A barrel contains exactly 9 liters of red wine.
Max is going to a party and wishes to share 8 liters of wine equally with the seven other partygoers, who all hold 1 liter glasses. Max wants to keep one liter for when he gets home.
He only has two other containers that will hold exactly 5 liters and 2 liters respectively.
What is the quickest way for him to measure 8 liters into the barrel to take to the party?
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Solution
The trick is to measure 1 litre for Max, rather than trying to measure out the 8 litres for the party.
Starting with the 9-litre barrel:
- First pour: Fill the 5-litre container from the barrel.
→ Barrel: 4 L | 5-L container: 5 L | 2-L container: 0 L - Second pour: Pour from the 5-litre container into the 2-litre container until the 2-litre container is full.
→ Barrel: 4 L | 5-L container: 3 L | 2-L container: 2 L - Third pour: Pour the 2 litres back into the barrel.
→ Barrel: 6 L | 5-L container: 3 L | 2-L container: 0 L - Fourth pour: Pour from the 5-litre container into the 2-litre container until it is full. This leaves exactly 1 litre in the 5-litre container.
→ Barrel: 6 L | 5-L container: 1 L | 2-L container: 2 L - Fifth pour: Pour the 2 litres from the small container into the barrel.
→ Barrel: 8 L | 5-L container: 1 L | 2-L container: 0 L
And that’s it. Max keeps the 1 litre in the 5-litre container, while the barrel now contains exactly 8 litres to take to the party.
Answer: 5 pourings.
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