MathDB

Bundeswettbewerb Mathematik 1987 Problem 1.2

Source: Bundeswettbewerb Mathematik 1987 Round 1

October 9, 2022

combinatoricsSubsetcardinalitynumber

Problem Statement

Let

n

be a positive integer and

M=\{1,2,\ldots, n\}.

A subset

T\subset M

is called heavy if each of its elements is greater or equal than

|T|.

Let

f(n)

denote the number of heavy subsets of

M.

Describe a method for finding

f(n)

and use it to calculate

f(32).