MathDB
Putnam 1996 A4

Source:

June 4, 2014
Putnamcollege contests

Problem Statement

SS be a set of ordered triples (a,b,c)(a,b,c) of distinct elements of a finite set AA. Suppose that
[*] (a,b,c)∈S  ⟺  (b,c,a)∈S(a,b,c)\in S\iff (b,c,a)\in S [*] (a,b,c)∈S  ⟺  (c,b,a)∉S(a,b,c)\in S\iff (c,b,a)\not\in S [*] (a,b,c),(c,d,a) both ∈S  ⟺  (b,c,d),(d,a,b) both ∈S(a,b,c),(c,d,a)\text{ both }\in S\iff (b,c,d),(d,a,b)\text{ both }\in S Prove there exists g:A→Rg: A\to \mathbb{R}, such that gg is one-one and g(a)<g(b)<g(c)  ⟹  (a,b,c)∈Sg(a)<g(b)<g(c)\implies (a,b,c)\in S
Back to ProblemsView on AoPS