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

To answer this question, we need to look at the pairs of numbers in the set {1, 2, 3, 4, 5, 6} that add up to 7. These pairs are (1,6), (2,5), and (3,4).

So, to guarantee that at least one pair of these numbers add up to 7, we would need to select 4 numbers.

Here's why:

In the worst-case scenario, you could pick three numbers and none of them form a pair that adds up to 7. For example, you could pick 1, 2, and 3. None of these numbers form a pair that adds up to 7.

However, once you pick a fourth number, you are guaranteed to have at least one pair that adds up to 7. For example, if you have already picked 1, 2, and 3, and then you pick 4, you now have the pair (3,4) that adds up to 7.

So, you need to select at least 4 numbers from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one pair of these numbers add up to 7.