+++
title = "24 Birthday Problems"
+++

* Q1

** a)
Use the formulae

\[\sum_{k=1}^N k = \frac{N}{2}(N+1)\]
and \[\sum_{k=1}^N k^2 = \frac{N}{6}(N+1)(2N+1)\]
to evaluate
\[\sum_{k=1}^N (4k+3)^2\]

** b)