Finding a Counterfeit Coin


I got this problem from Rustan Leino, who got it from Ernie Cohen. He'd also heard it from a student who got it from Ernie at Marktoberdorf.

I solved it and wrote up my solution.


You have 12 coins, 11 of which are the same weight and one counterfeit coin which has a different weight from the others. You have a balance that in each weighing tells you whether the two sides are of equal weight, or which side weighs more. How many weighings do you need to determine which is the counterfeit coin, and whether it weighs more or less than the other coins? How can you determine these in that number of weighings?

Solution     Reveal