Question

How many numbers must be selected from the set left curly bracket 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 right curly bracket in order to guarantee that at least one pair adds up to 11

Answer 1

6 numbers

Explanation:

Given

`x = \{1,2,3,4,5,6,7,8,9,10\}`

Required

Pairs that add up to 11

The pairs are:

`x = \{\{1,10\},\{2,9\},\{3,8\},\{4,7\},\{5,6\}\}`

In the above set, we have:

`n(x) =5`

Using pigeonhole principle

This principle implies that, there is at least 1 more pair.

Hence, the numbers that must be selected to guarantee the required sum of 11 is:

`n= 5+1` --- The 1 represents (at least 1 more)

`n=6`