MathDB

Putnam 1995 B1

Source:

July 1, 2014

Putnamcollege contests

Problem Statement

For a partition

\pi

of

\{1, 2, 3, 4, 5, 6, 7, 8, 9\}

, let

\pi(x)

be the number of elements in the part containing

x

. Prove that for any two partitions

\pi

and

\pi^{\prime}

, there are two distinct numbers

x

and

y

in

\{1, 2, 3, 4, 5, 6, 7, 8, 9\}

such that

\pi(x) = \pi(y)

and \pi^{\prime}(x) = \pi^{\prime}(y).

Back to Problems View on AoPS