MathDB

6

Part of 1988 Irish Math Olympiad

Problems(1)

Group Among n Blocks with Weights

Source: 1988 IrMO Paper 1 Problem 6

9/28/2017
Suppose you are given nn blocks, each of which weighs an integral number of pounds, but less than nn pounds. Suppose also that the total weight of the nn blocks is less than 2n2n pounds. Prove that the blocks can be divided into two groups, one of which weighs exactly nn pounds.
combinatorics