MathDB
Weighted Blocks

Source: ISL 2019 C2

September 22, 2020
IMO ShortlistIMO Shortlist 2019combinatoricsinductionLocal argument

Problem Statement

You are given a set of nn blocks, each weighing at least 11; their total weight is 2n2n. Prove that for every real number rr with 0≤r≤2n−20 \leq r \leq 2n-2 you can choose a subset of the blocks whose total weight is at least rr but at most r+2r + 2.
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