You have two unmarked jugs: one with 3 liters and one with 5 liters. You have a tap with unlimited water. How can you measure exactly 4 liters?
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The jugs of agua
This problem has something especially clean: the quantity sought is not guessed, it is manufactured. It is a good example of a well-carried out elementary method, where each transfer prepares the next.
Hints
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- Don't try to get it close: try to make the desired quantity from exact leftovers.
- The decisive step is to leave a small amount in the smaller jug and reuse it.
- If you get the 3 liter jug to contain 2, the 5 liter jug can be 4.
Solution
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Answer: Yes: you can leave exactly 4 liters in the 5 liter jug. Explanation: 1. Fill the 5 liter jug.
- Pour it into the 3 liter container until it is full. There are 2 liters left in the 5.
- Empty the 3 liter jug.
- Transfer those 2 liters to the 3-liter jug.
- Fill the 5 liter jug again.
- Pour from number 5 to number 3 only until the latter is complete. Since the 3-liter jug already had 2 liters, it only holds 1 more liter. That liter comes out of the 5-size jug, so there are exactly 4 liters left in it.
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