11.6

Part of 2024 All-Russian Olympiad Regional Round

Problems(1)

Easy problem with weights

Source: 2024 All-Russian Olympiad Regional Round

Teacher has 100 weights with masses

1

2

\dots

100

g. He wants to give 30 weights to Petya and 30 weights to Vasya so that no 11 Petya's weights have the same total mass as some 12 Vasya's weights, and no 11 Vasya's weights have the same total mass as some 12 Petya's weights. Can the teacher do that?

weightsalgebraeasy