MathDB

Maximum size of a subset S

Source: IMO Shortlist 1996, C3, Iran PPCE 1997, E2, P1

August 9, 2008

combinatoricsAdditive combinatoricsAdditive Number TheoryExtremal combinatoricsSubsetsIMO Shortlist

Problem Statement

Let

k,m,n

be integers such that 1 < n \leq m \minus{} 1 \leq k. Determine the maximum size of a subset

S

of the set \{1,2,3, \ldots, k\minus{}1,k\} such that no

n

distinct elements of

S

add up to

m.