You have 20 pounds of flour that must be distributed into 10 sacks of 2 pounds each.

At your disposal is a scale, and two weights: a 5 pound one and a 9 pound one.

How can you complete this job in only 9 weighings?

Weighing 1: Put the 9 lb weight on one side and the 5 lb on the other. Fill a sack on the 5 lb side, this gives you a 4 lb sack of flour.

Weighing 2: Place all the weights and the 4 lb sack on one side of the scale (18 lbs total) and place the 20 lb sack on the other side. Remove flour until they balance. You now have your first 2 lb bag of flour!!

Weighing 3: Replace the 4 lb bag of flour with the 2 lb bag (16 lbs). Remove 2 lbs of flour again giving your second 2 lb bag.

Weighing 4-8: Repeat the above process, by using the appropriate weights/sacks, decreasing by 2 lbs each time.
On the last weighing you will have seven 2 lb sacks and 2 lbs left from the orignal 20 lbs. Just pour that into a sack, and now there are eight 2 lb sacks and one 4 lb sack.

Final weighing: Place the 4 lb sack on one side and a 2 lb on the other. Remove 2 lbs into teh fianl sack. Finished!!

Posted by Dan on 2002-05-09 06:14:41