Oct 17, 2018

Interview Classic

You have 8 coins which are all the same weight, except for one which is slightly heavier than the others (you don't know which coin is heavier). You also have an old‐style balance, which allows you to weigh two piles of coins to see which one is heavier (or if they are of equal weight). What is the fewest number of weighings that you can make which will tell you which coin is the heavier one?

Good answer: Weigh 3 coins against 3 coins. If one of the groups is heavier, weigh one of its coins against another one of its coins; this allows you to identify the heavy coin. If the two groups balance, weigh the two leftover coins.

Not‐so‐good answer: Weigh 4 coins against 4 coins. Discard the lighter coins, and weigh 2 coins against 2 coins. Discard the lighter coins and weigh the remaining two coins.