# Pigeon Hole Principle

• Aug 31st 2009, 07:49 AM
problem
Pigeon Hole Principle
A professor teaching a Mathematics course gives a multiple choice quiz that has 10 questions,each with four possible answers.What is the minimum number of students that must be in the professor's class in order to guarantee that at least 3 paper sheets are identical?
(Assume that no answers are left blank)

Can anyone help me??(Worried)
• Aug 31st 2009, 07:59 AM
Isomorphism
Quote:

Originally Posted by problem
A professor teaching a Mathematics course gives a multiple choice quiz that has 10 questions,each with four possible answers.What is the minimum number of students that must be in the professor's class in order to guarantee that at least 3 paper sheets are identical?
(Assume that no answers are left blank)

Can anyone help me??(Worried)

Since there are \$\displaystyle 4^{10}\$ different possibilities of answers, if there were a minimum of \$\displaystyle 4^{10} + 1\$ students, some two paper sheets would definitely be identical.