5) × 1) × (3 + 4) or ((5 - (3 × 4)) ^ 2) / 1 or (5 - (4 × 3)) ^ (2 / 1) or (3 + 4) ^ (2 × (1 ^ 5)) or (1 - (5 + 3)) ^ (4 - 2)
50 = 5 × ((4 + (1 + 3)) + 2) or ((3 - (1 / 2)) × 5) × 4 or ((4 × 3) - 2) / (1 / 5) or ((4 + 1) ^ 3) × (2 / 5) or (5 × 1) × (4 + (2 × 3))
51 = ((4 ^ 2) + (1 ^ 5)) × 3 or (2 + 1) × ((4 × 3) + 5) or ((3 × 4) + 5) × (1 + 2) or 3 + (4 × ((5 + 1) × 2)) or (5 × (4 + (3 × 2))) + 1
52 = (5 - 1) + (3 × (4 ^ 2)) or (4 × 1) × (3 + (2 × 5)) or (5 + ((2 ^ 4) × 3)) - 1 or (5 + (4 × 2)) × (1 + 3) or (3 ^ (4 - 1)) + (5 ^ 2)
53 = 1 + (4 × (3 + (5 × 2))) or (5 + ((2 ^ 4) × 3)) ^ 1 or (4 × (3 + (5 × 2))) + 1 or 5 + (1 × ((4 ^ 2) × 3)) or (5 / 1) + ((4 ^ 2) × 3)
54 = (5 + 1) + (3 × (2 ^ 4)) or (3 × 1) × ((5 + 4) × 2) or (1 + 5) × ((3 + 2) + 4) or (3 × (5 - (1 / 2))) × 4 or ((4 + 5) / 1) × (2 × 3)
55 = (4 + 1) × ((3 × 2) + 5) or (1 × 5) × (3 + (4 × 2)) or (5 × (3 + (2 × 4))) / 1 or ((4 ^ 3) + 1) - (2 × 5) or ((3 × 2) + 5) × (1 + 4)
56 = (3 ^ 4) - (5 ^ (2 / 1)) or ((3 ^ 1) ^ 4) - (5 ^ 2) or (2 × (3 + 4)) × (5 - 1) or (2 + 5) × ((1 + 4) + 3) or (3 + 5) × ((2 + 4) + 1)
57 = ((4 ^ 3) - (5 + 2)) ^ 1 or ((2 ^ (1 + 5)) - 4) - 3 or ((5 × (2 + 1)) × 4) - 3 or (4 ^ (1 × 3)) - (2 + 5) or (((4 × 5) - 2) + 1) × 3
58 = 4 + ((3 ^ 2) × (5 + 1)) or ((5 + 1) × (3 ^ 2)) + 4 or (1 + ((4 ^ 3) - 5)) - 2 or (((3 × 5) - 1) × 4) + 2 or (3 × (5 × 4)) - (2 × 1)
59 = (((3 + 5) ^ 2) - 1) - 4 or (4 ^ 3) - (5 ^ (2 - 1)) or (4 ^ 3) - (5 / (1 ^ 2)) or ((5 × (4 × 3)) - 2) + 1 or (1 ^ 2) × ((4 ^ 3) - 5)
60 = (5 × (3 ^ (1 ^ 2))) × 4 or (5 ^ 1) × ((2 ^ 3) + 4) or (3 × (4 × 5)) × (1 ^ 2) or ((1 ^ 2) × 4) × (3 × 5) or ((4 ^ 3) - 1) - (5 - 2)
61 = ((2 - 5) / 1) + (4 ^ 3) or (4 ^ (5 - 2)) - (3 ^ 1) or (4 ^ (3 × 1)) + (2 - 5) or (2 / 1) - (5 - (4 ^ 3)) or (1 × 2) + ((4 ^ 3) - 5)
62 = ((4 ^ (1 ^ 5)) ^ 3) - 2 or 1 + ((4 ^ 3) + (2 - 5)) or 1 - ((5 - (4 ^ 3)) - 2) or 1 × (2 + ((5 × 4) × 3)) or ((4 ^ (2 + 1)) - 5) + 3
63 = (3 × 1) × ((5 ^ 2) - 4) or 3 - (4 - (2 ^ (5 + 1))) or (3 × (5 + (2 ^ 4))) / 1 or (5 × (4 × 3)) + (1 + 2) or (3 × (5 × 4)) + (2 + 1)
64 = (2 ^ (4 + 1)) × (5 - 3) or (2 × 4) / (1 / (5 + 3)) or (3 + (1 ^ 5)) × (4 ^ 2) or (1 ^ 3) × (4 ^ (5 - 2)) or (4 × 2) ^ ((5 - 3) / 1)
