### In Particular

Write 100 as the sum of two positive integers, one divisible by 7 and the other divisible by 11. Then find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers.

### