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Fill the 5-quart jug. Transfer its contents onto the 3-quart jug until it is full.
The remaining water in the 5-quart jug amounts to 2 quarts.
Dump the contents of the 3-quart jug and transfer the 2 quarts to it.
Fill the 5-quart jug again and transfer its contents into the partially filled 3-quart jug until it is full, again. Now the 3-quarts jug is full and the 5-quarts jug has 4 quarts in it.