Theres a puzzle that GPT seems entirely incapable of solving. I have come up with a few approaches but they all result in failure. In interested in others approaches or successes.

The puzzle is this. You have 2 jugs. 1 holds 1 liter. The other holds 3 liters. Neither is marked so you must fill completely in order to know how much you’ve poured in from the tap. There are 2 taps. One tap gives blue water and the other gives yellow water.

In the fewest steps possible, obtain exactly 3 liters of an even mixture of boue and yellow water.

Here is an example prompt I’ve used:

“”"

I have 2 jugs. The first jug is called Jug A and holds 1 liter of fluid. The second jug is called Jug B and hold 3 liters of fluid. Neither jar is marked. I have 2 liquids. Blue and Yellow. Using a series of steps get me 3 liters of an equal mixture of Blue and Yellow.

The steps that you can use are

A. Fill Jug A with Yellow.

B. Fill Jug B with Yellow.

C. Fill Jug A with Blue.

D. Fill Jug B with Blue.

E. Empty Jug A into Jug B.

F. Pour Jug B into Jug A until jug A is full…

G. Empty Jug A onto the floor.

H. Empty Jug B onto the floor.

Hint: If you pour a mixture from a larger jug into a smaller jug, that mixture will be represented as fractional values in the smaller jug. This is not true the other way around.

Hint: You must think laterally.

Hint: a full jug cannot be filled.

Tell me the first thing you do.

“”"

I’ve also broken it down into a multi-step process with recurring prompts such as

“”"

What is the current state of the puzzle? Before you answer, consider the rules of the compoents of the situationa nd evaluate the logical outcome.

What are the facts and rules of the puzzle?

Logically, what are the available options at this point?

Are all of those options logically possible given the state of the puzzle? Remove any that are contradictory to the current state of the puzzle.

select the best option and proceed.

“”"

(Delivered individually of course). Tried using both 3 and 4.

Through the api, I’ve effectively isolated every decision point so that every decision is itemized. So, for example, i don’t prompt it to tell me what available options there are. I feed it each option and ask if it can do it.

No luck. It fumbles at out before the 5th appripritate step in a 10 step solution to this puzzle.

I have some ideas about building infrastructure outside of GPT to do this but that defeats the purpose of the exercise somewhat.

Do you think this is solveable by GPT?

Before you ask, already using chain of thought, roles, prompt variations, etc. About the only thing i didn’t do was have agents discuss options until they reach a consensus (like SmartGPT).