Maths Olympiad Prep

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Combinatorics Difficulty 5.4 AIME, harder Find the answer

3. How to measure 2 liters of water when you are near a river and have two buckets with a capacity of 10 liters and 6 liters? (2 liters of water should end up in one bucket).

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution. Let's write the sequence of filling the buckets in the form of a table:

Bucket with a capacity of 10 litersBucket with a capacity of 6 litersComment
Initially0 liters0 liters
Step 110 liters0 litersThe first bucket is filled from the river
Step 24 liters6 litersPoured from the first bucket into the second until it is full
Step 34 liters0 litersPoured the second bucket back into the river
Step 40 liters4 litersPoured from the first bucket into the second
Step 510 liters4 litersThe first bucket is filled from the river
Step 68 liters6 litersPoured from the first bucket into the second until it is full
Step 78 liters0 litersPoured the second bucket back into the river
Step 82 liters6 litersPoured from the first bucket into the second until it is full

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.