Question

Suppose we are given three pitchers of water, of sizes 10 quarts, 7 quarts, and 4 quarts. Initially the 10-quart pitcher is full and the other two empty. We can pour water from one pitcher into another, pouring until the receiving pitcher is full or the pouring pitcher is empty. Is there a way to pour among pitchers to obtain exactly 2 quarts in the 7- or 4-quart pitcher? If so, find a minimal sequence of pourings to get 2 quarts in the 7-quart or 4-quart pitcher

Answer 1

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

Explanation: Begin by pouring the liquid of the 10 quarts pitcher into the 7 quarts pitcher until it is full, this would leave the 10 quarts pitcher with only three quarts of liquid. Continue by pouring the liquid from the 7 quarts pitcher into the 4 quarts pitcher until full, this would result in the 7 quarts pitcher with only 3 quarts of liquid. Pour the remaining three quarts of liquid of the 10 quarts pitcher into the 7 quarts pitcher, this would render the 10 quarts pitcher empty, and the 7 quarts pitcher with  6 quarts of liquid. Then, continue by pouring the full content of the 4 quarts pitcher into the 10 quarts pitcher, rendering the 4 quarts pitcher empty and the 10 quarts pitcher with 4 quarts of liquid. Finally, pour the liquid from the 7 quarts pitcher into the 4 quarts pitcher until it is full, resulting in the 7 quarts pitcher with only two quarts of liquid, the 10 quarts pitcher with four quarts of liquid and the 4 quarts pitcher completely full.

If you would like to get the 4 quarts pitcher with only 2 quarts of liquid, continue the process by emptying the contents of the 4 quarts pitcher into the 10 quarts pitcher, which would now hold eight quarts of liquid. Then, pour all the contents of the 7 quarts pitcher into the 4 quarts pitcher, resulting in said pitcher having 2 quarts of liquid, rendering the 7 quarts pitcher empty.