In a physics class, the teacher set up the following experiment. He placed 16 weights with masses of $1, 2, 3, \ldots, 16$ grams on a balance scale so that one of the pans was heavier. Fifteen students took turns leaving the classroom and each took one weight, and after each student left, the balance changed its position and the opposite pan became heavier. Which weight could have remained on the scale?
Since at any given moment the masses on the scales differed by at least 1 gram, in order for the opposite scale to outweigh, it is necessary to remove a weight of no less than two grams. Therefore, no student could have taken a 1-gram weight when leaving the class.

## Answer

A 1-gram weight remained on the scales.