65 = ((3 ^ 2) + 4) × (5 ^ 1) or (5 ^ 1) × ((2 ^ 4) - 3) or ((5 × 2) + 3) × (4 + 1) or 4 + ((2 ^ (1 + 5)) - 3) or (3 × (2 + (4 × 5))) - 1
66 = 4 × ((5 + (1 / 2)) × 3) or 4 - (2 + ((1 - 5) ^ 3)) or 2 × ((4 × (5 + 3)) + 1) or ((4 / (1 ^ 5)) ^ 3) + 2 or (4 / 2) + ((5 - 1) ^ 3)
67 = ((4 ^ 3) + 5) - (1 × 2) or ((1 ^ 5) + (4 ^ 3)) + 2 or 1 + ((2 + (5 × 4)) × 3) or (5 - 2) + (4 ^ (3 ^ 1)) or (4 ^ 3) + ((5 - 2) / 1)
68 = 5 + ((4 ^ 3) - (1 ^ 2)) or 1 - ((2 - 5) - (4 ^ 3)) or ((5 × 3) + 2) × (4 ^ 1) or ((3 × 5) + 2) × (4 × 1) or ((3 × 5) + 2) × (4 / 1)
69 = (4 ^ 3) - (5 × (1 - 2)) or 1 + (((5 × 3) + 2) × 4) or (1 + 2) × ((4 × 5) + 3) or ((4 ^ 3) + 5) × (1 ^ 2) or (((4 + 3) × 5) × 2) - 1
70 = (2 / 1) × ((3 + 4) × 5) or ((3 ^ 4) - (5 × 2)) - 1 or (5 × ((3 + 4) × 2)) ^ 1 or 5 × ((2 / 1) + (4 × 3)) or (4 + 3) × (1 × (2 × 5))
71 = (5 + (4 ^ 3)) + (2 × 1) or (3 ^ 4) - (5 / (1 / 2)) or (3 ^ 4) - (5 × (2 / 1)) or (3 ^ 4) - (2 / (1 / 5)) or (3 ^ (4 / 1)) - (2 × 5)
72 = (5 + (2 - 1)) × (3 × 4) or (4 + (2 ^ 3)) × (1 + 5) or (2 ^ 3) × (4 + (1 × 5)) or (2 + 5) + ((4 ^ 3) + 1) or (3 × (5 ^ 2)) + (1 - 4)
73 = ((3 ^ 4) - 1) - (2 + 5) or ((3 ^ 4) - (1 + 2)) - 5 or ((3 × 5) × (4 + 1)) - 2 or ((3 ^ 4) - (2 + 1)) - 5 or ((5 + 4) × (2 ^ 3)) + 1
74 = ((5 × 2) + (4 ^ 3)) ^ 1 or (((3 ^ 4) - 5) - 2) ^ 1 or (5 × 2) + ((4 ^ 1) ^ 3) or 1 × ((5 × 2) + (4 ^ 3)) or (3 ^ (4 ^ 1)) - (5 + 2)
75 = 3 × ((1 × 5) ^ (4 - 2)) or (1 + ((3 ^ 4) - 2)) - 5 or ((4 - 1) + 2) × (5 × 3) or (5 × (4 - 1)) × (3 + 2) or (1 + (3 ^ 4)) - (5 + 2)
76 = ((2 ^ 4) + 3) × (5 - 1) or (3 / (5 ^ (2 - 4))) + 1 or ((5 × (2 ^ 4)) - 1) - 3 or ((2 ^ 4) × 5) - (3 + 1) or (3 × (5 ^ 2)) + (1 ^ 4)
77 = (5 × (4 ^ 2)) - (3 / 1) or (((2 ^ 4) × 5) × 1) - 3 or ((3 ^ 4) - 1) + (2 - 5) or ((4 ^ 2) / (1 / 5)) - 3 or ((5 × 2) + 1) × (3 + 4)
78 = 3 × ((5 ^ (4 - 2)) + 1) or (4 × (5 × (3 + 1))) - 2 or (((5 + 4) ^ 2) - 3) ^ 1 or ((5 × (4 ^ 2)) - 3) + 1 or (((2 - 5) ^ 1) ^ 4) - 3
79 = (2 + (1 - 5)) + (3 ^ 4) or (1 + ((5 + 4) ^ 2)) - 3 or (3 ^ 4) - ((1 ^ 5) × 2) or ((3 ^ 4) - 2) ^ (1 ^ 5) or ((1 + 2) ^ 4) - (5 - 3)
80 = (5 × (2 × (3 - 1))) × 4 or ((2 - (1 - 3)) × 5) × 4 or (2 ^ 3) × ((4 + 1) + 5) or (3 ^ 4) - (1 ^ (2 ^ 5)) or (((4 + 1) ^ 2) × 3) + 5
