Comment by gloosx

1 year ago

There is no ambiguity, the problem is that three numbers, divided together, without the order specified, must be equal to their sum.

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."?

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gloosx

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johndough  1 year ago

> There is no ambiguity

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

However, I do not think that this ambiguity is the reason why OpenAI o1 fails here. It simply started with an untractable approach to solve this problem (plugging in random numbers) and did not attempt a more promising approach because it was not trained to do so.

  • gloosx  1 year ago

    So, there is no chance to answer the original question incorrectly by picking any specific order.

    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.