Question

explain pigeonhole principle. using this principle show that in any group of 36 people , we can always find 6 people who were born on the same day of week?

Answer 1

i might not explain this well enough but i give it a shot

A week = 7 days
since there are 36 people then there is at least \[\lfloor \frac{ 36 }{ 7 } \rfloor \] =5 people born at the same day since you cant have 36 days when there is a maximum of 7 days by the pigeon hole principle but since there is 36 people there is still 1 person remaining and that last person remaining will take up a day that is the same as 5 other people

Answer 2

Assume there are at most 5 people born on the same day.
There are 7 days in a week.
So at most the total number of people will be 7*5 = 35.
But here we have 36 people. And so the 36th person has to be born on one of the 7 days making the total number of people born on that day 6.