Three litres from a 12 and a 5

Question

You have an unmarked 12-litre jug and an unmarked 5-litre jug, a tap, and a drain. The usual moves apply: fill, empty, or pour until the source runs dry or the target is full. Leave exactly 3 litres in one of the jugs. What is the fewest number of moves?

Accepted Answer

Six moves. State written as (12-jug, 5-jug). 1. Fill the 5: (0, 5) 2. Pour into the 12: (5, 0) 3. Fill the 5: (5, 5) 4. Pour into the 12: (10, 0) 5. Fill the 5: (10, 5) 6. Pour into the 12 until it is full; only 2 litres fit, leaving 3 litres in the 5-litre jug: (12, 3) Why this works. Two full small jugs put 10 litres in the big jug, leaving a gap of exactly 2 litres. Pouring a third full small jug into that gap uses 2 and strands 3. In symbols, 3 = 3 × 5 minus 12: three fills of the small jug, one overflow of the big one. A note on strategy. Almost every two-jug puzzle is solved by one of t…

Three litres from a 12 and a 5

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