Measure exactly 6 litres with a 7 and a 4

Question

You have two jugs with no markings: one holds exactly 7 litres, the other exactly 4 litres. There is a tap to fill either jug and a drain to empty either jug. You cannot judge levels by eye, you only ever know a jug is completely full, completely empty, or holds an amount you can deduce by transferring.

Using only filling, emptying, and pouring one jug into the other, measure out exactly 6 litres.

Accepted Answer

Aim to leave exactly 6 litres in the 7-litre jug. Track the pair (7-jug, 4-jug): 1. Fill the 7-jug from the tap → (7, 0). 2. Pour 7-jug into 4-jug until the small one is full. That moves 4 litres over → (3, 4). 3. Empty the 4-jug down the drain → (3, 0). 4. Pour the 7-jug's 3 litres into the 4-jug → (0, 3). 5. Fill the 7-jug again from the tap → (7, 3). 6. Pour from the 7-jug into the 4-jug until the small one is full. The 4-jug already holds 3, so it only accepts 1 more litre, leaving 7 - 1 = 6 in the big jug → (6, 4). The 7-litre jug now holds exactly 6 litres. Why it must work. Because 7 a…

Measure exactly 6 litres with a 7 and a 4

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