```
```#mathsonamug #maths pic.twitter.com/9WbMgghlfB

— Dr. Sean (@seanelvidge) January 12, 2016

This is one of my favourite puzzles. It is a simple, life long game. Using exactly four 4s make as many numbers as you can. You can use the operators \(+,\,-,\,\times,\,\div,\,!,\,\mbox{^},\,.,\,\sqrt{},\Gamma\) and concatenation. You *must* use all four 4s. Let me start you off with a couple:

\(\begin{align*}

0 &= 44 – 44, \\

1 &= \frac{44}{44}, \\

2 &= \frac{4}{4} + \frac{4}{4}.

\end{align*}\)

The value on the mug is a solution for the number 169.