Measure 4 litres with a 3 and a 5 jug

Question

You have a 3-litre jug and a 5-litre jug, both unmarked, and an unlimited supply of water. You can fill either jug to the top, empty either jug completely, or pour water from one jug into the other until either the source is empty or the destination is full. Measure out exactly 4 litres of water.

Accepted Answer

Here is one clean sequence. Track the pair (3-jug, 5-jug): 1. Fill the 5-jug. State: (0, 5). 2. Pour the 5-jug into the 3-jug until the 3-jug is full (3 litres move). State: (3, 2). 3. Empty the 3-jug. State: (0, 2). 4. Pour the 5-jug's remaining 2 litres into the 3-jug. State: (2, 0). 5. Fill the 5-jug again. State: (2, 5). 6. Pour from the 5-jug into the 3-jug until the 3-jug is full. The 3-jug needs only 1 more litre, so 1 litre moves. State: (3, 4). The 5-jug now holds exactly 4 litres. Why it works in general. Every operation changes the total by a multiple of 3 or 5, so the reachable am…

Measure 4 litres with a 3 and a 5 jug

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