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?
1st weigh: split flour into 10-lb bags.
Result: 2 10-pounders (probably in multiple bags)
2nd weigh: 9-lb weight on one side against 5-lb weight plus enough flour from one bag to have scale balance.
Result: 1 10-pounder, 1 4-pounder, 1 6-pounder
3rd weigh: repeat 2nd step, pouring from the 6-lb bag to match the two weights.
Result: 1 10-pounder, 2 4-pounders, 1 2-pounder
4th & 5th weighs: Repeat 2nd and 3rd steps pouring from the 10-lb bag to match the weights.
Result: 4 4-pounders, 2 2-pounders
6th - 9th weighs: For the next 4 weighs, split a 4-lb bag into 2 2-lb bags.
Result: 10 2-pounders, and probably a crapload of loose flour in the air.
Differnt first weighing