81 = (4 + 5) ^ ((3 - 2) + 1) or ((4 ^ 2) × 5) + (1 ^ 3) or ((3 + 1) + 5) ^ (4 / 2) or ((1 + (4 / 2)) ^ 5) / 3 or ((2 ^ 3) + 1) × (4 + 5)
82 = (5 × (1 + (4 ^ 2))) - 3 or (5 × ((3 - 1) ^ 4)) + 2 or (3 × ((5 ^ 2) + 1)) + 4 or (1 ^ 3) + ((2 - 5) ^ 4) or (((2 ^ 4) + 1) × 5) - 3
83 = 5 + ((3 ^ 4) - (2 + 1)) or (3 + (5 × (4 ^ 2))) ^ 1 or ((3 ^ 4) + (5 - 1)) - 2 or (5 + (3 ^ 4)) - (1 + 2) or (3 + ((4 ^ 2) × 5)) × 1
84 = ((4 × (5 + 2)) ^ 1) × 3 or (4 × (5 + 2)) × (3 / 1) or (4 ^ 1) × (3 × (5 + 2)) or (5 + 2) / ((1 / 3) / 4) or 1 + (3 + (5 × (2 ^ 4)))
85 = (3 + 1) + ((5 + 4) ^ 2) or ((5 - 2) ^ 4) + (1 + 3) or (1 + ((3 ^ 4) - 2)) + 5 or (3 + ((5 + 4) ^ 2)) + 1 or ((5 - 2) ^ 4) + (3 + 1)
86 = (3 ^ 4) - (5 / (1 - 2)) or (((5 ^ 2) + 4) × 3) - 1 or (((5 - 1) ^ 4) + 2) / 3 or 5 - ((1 - 2) × (3 ^ 4)) or (((1 - 5) ^ 4) + 2) / 3
87 = 2 - ((1 - (3 ^ 4)) - 5) or 2 + (5 + ((3 ^ 4) - 1)) or 2 - ((1 - 5) - (3 ^ 4)) or ((3 ^ 4) + 2) - (1 - 5) or (3 ^ 4) + (5 + (1 ^ 2))
88 = ((5 ^ 2) - 3) × (4 ^ 1) or (2 + (5 + (3 ^ 4))) ^ 1 or (2 + (3 ^ 4)) + (1 × 5) or ((1 + (2 ^ 4)) × 5) + 3 or ((5 + (3 ^ 4)) + 2) × 1
89 = (2 + (3 ^ 4)) + (1 + 5) or (3 ^ (5 - 1)) + (4 × 2) or (4 ^ (3 ^ 1)) + (5 ^ 2) or 1 - ((3 - (5 ^ 2)) × 4) or (((1 + 2) ^ 4) + 5) + 3
90 = (1 + (3 ^ 2)) × (4 + 5) or ((4 + 2) × 1) × (5 × 3) or 2 × (3 × ((4 - 1) × 5)) or ((4 + 2) × 5) × (3 / 1) or (3 × (4 + 2)) × (5 / 1)
91 = 1 + ((3 × 5) × (4 + 2)) or ((3 × (2 ^ 5)) - 1) - 4 or (3 ^ (1 × 4)) + (5 × 2) or (((2 ^ 5) × 3) - 4) - 1 or (5 × 2) + (3 ^ (4 × 1))
92 = (1 + (3 ^ 4)) + (5 × 2) or (3 ^ 4) + (1 + (2 × 5)) or (((5 ^ 2) + 1) - 3) × 4 or (((5 ^ 2) - 3) + 1) × 4 or 1 × ((3 × (2 ^ 5)) - 4)
93 = (((4 - 2) ^ 5) - 1) × 3 or (1 + (5 × (4 + 2))) × 3 or ((1 + 5) × 2) + (3 ^ 4) or 3 × (1 + (5 × (2 + 4))) or (((4 / 2) ^ 5) - 1) × 3
94 = (5 × ((2 ^ 4) + 3)) - 1 or (5 × (3 + (4 ^ 2))) - 1 or (((4 ^ 2) + 3) × 5) - 1 or (5 × ((4 ^ 2) + 3)) - 1 or (((2 ^ 4) + 3) × 5) - 1
95 = ((4 × 5) - 1) × (3 + 2) or ((2 ^ 5) + (4 ^ 3)) - 1 or ((2 ^ 4) + 3) × (5 / 1) or ((3 + (4 ^ 2)) × 5) ^ 1 or (1 × 5) × ((4 ^ 2) + 3)
96 = (5 - 1) × (3 × (2 × 4)) or (2 ^ 5) × ((1 ^ 4) × 3) or ((2 + 1) + 5) × (3 × 4) or ((5 × 3) + 1) × (2 + 4) or ((4 × 2) × 3) × (5 - 1)
