Exactly one litre from a 7 and a 5

Question

You have two jugs with no markings: one holds exactly 7 litres, the other exactly 5 litres. There is a tap with unlimited water and a drain. A "move" is one of: fill a jug to the top, empty a jug completely, or pour from one jug into the other until the source is empty or the target is full.

Measure out exactly 1 litre. Then find the smallest number of moves in which it can be done.

Accepted Answer

Eight moves. Write the state as (7-litre jug, 5-litre jug). 1. Fill the 5: (0, 5) 2. Pour into the 7: (5, 0) 3. Fill the 5: (5, 5) 4. Pour into the 7 until it is full; 2 litres go across: (7, 3) 5. Empty the 7: (0, 3) 6. Pour the 3 into the 7: (3, 0) 7. Fill the 5: (3, 5) 8. Pour into the 7 until full; 4 litres go across, leaving 1 litre in the 5-litre jug: (7, 1) Why this pattern works. Each cycle of "fill the small jug, pour into the big jug, empty the big jug when full" shifts the water level by 5 litres modulo 7. The leftover amounts you see in the small jug go 3, then 1: you are effectiv…

Exactly one litre from a 7 and a 5

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