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Chapter 5: Problem 2

Show that if eight people are in a room, at least two of them have birthdays that occur on the same day of the week.

Short Answer

Expert verified
By applying the Pigeonhole Principle, it can be proven that if eight people are in a room, at least two of them have birthdays occurring on the same day of the week.

Step by step solution

01

Understanding the Problem

The problem is to prove that if there are eight people in a room, at least two of them have birthdays on the same day of the week. The crucial aspect to understand here is that there are only seven days in a week.
02

Application of Pigeonhole Principle

According to the Pigeonhole Principle, if there are eight 'items' (eight people with birthdays in this case) and they are put into seven 'containers' (the seven days of the week), then at least one container must contain more than one item. Therefore, at least one day of the week must be the birthday for more than one person.

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