Question

Explain pigeon hole 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

There are 7 days in the week.
Pidgeon hole principle says at least one hole (day of the week) that:
\[\left\lceil\frac{36}{7} \right\rceil = 6\]
will have at least \(6\) pidgeons (birthdays).

Answer 2

If you have \(p\) pigeons and \(h\) holes, then some hole must have at least \(k\) pidgeons: \[
\left\lceil \frac{p}{h} \right\rceil =k
\]