97 = (((5 ^ 2) × 4) - 3) × 1 or ((5 ^ 2) × 4) - (3 × 1) or (2 ^ 4) + (3 ^ (5 - 1)) or ((5 ^ 2) × (4 / 1)) - 3 or ((5 ^ 2) × 4) - (3 ^ 1)
98 = (4 × (5 ^ 2)) + (1 - 3) or ((4 × (5 ^ 2)) - 3) + 1 or 1 - (3 - ((5 ^ 2) × 4)) or (4 × (5 ^ 2)) - (3 - 1) or (((5 ^ 2) × 4) + 1) - 3
99 = ((2 ^ 4) × (5 + 1)) + 3 or ((1 + 5) × (2 ^ 4)) + 3 or (4 + ((2 ^ 5) × 3)) - 1 or 3 × ((1 ^ 4) + (2 ^ 5)) or ((3 + 2) × (5 × 4)) - 1
100 = (((2 + 3) × 5) × 4) ^ 1 or ((5 × 4) ^ 2) / (3 + 1) or (2 + 3) × (5 / (1 / 4)) or ((3 + 2) × 4) × (1 × 5) or (4 / 1) × (5 × (2 + 3))
101 = ((5 ^ 2) × 4) + (1 ^ 3) or (1 + 4) + (3 × (2 ^ 5)) or (((5 ^ 2) + 1) × 4) - 3 or 1 + (((2 ^ 5) × 3) + 4) or ((2 ^ 5) × 3) + (1 + 4)
102 = (3 + ((5 ^ 2) × 4)) - 1 or 3 + (((5 ^ 2) × 4) - 1) or 2 + (4 × (5 ^ (3 - 1))) or 3 - (1 - ((5 ^ 2) × 4)) or (3 - 1) + (4 × (5 ^ 2))
103 = ((5 ^ 2) × 4) + (3 / 1) or (((5 ^ 2) × 4) / 1) + 3 or 3 + (4 × ((5 ^ 2) × 1)) or (1 × 3) + (4 × (5 ^ 2)) or (4 × (5 ^ 2)) + (3 / 1)
104 = 1 + (3 + ((5 ^ 2) × 4)) or (3 + (1 / 4)) × (2 ^ 5) or (((2 + 3) × 5) + 1) × 4 or (((3 - 1) × 5) ^ 2) + 4 or ((4 × (5 ^ 2)) + 3) + 1
105 = (4 + 3) × ((1 + 2) × 5) or (5 ^ 2) - (1 - (3 ^ 4)) or (5 + 2) × ((1 + 4) × 3) or (3 × (5 + 2)) × (4 + 1) or (1 + 4) × ((2 + 5) × 3)
106 = ((3 × 1) ^ 4) + (5 ^ 2) or (3 ^ 4) + ((5 / 1) ^ 2) or (5 ^ 2) + (3 ^ (4 / 1)) or ((5 ^ 2) / 1) + (3 ^ 4) or ((3 ^ 4) + (5 ^ 2)) / 1
107 = (((2 ^ 5) + 4) × 3) - 1 or 3 + ((1 + (5 ^ 2)) × 4) or (((5 ^ 2) + 1) × 4) + 3 or (3 ^ 4) + ((5 ^ 2) + 1) or 1 + ((5 ^ 2) + (3 ^ 4))
108 = (4 + 2) × (3 × (5 + 1)) or ((5 - 2) ^ 3) × (4 × 1) or (3 × 4) × ((5 × 2) - 1) or ((5 + 1) × 3) × (4 + 2) or 2 × (((5 + 1) ^ 3) / 4)
109 = (5 ^ 3) - (4 ^ (2 ^ 1)) or ((5 ^ 3) - (4 ^ 2)) ^ 1 or 1 + (4 × (3 ^ (5 - 2))) or ((1 × 5) ^ 3) - (2 ^ 4) or (5 ^ 3) - ((2 ^ 4) / 1)
110 = 5 × (((4 + 1) ^ 2) - 3) or (2 × 5) × ((3 × 4) - 1) or (((4 + 1) ^ 2) - 3) × 5 or (5 ^ 3) + (1 - (2 ^ 4)) or (((3 × 4) - 1) × 5) × 2
111 = ((3 + (5 ^ 2)) × 4) - 1 or (4 + (1 + (2 ^ 5))) × 3 or ((4 + 1) + (2 ^ 5)) × 3 or 3 × (((2 ^ 5) + 4) + 1) or 3 × (((2 ^ 5) + 1) + 4)
112 = (3 + (5 ^ 2)) × (4 ^ 1) or (4 × (3 + (5 ^ 2))) ^ 1 or (3 ^ 4) + ((2 ^ 5) - 1) or 2 × (4 × ((3 × 5) - 1)) or (4 × (2 + 5)) × (1 + 3)
