Water Pouring Puzzle: Obtaining 2 Quarts

Is it possible to obtain exactly 2 quarts in the 7- or 4-quart pitcher?

Explain whether it is possible to achieve this and if so, what is the minimal sequence of pourings to get 2 quarts in the 7-quart or 4-quart pitcher.

Answer:

It is possible to obtain 2 quarts in either the 7 quarts pitcher or the 4 quarts pitcher.

To achieve 2 quarts in either the 7-quart or 4-quart pitcher, we can follow these steps:

1. Pour the 10-quart pitcher into the 7-quart pitcher until it is full, leaving the 10-quart pitcher with 3 quarts.
2. Pour the 7-quart pitcher into the 4-quart pitcher until full, leaving the 7-quart pitcher with 3 quarts.
3. Pour the remaining 3 quarts from the 10-quart pitcher into the 7-quart pitcher, making it 6 quarts full.
4. Empty the 4-quart pitcher and pour all 6 quarts from the 7-quart pitcher into the 4-quart pitcher, resulting in the 4-quart pitcher with 2 quarts.

If you want to achieve 2 quarts in the 7-quart pitcher, continue with the following steps:

1. Empty the 4-quart pitcher into the 10-quart pitcher, leaving the 10-quart pitcher with 8 quarts.
2. Pour the 7-quart pitcher into the 4-quart pitcher, resulting in the 4-quart pitcher containing 2 quarts.

Following these steps will successfully obtain 2 quarts in either the 7-quart or 4-quart pitcher.