MathDB

8

Part of 2011 Korea Junior Math Olympiad

Problems(1)

n students each having r positive integers, nr integers all different, classes

Source: KJMO 2011 p8

5/4/2019
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≤4rk \le 4r (b) If a student AA has the number mm, then the student BB in the same class can't have a number ℓ\ell such that (m−1)!<ℓ<(m+1)!+1(m - 1)! < \ell < (m + 1)! + 1
number theorycombinatoricscombinationSubsets