Split 10 litres of cider into two equal shares

Question

Two friends want to split a jug of cider evenly. They have a 10-litre jug that is completely full, plus an empty 7-litre jug and an empty 3-litre jug. There is no tap and no drain, not a drop may be spilled or added. The only legal move is to pour from one jug into another until the source empties or the target fills.

Divide the cider into two equal 5-litre shares.

Accepted Answer

Since 5 litres cannot fit in the 3-litre jug, the two shares must end up as 5 in the 10-jug and 5 in the 7-jug. Track the triple (10-jug, 7-jug, 3-jug), starting full at (10, 0, 0): 1. Pour the 10-jug into the 7-jug until it fills → (3, 7, 0). 2. Pour the 7-jug into the 3-jug until it fills → (3, 4, 3). 3. Pour the 3-jug back into the 10-jug → (6, 4, 0). 4. Pour the 7-jug into the 3-jug until it fills → (6, 1, 3). 5. Pour the 3-jug back into the 10-jug → (9, 1, 0). 6. Pour the 7-jug's last litre into the 3-jug → (9, 0, 1). 7. Pour the 10-jug into the 7-jug until it fills → (2, 7, 1). 8. Pour …

Split 10 litres of cider into two equal shares

Your answer

More Brainteasers questions