MathDB

{A,B,C} is a partition of {1,2,...3n} and |A|=|B|=|C|=n

Source: India tst 2003 p9

March 15, 2012

inequalitiesinductionnumber theorycombinatorics proposedcombinatorics

Problem Statement

Let

n

be a positive integer and

\{A,B,C\}

a partition of

\{1,2,\ldots,3n\}

such that

|A|=|B|=|C|=n

. Prove that there exist

x \in A

y \in B

z \in C

such that one of

x,y,z

is the sum of the other two.