Mirtes works in a department with seven other colleagues, making a total of eight. On January $1^{-0}$, Mirtes comments that this year two of the employees in the department will have their birthdays on the same day of the week, because there are seven days in a week and eight colleagues.

a) Using Mirtes' idea, determine the minimum number of employees the department would need to ensure that two people have the same zodiac sign.

b) What is the minimum number of employees the department would need to ensure that at least four of them have their birthdays on the same day of the week this year?
Solution

a) There are twelve signs. Therefore, to ensure that two people have the same sign, thirteen people are enough!

b) There are seven days in a week. Therefore, to ensure that at least four people have their birthday on the same day of the week this year, we will need $3 \times 7+1=22$ people!