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subset of {1,2,..,100} with 48 elements has 11/(a+b) (HOMC 2009 J Q11)

Source:

July 25, 2019

combinatoricsnumber theorydivisible

Problem Statement

Let

A = \{1,2,..., 100\}

and

B

is a subset of

A

having

48

elements. Show that

B

has two distint elements

x

and

y

whose sum is divisible by

11