MathDB

A=\{1,2,\ldots,n\} maxX>minY

Source: China second round 2018 (B) Q3

June 22, 2019

combinatorics

Problem Statement

Let set

A=\{1,2,\ldots,n\} ,

and

X,Y

be two subsets (not necessarily distinct) of

A.

Define that

\textup{max} X

and

\textup{min} Y

represent the greatest element of

X

and the least element of

Y,

respectively. Determine the number of two-tuples

(X,Y)

which satisfies

\textup{max} X>\textup{min} Y.

Back to Problems View on AoPS