113 = (4 × ((2 + 1) ^ 3)) + 5 or ((3 ^ 4) / 1) + (2 ^ 5) or ((1 × 2) ^ 5) + (3 ^ 4) or ((2 ^ 5) + (3 ^ 4)) ^ 1 or ((2 ^ 5) × 1) + (3 ^ 4)
114 = ((4 ^ 2) + 3) × (5 + 1) or (2 ^ 5) + (1 + (3 ^ 4)) or (1 + (2 ^ 5)) + (3 ^ 4) or (3 + (2 ^ 4)) × (1 + 5) or 1 + ((3 ^ 4) + (2 ^ 5))
115 = 5 × (((1 + 2) ^ 3) - 4) or 5 × ((2 × (3 × 4)) - 1) or (4 × ((2 ^ 5) - 3)) - 1 or (((3 × 2) × 4) - 1) × 5 or 5 × (((2 × 4) × 3) - 1)
116 = (3 + ((5 ^ 2) + 1)) × 4 or 4 × (1 × ((2 ^ 5) - 3)) or (4 × 1) × ((2 ^ 5) - 3) or (((3 × 4) - 1) ^ 2) - 5 or 2 × ((4 ^ 3) - (1 + 5))
117 = ((5 ^ 3) ^ 1) - (2 × 4) or ((1 × 5) ^ 3) - (2 × 4) or (5 ^ 3) - (4 × (2 × 1)) or 1 × ((5 ^ 3) - (4 × 2)) or ((5 ^ 3) × 1) - (2 × 4)
118 = (((3 ^ 5) + 1) / 2) - 4 or ((5 ^ 3) - (2 + 4)) - 1 or 1 + ((5 ^ 3) - (2 × 4)) or ((5 ^ 3) - (4 + 2)) - 1 or (((5 ^ 3) - 4) - 2) - 1
119 = (5 ^ (4 - 1)) - (2 × 3) or ((5 ^ 3) - (4 + 2)) / 1 or ((5 ^ 3) - (4 × 1)) - 2 or ((5 ^ 3) - (4 / 1)) - 2 or ((5 ^ 3) - 2) - (1 × 4)
120 = ((2 + (4 - 1)) ^ 3) - 5 or 2 / (((1 / 3) / 5) / 4) or (1 × 4) × (2 × (5 × 3)) or (1 × (4 × 5)) × (3 × 2) or (2 × 3) × ((4 ^ 1) × 5)
121 = (4 × (1 - 2)) + (5 ^ 3) or (4 - (3 × 5)) ^ (2 / 1) or ((5 × 3) - 4) ^ (2 ^ 1) or (5 - (2 ^ 4)) ^ (3 - 1) or ((2 + 4) + 5) ^ (3 - 1)
122 = (2 × (4 ^ 3)) - (1 + 5) or ((5 ^ 3) + 2) - (4 + 1) or (2 × ((3 ^ 5) + 1)) / 4 or ((3 ^ 5) + 1) / (4 - 2) or ((5 ^ 3) - (4 + 1)) + 2
123 = ((2 ^ (3 + 4)) - 5) ^ 1 or 1 × (((5 ^ 3) + 2) - 4) or ((5 ^ 3) - 4) + (2 ^ 1) or (((5 ^ 3) + 2) × 1) - 4 or (2 / 1) - (4 - (5 ^ 3))
124 = (2 + 1) + ((5 ^ 3) - 4) or (2 + (5 ^ 3)) + (1 - 4) or 3 + ((5 ^ (2 + 1)) - 4) or 2 + ((5 ^ 3) + (1 - 4)) or ((5 ^ 3) + 2) - (4 - 1)
125 = (5 × (3 + 2)) × (1 + 4) or ((5 ^ 4) / 1) / (3 + 2) or ((3 + 2) ^ 4) / (5 × 1) or (5 ^ 1) ^ (4 + (2 - 3)) or (5 / (3 - 2)) ^ (4 - 1)
126 = (5 ^ (2 + 1)) + (4 - 3) or 2 × ((4 ^ 3) - (1 ^ 5)) or 4 - ((2 - (5 ^ 3)) + 1) or 4 + ((5 ^ (1 + 2)) - 3) or (3 × ((4 × 5) + 1)) × 2
127 = (4 / 2) + (1 × (5 ^ 3)) or (4 - (2 - (5 ^ 3))) ^ 1 or (4 + ((5 ^ 3) - 2)) ^ 1 or ((5 × 1) ^ 3) + (4 / 2) or (5 ^ 3) + ((4 / 2) ^ 1)
128 = ((4 ^ 3) × 2) / (1 ^ 5) or (2 ^ (4 + 3)) × (1 ^ 5) or ((3 + 5) × (2 ^ 4)) ^ 1 or 1 + ((5 ^ 3) - (2 - 4)) or (3 - 1) ^ (5 + (4 - 2))
