Water Jug Puzzle discussion thread
No. LLMs are capable enough to give a complete solution.
My rewriting of the problem, orienting the language towards the problem-solving agent, and stating its permissible actions that can be sequenced, clearly:
You are provided 2 jugs, neither of which is marked in sub-units of its full capacity.
- 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.
Two colored liquids can be dispensed to fill any jug: Blue or Yellow. Goal: Using a series of steps, provide a total of 3 liters contained in jugs, comprised of an equal mixture of Blue and Yellow liquids.
The actions that that are possible at any step: 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.
Provide the correct sequence of steps to yield three contained liters of an equal mixture: 1.5 liters blue; 1.5 liters yellow.
GPT-5.2 xhigh
Start with both jugs empty.
I’ll track the amounts of Blue (B) and Yellow (Y) in each jug after every step.
Capacities: Jug A = 1 L, Jug B = 3 L.
Sequence of actions (letters)
C, E, A, E, F, G, A, E, C, E
What happens at each step
| Step | Action | Jug A contents | Jug B contents |
|---|---|---|---|
| 1 | C (Fill A with Blue) | 1 L = (1B, 0Y) | 0 L |
| 2 | E (Empty A into B) | 0 L | 1 L = (1B, 0Y) |
| 3 | A (Fill A with Yellow) | 1 L = (0B, 1Y) | 1 L = (1B, 0Y) |
| 4 | E (Empty A into B) | 0 L | 2 L = (1B, 1Y) (a 50/50 mix) |
| 5 | F (Pour B into A until A is full) | 1 L = (0.5B, 0.5Y) | 1 L = (0.5B, 0.5Y) |
| 6 | G (Empty A onto the floor) | 0 L | 1 L = (0.5B, 0.5Y) |
| 7 | A (Fill A with Yellow) | 1 L = (0B, 1Y) | 1 L = (0.5B, 0.5Y) |
| 8 | E (Empty A into B) | 0 L | 2 L = (0.5B, 1.5Y) |
| 9 | C (Fill A with Blue) | 1 L = (1B, 0Y) | 2 L = (0.5B, 1.5Y) |
| 10 | E (Empty A into B) | 0 L | 3 L = (1.5B, 1.5Y) |
Result
At the end:
- Jug B contains 3 liters total
- Composition is 1.5 L Blue + 1.5 L Yellow (an equal mixture)
- Jug A is empty
That meets the goal exactly.
Optional (if you prefer the 3 liters split between the two jugs)
After step 10, do:
- F (Pour Jug B into Jug A until Jug A is full)
Then you’ll have:
- Jug A: 1 L of 50/50 mix
- Jug B: 2 L of 50/50 mix Total still 3 L, still 1.5 L blue and 1.5 L yellow overall.
Or my own phrasing before getting an AI answer:
Fill the 3L jug with 1L blue and 1L yellow from the 1L jug. 50% Transfer that mixture to the 1L jug and dump the rest: 50% still 1L of 50% Back to the 3L jug, and measure out another 1L + 1L.
The AI just measures how much it discards instead of how much it keeps.
Discussion in the ATmosphere