Question

Show that at least three of any 25 days chosen must fall in the same month of the year.

Short answer

At least 3 of any 25 days taken must be on the same month of the year.

Step-by-step solution

Introduction

The purpose is to show that at least 3 of any 25 days taken must come in the same month of the year.

Prove the result by contradiction.

Prove by contradiction

If there were at most 2 days of any 25 days taken that must come in the same month of the year.

As there are 12 months in a year and 2 days could be taken per month.

Then\(2 \times 12 = 24\)days account for 12 months.

This contradicts from taking 25 days.

Therefore, at least 3 of any 25 days taken must be on the same month of the year.