Copyright © University of Cambridge. All rights reserved.
'Spot the Fake' printed from https://nrich.maths.org/
One coin among $N$ identical-looking coins is a fake and is slightly heavier than the others, which all have the same weight. To compare two groups of coins you are allowed to use a set of scales with two pans which balance exactly when the weight in each pan is the same. What is the largest value of $N$ for which the fake coin can be identified using a maximum of two such comparisons?
If you liked this problem,
here is an NRICH task that challenges you to use similar mathematical ideas.