Sample Problems: Applying The Pigeon Hole Principle

• (A) Given 9 different types of beer steins to fill at a local pub, how many steins would it take to insure that at least one type of stein is filled three times? (19)
• (B) There are 8 different flavors of ice cream. What is the minimum number of children needed to insure that at least one flavor is ordered by at least three children? (17)
• (C) There are four different types of pizza: pepperoni, sausage, cheese, mushroom. What is the minimum number of people required to insure that at least one type of pizza is ordered by at least three people? (9)
• (D) What is the minimum number of customers needed to insure that at least one category of video is rented by at least three customers? The categories are Romance, Horror, Action, Mystery, Comedy (11)
• (E) A sports team, Team Q, participates in a conference of 10 teams. What is the minimum number of games Team Q must play to insure that they play at least one team twice? (10)
• (F) The colors of M & Ms are: red, green, brown, yellow, blue, and orange. How many M & Ms would you have to grab from a package to ensure that you have grabbed at least three of one color? (13)
• (G) Given three electives, how many students, choosing only one elective each, will be needed to assure at least 24 students are in one of the electives? (70)
• (H) Ten classes are offered. Each person enrolls in one class. How many students will have to enroll to insure at least one class size to be at least 8? (71)
• (I) There are six summer classes offered at ISU. What would be the least number of people needed to sign up for classes to insure that there are 8 people in at least one class? (43)
• (J) How many students and televisions would there be to ensure that the basic cable television show was being watched by more than one child? The number of basic cable stations is C. (C + 1)