Which backpack has the bomb?
(Editor’s Note: The following story is fictitious. It is presented as a mental exercise for amusement only.)
Acting on a tip from an informant, Israeli troops invaded a school building in Ramallah operated by UNRWA, and seized nine schoolbags. Eight of the nine bags had schoolbooks but the ninth had a bomb in it. The task for the troops was to quickly identify the bag with the bomb and return the other bags to the children. The bags couldn’t be opened because that would risk detonating the bomb. However, the soldiers brought a scale with them. Let’s assume that the eight bags with schoolbooks had identical weights but the bag with the bomb weighed more.
What is the minimum number of weightings needed to identify the bag with the bomb and how was it done? For solution, click here:
Only two weightings are needed to identify the bag with the bomb. First divide the nine bags into groups of three and compare the masses of two groups. If one trio is heavier, simply compare two bags from that one, and it’s done. However, if the two triplets have the same mass, then it’s only necessary to compare two backpacks from the trio that was left out.
(Adapted from a puzzle by Alex Stone in Discover Magazine, April 2007)