You can find solutions for a / b / c, or b / c / a, or c / a / b, any combination of them and the solution will be correct according to the problem description.
Besides, what's does it even has to do with it concluding with confidence: "The fundamental issue is that division tends to make numbers smaller. It's mathematically impossible to find three numbers where these operations result in the same value."?
Yet you give three different interpretations:
> You can find solutions for a / b / c, or b / c / a, or c / a / b
This is a clear case of ambiguity.
Even the classic question is ambiguous: "Which 3 numbers give the same result when added or multiplied together?"
Lets say the three numbers are x, y and z and the result is r. A valid interpretation would be to multiply/add every pair of numbers:
x * y = r
y * z = r
x * z = r
x + y = r
y + z = r
x + z = r
Logically speaking, the original problem has just one interpretation, i hope you would agree it is by no means ambiguous:
((a / b / c) = a + b + c) | ((a / c / b) = a + b + c) | ((b / a / c) = a + b + c) | ((b / c / a) = a + b + c) | ((c / a / b) = a + b + c) | ((c / b / a) = a + b + c) | ...(other 6 combinations) = true
This interpretation would indeed find all possible solutions to the problem, accounting for any potential ambiguity in the division order.
Moreover, addition is commutative so it doesn't matter what order the division is in since a/b/c = a+b+c = c+a+b = ...
So I'd say that the model pointing this out is actually a mistake and it managed to trick you. Classic LLM stuff: spit out wrong stuff in a convincing manner.