9

Part of 2003 India IMO Training Camp

Problems(1)

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

Source: India tst 2003 p9

n

be a positive integer and

\{A,B,C\}

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

z \in C

. 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.

inequalitiesinductionnumber theorycombinatorics proposedcombinatorics