The bucket and jug puzzle
✓ With solution
A 9-litre bucket, a 4-litre jug and no markings. How do you get exactly 6 litres?
Grandma needs exactly 6 litres of water in the bucket. You have a tap, a 9-litre bucket and a 4-litre jug, with no measuring marks on either. You can fill either one to the top from the tap, empty it out completely, or pour from one into the other until the other is full or the first is empty.
How do you end up with exactly 6 litres in the bucket?
Show a hint
Fill the bucket, then use the jug to take water out of it twice. What's left? And how could a jug that isn't quite empty help?
Show the answer
Answer: Get 1 litre into the jug, then fill the bucket and top up the jug from it: 9 − 3 = 6. Fill the bucket (9 litres). Pour from it into the jug until the jug is full, leaving 5 in the bucket, then empty the jug. Do it again, leaving 1 litre in the bucket, and empty the jug. Pour that 1 litre into the jug. Fill the bucket again and pour from it into the jug until the jug is full: the jug already has 1 litre, so it takes only 3, leaving 9 − 3 = 6 litres in the bucket. That is eight steps (fill, empty or pour), and there is no shorter way.
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