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 ?
With Claude 3.5 Sonnet: one shot just the prompt given by LeCun:
"Let me solve this step by step.
1. Let's first understand what happens between adjacent gears:
* When one gear rotates clockwise, the gear meshed with it must rotate counterclockwise
* This alternating pattern continues through the chain of gears
2. Starting from gear 3 rotating clockwise:
* Gear 3: Clockwise
* Gear 4: Counterclockwise
* Gear 5: Clockwise
* Gear 6: Counterclockwise
* Gear 7: Clockwise
However, we need to check something important! Since the gears form a complete circle with an odd number of gears (7), this creates an impossible situation. Each gear must mesh with both its neighbors, but with an odd number of gears, this would force a gear to rotate in two directions at once.
Therefore, it's actually impossible to arrange 7 gears in a circle where each meshes with its neighbors. A circle of meshing gears must have an even number of gears to work mechanically.
This is the key insight that makes this a trick question - such an arrangement couldn't actually function in reality."
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.
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 ?
With Claude 3.5 Sonnet: one shot just the prompt given by LeCun:
"Let me solve this step by step.
1. Let's first understand what happens between adjacent gears:
* When one gear rotates clockwise, the gear meshed with it must rotate counterclockwise
* This alternating pattern continues through the chain of gears
2. Starting from gear 3 rotating clockwise:
* Gear 3: Clockwise
* Gear 4: Counterclockwise
* Gear 5: Clockwise
* Gear 6: Counterclockwise
* Gear 7: Clockwise
However, we need to check something important! Since the gears form a complete circle with an odd number of gears (7), this creates an impossible situation. Each gear must mesh with both its neighbors, but with an odd number of gears, this would force a gear to rotate in two directions at once.
Therefore, it's actually impossible to arrange 7 gears in a circle where each meshes with its neighbors. A circle of meshing gears must have an even number of gears to work mechanically.
This is the key insight that makes this a trick question - such an arrangement couldn't actually function in reality."
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.