MathDB

18

Part of 1987 IMO Shortlist

Problems(1)

Determine the smallest h(r) (IMO SL 1987-P18)

Source:

8/19/2010
For any integer r≥1r \geq 1, determine the smallest integer h(r)≥1h(r) \geq 1 such that for any partition of the set {1,2,⋯ ,h(r)}\{1, 2, \cdots, h(r)\} into rr classes, there are integers a≥0 ;1≤x≤ya \geq 0 \ ; 1 \leq x \leq y, such that a+x,a+y,a+x+ya + x, a + y, a + x + y belong to the same class.
Proposed by Romania
combinatoricspartitionColoringRamsey TheorySet systemsIMO Shortlist