129 = (1 ^ 5) + (2 × (4 ^ 3)) or ((2 - 1) × (5 ^ 3)) + 4 or ((1 + (2 ^ 5)) × 4) - 3 or 1 + (2 ^ ((4 × 3) - 5)) or (2 ^ ((4 × 3) - 5)) + 1
130 = (3 + (5 ^ (4 - 1))) + 2 or (5 × (1 + (3 × 4))) × 2 or (5 ^ 3) + ((4 + 2) - 1) or 5 × (2 × ((3 × 4) + 1)) or (((2 ^ 5) × 4) - 1) + 3
131 = (4 × (2 ^ 5)) + (1 × 3) or ((4 + (5 ^ 3)) + 2) ^ 1 or (1 × 3) + ((2 ^ 5) × 4) or 5 - ((1 - (4 ^ 3)) × 2) or (1 × (5 ^ 3)) + (2 + 4)
132 = (2 ^ (4 + 3)) + (5 - 1) or 5 + (2 + ((1 + 4) ^ 3)) or 2 + (1 + (4 + (5 ^ 3))) or ((5 ^ 3) + 4) + (1 + 2) or (((5 × 2) + 1) × 3) × 4
133 = ((5 ^ 3) + (4 × 2)) ^ 1 or (5 ^ 1) + ((4 ^ 3) × 2) or (((4 ^ 3) × 2) + 5) / 1 or ((2 ^ (4 + 3)) + 5) / 1 or (5 + ((4 ^ 3) × 2)) × 1
134 = ((2 ^ (4 + 3)) + 1) + 5 or (5 ^ 3) + ((4 × 2) + 1) or (2 ^ (3 + 4)) + (1 + 5) or ((4 ^ 3) × 2) + (1 + 5) or (5 + ((4 ^ 3) × 2)) + 1
135 = ((2 + 1) ^ 4) × (5 / 3) or 5 × (((2 + 1) ^ 4) / 3) or 5 / (3 / ((2 + 1) ^ 4)) or 3 × (5 × (1 + (2 × 4))) or ((2 × 4) + 1) × (5 × 3)
136 = (1 + (4 ^ 2)) × (5 + 3) or 2 × (((5 - 1) ^ 3) + 4) or 4 × (3 + ((2 ^ 5) - 1)) or (1 + (4 ^ 2)) × (3 + 5) or 2 × ((5 + (4 ^ 3)) - 1)
137 = (5 × (3 ^ (4 - 1))) + 2 or ((3 ^ (4 - 1)) × 5) + 2 or (4 × (2 + 1)) + (5 ^ 3) or 2 - (5 × ((1 - 4) ^ 3)) or (3 × 4) + (5 ^ (2 + 1))
138 = (2 × (5 + (4 ^ 3))) × 1 or (((4 ^ 3) + 5) × 2) × 1 or (1 × 2) × ((4 ^ 3) + 5) or (2 × ((4 ^ 3) + 5)) × 1 or 2 × (5 + ((4 / 1) ^ 3))
139 = ((5 + (4 ^ 3)) × 2) + 1 or ((4 × 3) ^ 2) - (5 / 1) or 1 × (((3 × 4) ^ 2) - 5) or (((2 ^ 5) + 3) × 4) - 1 or 4 + ((3 ^ (1 + 2)) × 5)
140 = (5 ^ 3) - (1 - (2 ^ 4)) or ((5 ^ 3) - 1) + (4 ^ 2) or (5 × 4) × (1 + (3 × 2)) or (((2 ^ 5) + 3) × 4) ^ 1 or 5 × (((3 × 2) + 1) × 4)
141 = ((3 + (2 ^ 5)) × 4) + 1 or ((2 ^ 4) + (5 ^ 3)) / 1 or (5 ^ 3) + ((1 × 2) ^ 4) or (2 ^ 4) + (5 ^ (3 / 1)) or (5 ^ 3) + (4 ^ (2 ^ 1))
142 = ((4 ^ 2) + 1) + (5 ^ 3) or (4 ^ 2) + (1 + (5 ^ 3)) or (1 + (4 ^ 2)) + (5 ^ 3) or (2 ^ 4) + (1 + (5 ^ 3)) or ((5 ^ 3) + (2 ^ 4)) + 1
143 = (((4 + 3) + 5) ^ 2) - 1 or ((4 + (5 + 3)) ^ 2) - 1 or ((4 + (3 + 5)) ^ 2) - 1 or ((5 + (4 + 3)) ^ 2) - 1 or (((3 + 5) + 4) ^ 2) - 1
144 = (((3 + 5) + 4) ^ 2) × 1 or (3 × ((5 + 1) × 4)) × 2 or (5 + (4 + 3)) ^ (2 ^ 1) or (2 ^ (3 + 1)) × (4 + 5) or (1 + 5) × ((2 × 4) × 3)
