Question

Prove that in a group of 25 people, some three of them must have birthdays in the same month. Please provide a step-by-step explanation.

Answer 1

Pigeonhole Principle:

If there are n+1 number of pigeons and and they assigned to n number of pigeonholes then atleast one pigeonhole must contains two or more pigeons.

We have 25 people in a group and there are 12 months in a year

N=25 and K=12

So according to pigeonhole principle,

Three people in a group must have birthdays in a same month if ceil(N/K)>=3

So,ceil(25/12)=ceil(2.0833)=3

Therefore, by pigeonhole principle we can say that some three of them must have birthdays in the same same month.