Two Jugs: 4 L and 9 L
Read the puzzle
There is a 4 L jug, a 9 L jug, a tap and a drain. Filling a jug from the tap, emptying a jug down the drain, or pouring one jug into the other each counts as 1 move. A pour stops when one jug is empty or the other is full. The jugs have no markings. What is the fewest number of moves to end with exactly 6 L in the 9 L jug?
Filling, emptying or pouring a jug counts as 1 move each. Fewest moves to get exactly 6 L in the 9 L jug?
Pour from the full 9 L jug into the 4 L jug twice.
8 moves
Fill 9, pour into 4, empty 4, pour again (1 L left), empty 4, pour in the 1 L, fill 9, top up 4: 6 L.
How to solve it
Write the state as (4 L jug, 9 L jug) and count each move.
Fill the big jug: (0, 9). Pour into the small jug: (4, 5). Empty the small jug: (0, 5). Pour again: (4, 1). So far 9 - 4 - 4 = 1 L is left in the big jug after 4 moves.
Empty the small jug: (0, 1). Pour the 1 L across: (1, 0). Fill the big jug: (1, 9). Top up the small jug, which needs only 3 L: (4, 6). That is 8 moves in total, and 9 - 3 = 6 L stays in the big jug.
The usual wrong answer comes from starting with the small jug and always pouring it into the big one. That route does reach 6 L, but only after 16 moves, because it builds 8, then 3, then 7, then 2, then 6 L along the way. Another slip is skipping the empty moves when counting.
The answer is 8 moves. Takeaway: aim to leave a small amount (here 1 L) in the small jug so the final top-up removes exactly what you do not need.
Learn the method: How to Solve Water Jug Puzzles, Step by Step
