Published: Aug 3, 2024
Somebody asked in some channel:
“Given six numbers: 1, 2, 3, 4, 5, 22; and 5 operators: +, -, ×, ÷ and =. Is it possible to arrange these numbers and operators into a statement that is true? You must use all of the numbers and operators given.
Example: 1 + 2 - 3 × 4 ÷ 5 = 22 (not true)”
My approach
SPOILER ALERT!
At first I tried to sort the numbers and operators manually but with no luck.
I wrote a quick Python script to programmatically generate all possible statements and evaluate all of them.
1import itertools
2
3def execute(num, ops):
4 s = "float("
5 ops += " "
6 for i in range(6):
7 a = num[i]
8 b = ops[i]
9
10 s += a + b
11
12 if b == "=":
13 s += "float("
14
15 s += ")"
16 s = s.replace("6", "22").replace("=", ")==")
17
18 left, right = s.split("==")
19 print(s, end="")
20 exec(f"print({s}, {left}, {right})")
21
22def iterate():
23 ops = '+-*/='
24 numbers = '123456'
25 perms = list(itertools.permutations(ops))
26 perms = [''.join(i) for i in perms]
27 nums = list(itertools.permutations(numbers))
28 nums = [''.join(i) for i in nums]
29
30 for perm in perms:
31 for num in nums:
32 execute(num, perm)
33
34iterate()
The code is horribly unoptimized and ugly, but at least it gets the job done…
The code prints out a total of 86400 statements. After searching the output dump, it looks like none of them is true.
Afterwords
I wonder if these kinds of problems are possible to mathematically prove that there are no solutions (or otherwise)? If you do came up with a different approach, I would love to see it.
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