Problem #7 MEDIUM
Measuring Water with Pitchers
Amazon Math Logic
Problem Statement
You are standing next to a water tap and have two empty pitchers: one that holds exactly 5 liters of water, and another that holds exactly 3 liters.
The pitchers do not have any markings on them, so you cannot estimate fractional amounts.
How can you measure out exactly 4 liters of water using only these two pitchers?
Answer & Quick Explanation
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Fill the 5-liter pitcher, pour into the 3-liter pitcher until full (leaving 2L), empty the 3-liter pitcher, transfer the 2L, fill the 5-liter pitcher again, and pour into the 3-liter pitcher until full (leaving exactly 4L).
Detailed Editorial Solution
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We can solve this puzzle by performing a sequence of fills, transfers, and drains.
Here is the step-by-step solution:
1. Fill the 5-liter pitcher completely.
2. Pour water from the 5-liter pitcher into the 3-liter pitcher until the 3-liter pitcher is full. You now have exactly 2 liters left in the 5-liter pitcher.
3. Empty the 3-liter pitcher.
4. Pour the 2 liters of water from the 5-liter pitcher into the 3-liter pitcher. The 3-liter pitcher now contains 2 liters, leaving room for exactly 1 more liter.
5. Fill the 5-liter pitcher completely again.
6. Pour water from the 5-liter pitcher into the 3-liter pitcher until it is full. Since the 3-liter pitcher already had 2 liters, it will take exactly 1 liter from the 5-liter pitcher.
This leaves exactly 4 liters of water in the 5-liter pitcher.