Unbeknownst to you, you are working for the FBI. You have had suspected narcotic smuggler Herb Boursin for years. Herb claims to be an importer of fine cheeses, in fact routine checks at customs have always shown large shipments of cheese. Finally, you catch a break. You hear a rumor that Herb will be importing ten cheese casings over the weekend, and that one of the cheese casings has been hollowed out and filled with narcotics. When you arrive at the scene Herb makes a run for it. Before chasing him, however, you want to make sure you take the contraband with you so his importing pals don’t hide the evidence. You know that nine of them actually contain cheese and weigh 100 grams. The other is filled with contraband and weighs 90 grams.

You have a large scale that can read out the exact weight of anything placed on it. Since time is of the essence here, you sit down and figure the fewest number of weighings needed to find the narcotics. What’s the fewest number of times you would have to use the scale to guarantee finding the casing that contains the contraband?

Solutions should be submitted to the St. Edward’s Problem of the Week Headquarters in André 305 by 3 p.m. Friday, February 18. The winner will be announced President's Day.