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John Shanly's avatar

I couldn't get the free chatgpt to answer the gear problem correctly even using some of the prompt engineering from the LeCun twitter thread. Can you post your log of a correct answer from an LLM ?

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Nigel Goddard's avatar

Might be ok as a philosopher, but useless at algebra and arithmetic

(from 2023, see recent at the end:

Me: What are four different integers a,b,c,d such that a*a + b*b = c*c + d*d ?

ChatGPT: Here are four different integers a, b, c, and d that satisfy the equation a^2 + b^2 = c^2 + d^2:

a = 1, b = 1, c = 2, d = 2

In this case, 1^2 + 1^2 = 2^2 + 2^2, which simplifies to 2 = 8, showing that this equation is not always true for all integer values of a, b, c, and d.

Me: a,b,c,d must be different integers, ie no pair are equal.

ChatGPT: I apologize for the oversight. Here's a set of four different integers a, b, c, and d such that a^2 + b^2 = c^2 + d^2:

a = 1, b = 2, c = 2, d = 1

In this case, 1^2 + 2^2 = 2^2 + 1^2, which simplifies to 5 = 5, satisfying the equation with distinct integer values.

Me:

But b = c and a=d. I said no pair could be equal

ChatGPT: I apologize for misunderstanding your previous request. Here's a set of four different integers a, b, c, and d such that no pair are equal, and a^2 + b^2 = c^2 + d^2:

a = 1, b = 2, c = 2, d = 3

In this case, 1^2 + 2^2 = 2^2 + 3^2, which simplifies to 5 = 13, satisfying the equation with distinct integer values.

At which point I gave up. Tried again today (Nov 24), but it still can't do arithmetic:

ChatGPT: To find four different integers a, b, c, and d such that:

a^2 + b^2 = c^2 + d^2

we can try values that make both sides of the equation equal.

One example solution is: a = 1, b = 7, c = 4, and d = 6.

Then: a^2 + b^2 = 1^2 + 7^2 = 1 + 49 = 50

and c^2 + d^2 = 4^2 + 6^2 = 16 + 36 = 50

Thus, 1^2 + 7^2 = 4^2 + 6^2, satisfying the condition with a = 1, b = 7, c = 4, and d = 6.

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