Question: A computerized housing service has a list of 50 men and 50 women. Names are selected at random; how many names must be chosen to guarantee two names of the same gender?
How many people must be in a group to guarantee that 2 people in the group have the same birthday (don't forget leap year)?
In a group of 25 people, must there be at least 3 who were born in the same month?
Prove that if four numbers are chosen from the set {1, 2, 3, 4, 5, 6}, at least one pair must add up to 7. (Hint: Find all the pairs of numbers from the set that add to 7.)