Solution: 2015 Winter Midterm - 7
Author: Michiel SmidQuestion
What is the minimum number of people needed so that we can guarantee that at least three of them
have the same birthday? (We ignore leap years; thus, a year has 365 days.)
(a)
$2 \cdot 365 + 1$
(b)
$365^2 + 1$
(c)
$2 \cdot 365$
(d)
$365^2$
Solution
To guarantee that at least two people share the same birthday, the first 365 people each have a different birthday.
The last person must have a birthday that is the same as one of the previous 365 people.
We can apply this to 3 people.
Thus, the minimum number of people needed is double 365 + 1.
$2 \cdot 365 + 1 = 731$