### Plum Tree

Label this plum tree graph to make it totally magic!

### Magic W

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

### 2-digit Square

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

# Screen Shot

##### Age 14 to 16 Challenge Level:
A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at $45^\circ$ before being reflected across to the opposite wall and so on until it hits the screen.

If the screen is $20$ metres down the corridor from the light source and if the corridor is $2$ metres wide, find the position on the screen where the point of light appears.

Part Two: Now remember that the screen is moveable. The distance, $d$, of the screen down the corridor can change, so the position where the point of light appears on the screen will depend on $d$. Can you find a function, expressing the position of the light on the screen in terms of $d$?

Part Three: If the ray leaves the source making an angle $\theta$ with the direction of the corridor, and the distance, $d$, of the screen down the corridor can still change, the position where the point of light appears on the screen will depend on $d$ and on $\theta$ . Can you find this function?