If you have a 9 qt pail and 4 qt pail how can you get exactly 6 qts?

Answer 1

Fill the 4 qt pail, and empty the contents into the 9 qt pail. Repeat. You should now have eight quarts in the 9 qt pail, and none in the 4 qt pail. Fill the 4 qt pail again, and fill the remaining space of the 9 qt pail with it, leaving a full 9 qt pail and a 4 qt pail with only three quarts in it. Empty the 9 qt pail, and dump the contents of the 4 qt pail into the 9 qt pail. There are now three quarts in the 9 qt pail. Fill the 4 qt pail and empty the contents into the 9 qt pail. Repeat this step without spilling anything. The second time, two quarts should go into the 9 qt pail, filling it up, and two should remain in the 4 qt pail. Empty the contents of the 9 qt pail, and transfer that of the 4 qt pail into the 9 qt pail. Fill the 4 qt pail and empty it into the 9 qt pail. There are now 6 quarts in the 9 qt pail. QED.