MathDB
Korea Second Round 2011

Source: Korea Second Round 2011 #7

August 21, 2011
inductioncombinatorics proposedcombinatorics

Problem Statement

There are nn students each having rr positive integers. Their nrnr positive integers are all different. Prove that we can divide the students into kk classes satisfying the following conditions.
(a) k≤4r k \le 4r
(b) If a student AA has the number mm, then the student BB in the same class can't have a number ll such that (m−1)!<l<(m+1)!+1 (m-1)! < l < (m+1)!+1
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