There are over 300 people in a movie theater. Prove that there has to be a month of the year when at least 26 of the movie goers have a birthday on the same day.
How do I prove this by contradiction?
number of pigeons = 300 , number of pigeonholes = 365
$number of pigeons/number of pigeonholes = 2$
You're looking at months, not days. So if there's less than $26$ people per month, then the number of people is less than or equal to $25\cdot 12 = 300$, which contradicts the assumption that there are over $300$ people.