Kenneth Rosen Edition 7 Exercise 6.2 Question 15 (Page No. 405)

Question

How many numbers must be selected from the set $\{1, 2, 3, 4, 5, 6\}$ to guarantee that at least one pair of these numbers add up to $7?$

Answer 1

Summation of THREE pairs {1, 6}, {2, 5} and{3, 4}  are equal to 7

There are THREE pairs of numbers that sum to 7.

You may select one of each of these pairs to get a set a set of numbers that will not add to 7.

If you select one more - you will have a pairs adding to 7.

Therefore 4 numbers must be selected to guarantee a sum of 7 for some pair.

Ans should be 4