Measuring Wine
You're at a vineyard and are given two empty wine bottles: one with a capacity of 3 liters and another with a capacity of 5 liters. There are no markings on the bottles except for their total volume. You have access to an unlimited supply of a rare vintage wine from a barrel. Your goal is to get exactly 4 liters of wine. How can you achieve this using only the two wine bottles?
Answer
To get exactly 4 liters of wine, follow these steps:
Fill the 5-liter bottle completely from the barrel. Now the 5-liter bottle contains 5 liters.
Pour wine from the 5-liter bottle into the 3-liter bottle until the 3-liter bottle is full. Now the 5-liter bottle contains \(5 - 3 = 2\) liters, and the 3-liter bottle contains 3 liters.
Empty the 3-liter bottle completely.
Pour the 2 liters from the 5-liter bottle into the empty 3-liter bottle. Now the 3-liter bottle contains 2 liters.
Fill the 5-liter bottle completely from the barrel again. Now the 5-liter bottle contains 5 liters.
Pour wine from the 5-liter bottle into the 3-liter bottle until the 3-liter bottle is full (it already contains 2 liters, so it only needs 1 more liter). Now the 5-liter bottle contains \(5 - 1 = 4\) liters, which is the desired amount.
Thus, you have exactly 4 liters of wine in the 5-liter bottle.