Solution for #12

To get seven gallons, fill the five gallon jug and dump what you can into the three gallon jug, filling it. There are now two gallons in the five gallon jug. Dump out the three gallon jug, and put the two gallons from the five gallon jug into the three gallon jug. Then fill the five gallon jug. The total is seven gallons.

To get four gallons, fill the three gallon jug, and dump it into the five gallon jug. Fill the three gallon jug again, and dump what you can into the five gallon jug. Now there is one gallon in the three gallon jug. Dump out the five gallon jug, and put the one gallon from the three gallon jug into the five gallon jug. Now fill the three gallon jug. The total is four gallons.