145 = 1 + ((5 + (4 + 3)) ^ 2) or (1 ^ 5) + ((3 × 4) ^ 2) or (4 + 1) × ((2 ^ 5) - 3) or (1 ^ 5) + ((4 × 3) ^ 2) or 1 + ((3 + (5 + 4)) ^ 2)
146 = ((3 ^ (2 + 4)) + 1) / 5 or (1 + (3 ^ (2 + 4))) / 5 or (1 + (3 ^ (4 + 2))) / 5 or ((3 ^ (4 + 2)) + 1) / 5
147 = (((4 × 5) + 1) ^ 2) / 3 or 3 + (4 × ((5 + 1) ^ 2)) or 3 + (((1 + 5) ^ 2) × 4) or (((1 + 5) ^ 2) × 4) + 3 or (((5 + 1) ^ 2) × 4) + 3
148 = ((3 × (1 - 5)) ^ 2) + 4 or 5 + (((3 × 4) ^ 2) - 1) or (((1 - 5) × 3) ^ 2) + 4 or 5 + (((4 × 3) ^ 2) - 1) or (((3 × 4) ^ 2) - 1) + 5
149 = (((3 × 4) × 1) ^ 2) + 5 or (5 + ((3 × 4) ^ 2)) ^ 1 or (5 + ((4 × 3) ^ 2)) ^ 1 or ((4 × 3) ^ 2) + (5 × 1) or 1 × (((3 × 4) ^ 2) + 5)
150 = 5 × ((4 + 1) × (3 × 2)) or ((1 + 4) × 2) × (5 × 3) or ((4 × 3) ^ 2) + (5 + 1) or (2 × 5) × (3 × (1 + 4)) or 3 × ((5 × (1 + 4)) × 2)
151 = (2 × ((3 ^ 4) - 5)) - 1 or (((3 ^ 4) - 5) × 2) - 1
152 = ((4 × 5) - 1) × (2 ^ 3) or 2 × ((3 ^ (4 × 1)) - 5) or ((3 ^ 4) - 5) × (1 × 2) or (((3 ^ 4) - 5) × 2) × 1 or (2 ^ 3) × ((5 × 4) - 1)
153 = 1 - (2 × (5 - (3 ^ 4))) or 1 - ((5 - (3 ^ 4)) × 2) or (((3 ^ 4) - 5) × 2) + 1 or 1 + (((3 ^ 4) - 5) × 2) or (2 × ((3 ^ 4) - 5)) + 1
154 = ((1 - 5) + (3 ^ 4)) × 2 or 2 × (1 + ((3 ^ 4) - 5)) or (((3 ^ 4) - 5) + 1) × 2 or 2 × ((1 + (3 ^ 4)) - 5) or ((3 ^ 4) + (1 - 5)) × 2
155 = (4 + ((1 + 2) ^ 3)) × 5 or (2 × ((3 ^ 4) - 1)) - 5 or ((3 ^ (1 + 2)) + 4) × 5 or 5 × (4 + ((1 + 2) ^ 3)) or (4 + (3 ^ (1 + 2))) × 5
156 = ((3 ^ 4) × 2) - (1 + 5) or 4 × (((5 + 1) ^ 2) + 3) or 4 × (((1 + 5) ^ 2) + 3) or (((3 ^ 4) × 2) - 1) - 5 or 4 × ((5 × (2 ^ 3)) - 1)
157 = ((2 × (3 ^ 4)) - 5) / 1 or ((3 ^ (4 / 1)) × 2) - 5 or ((2 ^ (1 + 4)) × 5) - 3 or ((3 ^ 4) / (1 / 2)) - 5 or (((3 ^ 4) × 2) - 5) / 1
158 = (1 - 5) + ((3 ^ 4) × 2) or (((3 ^ 4) × 2) + 1) - 5 or (2 × (3 ^ (5 - 1))) - 4 or (1 + ((3 ^ 4) × 2)) - 5 or ((2 × (3 ^ 4)) - 5) + 1
159 = (2 × (1 + (3 ^ 4))) - 5 or (2 × ((3 ^ 4) + 1)) - 5 or (5 / (2 / (4 ^ 3))) - 1 or (((3 ^ 4) + 1) × 2) - 5 or ((5 × (4 ^ 3)) / 2) - 1
160 = 1 × ((2 ^ 3) × (5 × 4)) or (5 × (3 + 1)) × (2 × 4) or ((5 × (4 ^ 3)) × 1) / 2 or 4 × ((1 + 3) × (5 × 2)) or 5 / (2 / (4 ^ (1 × 3)))
161 = 1 + ((5 × 4) × (2 ^ 3)) or ((3 ^ 4) × 2) - (1 ^ 5) or (5 × ((4 ^ 3) / 2)) + 1 or ((5 × (2 ^ 3)) × 4) + 1 or (2 × (3 ^ 4)) - (1 ^ 5)
