Question

The minimum number n of integers to be selected from the set S = {1, 2, ....., 9} so that the sum of two of the n integers is even is_______.

• A. 3
• B. 5
• C. 6
• D. 4

Answer 1

The correct option is A 3

option (a)

The sum of two even integers or two odd integers is even.

The pigeonholes are {1, 3, 5, 7, 9} and {2, 4, 6, 8}.

$\therefore$ The minimum number of integers required
= number of pigeonholes + 1
= 3