There are 101 coins, 50 of which are counterfeit and differ in weight by 1 gram from the genuine ones. Pete took one coin and wants to determine if it is counterfeit with one weighing on a scale with a needle showing the difference in weight between the pans. Can he do it?

#
Let's set aside Petya's coin. Divide the remaining 100 coins into two piles of 50 coins each and compare the weights of these piles. If they differ by an even number of grams, then the coin we are interested in is genuine. If the difference in weights is odd, then the coin is counterfeit.

## Answer

He can.