Show that if 7 integers are selected from the first 10 positive integers there must be at least 2 pairs of these integers with the sum 11. Is the conclusion true if 6 integers are selected instead of 7 How many numbers must be selected from the set {1,3,5,7,9,11,13,15} to guarantee that at least one pair of these numbers add up to 16.

Show that if 7 integers are selected from the first 10 positive integers there must be at least 2 pairs of these integers with the sum 11

Is the conclusion true if 6 integers are selected instead of 7

How many numbers must be selected from the set {1,3,5,7,9,11,13,15} to guarantee that at least one pair of these numbers add up to 16.