5

Part of 1989 Turkey Team Selection Test

Problems(1)

n weights weigh < 2n

Source: Turkey TST 1989 - P5

n\geq2

weights such that each weighs a positive integer less than

n

and their total weights is less than

2n

. Prove that there is a subset of these weights such that their total weights is equal to

n

inequalities proposedinequalities