162 = (3 - 1) × ((4 + 5) ^ 2) or (3 ^ 5) / ((2 / 4) + 1) or ((1 + 2) ^ 4) × (5 - 3) or (2 × ((4 - 1) ^ 5)) / 3 or (3 ^ 4) × (5 - (2 + 1))
163 = 3 + (5 × (2 ^ (4 + 1))) or 3 + ((2 ^ 5) × (1 + 4)) or ((2 ^ (1 + 4)) × 5) + 3 or 3 + ((2 ^ 5) × (4 + 1)) or ((3 ^ 4) × 2) + (1 ^ 5)
164 = ((1 ^ 5) + (3 ^ 4)) × 2 or 4 × (1 + (5 × (2 ^ 3))) or ((3 ^ 4) + (1 ^ 5)) × 2 or ((1 + (3 × 4)) ^ 2) - 5 or (((2 ^ 3) × 5) + 1) × 4
165 = (((3 ^ 4) - 1) × 2) + 5 or 5 × (1 + ((4 ^ 3) / 2)) or (1 + ((4 ^ 3) / 2)) × 5 or (2 × ((3 ^ 4) - 1)) + 5 or ((4 × (2 ^ 3)) + 1) × 5
166 = 5 - (1 - ((3 ^ 4) × 2)) or (2 × (3 ^ (5 - 1))) + 4 or 4 + (2 × (3 ^ (5 - 1))) or (2 / (3 ^ (1 - 5))) + 4 or (5 - 1) + (2 × (3 ^ 4))
167 = (5 + (2 × (3 ^ 4))) ^ 1 or ((2 × 1) × (3 ^ 4)) + 5 or 5 + (1 × (2 × (3 ^ 4))) or 5 + ((3 ^ 4) × (2 / 1)) or ((3 ^ 4) × 2) + (1 × 5)
168 = ((4 × 5) + 1) × (2 ^ 3) or (4 + 3) × ((5 ^ 2) - 1) or (1 + ((3 ^ 4) × 2)) + 5 or ((5 ^ 2) - 1) × (3 + 4) or (2 × (3 ^ 4)) + (1 + 5)
169 = (1 + ((5 + 3) + 4)) ^ 2 or ((3 + 4) + (1 + 5)) ^ 2 or ((5 + (3 + 4)) + 1) ^ 2 or ((1 + (3 ^ 4)) × 2) + 5 or ((3 × 4) + (1 ^ 5)) ^ 2
170 = 2 × ((3 ^ 4) + (5 - 1)) or (((3 ^ 4) - 1) + 5) × 2 or 2 × ((3 ^ 4) - (1 - 5)) or ((3 ^ 4) - (1 - 5)) × 2 or 2 × (((3 ^ 4) - 1) + 5)
171 = (3 ^ 2) × ((4 × 5) - 1) or ((4 × 5) - 1) × (3 ^ 2) or ((2 ^ (5 + 4)) + 1) / 3 or ((5 × 4) - 1) × (3 ^ 2) or (2 × ((3 ^ 4) + 5)) - 1
172 = 1 × (((3 ^ 4) + 5) × 2) or (1 × 2) × ((3 ^ 4) + 5) or 2 × (((3 ^ 4) + 5) × 1) or (((3 ^ 4) + 5) × 2) / 1 or 1 × (2 × (5 + (3 ^ 4)))
173 = 1 + (2 × ((3 ^ 4) + 5)) or 1 + (((3 ^ 4) + 5) × 2) or 1 + (2 × (5 + (3 ^ 4))) or (((3 ^ 4) + 5) × 2) + 1 or 1 + ((5 + (3 ^ 4)) × 2)
174 = (5 + (1 + (3 ^ 4))) × 2 or ((4 + 3) × (5 ^ 2)) - 1 or (((4 × 3) + 1) ^ 2) + 5 or 5 + ((1 + (4 × 3)) ^ 2) or (((3 ^ 4) + 1) + 5) × 2
175 = ((3 + 4) × (5 ^ 2)) ^ 1 or 1 × ((4 + 3) × (5 ^ 2)) or ((3 + 4) × (5 ^ 2)) × 1 or 5 × (((3 ^ 2) × 4) - 1) or (1 + 4) × (3 + (2 ^ 5))
176 = 4 × (((3 ^ 2) × 5) - 1) or 1 + ((4 + 3) × (5 ^ 2)) or 1 + ((5 ^ 2) × (4 + 3)) or ((5 ^ 2) × (3 + 4)) + 1 or ((3 + 4) × (5 ^ 2)) + 1
Answered by Alex Hall on October 29, 2020
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