### Upsetting Pitagoras

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

### Triangle Mid Points

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

### There and Back

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

# From Point to Point

##### Stage: 4 Challenge Level:

How can you get from $(10,66)$ to  $(20,12)$

using only integer multiples of the vectors

$\begin{pmatrix}2\\-3\end{pmatrix}$ and $\begin{pmatrix}3\\2\end{pmatrix}$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.