Upsetting Pitagoras

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

Triangle Midpoints

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 Short Challenge Level:

$x\begin{pmatrix}2\\-3\end{pmatrix} +y\begin{pmatrix}3\\2\end{pmatrix}=\begin{pmatrix}20\\12\end{pmatrix} -\begin{pmatrix}10\\66\end{pmatrix}=\begin{pmatrix}10\\-54\end{pmatrix}$

$2x+3y=10$
$-3x+2y=-54$

$6x+9y=30$
$-6x+4y=-108$

$13y=-78$
$y=-6$
$x=14$

$\begin{pmatrix}10\\66\end{pmatrix}+14\begin{pmatrix}2\\-3\end{pmatrix} -6\begin{pmatrix}3\\2\end{pmatrix}=\begin{pmatrix}20\\12\end{pmatrix}$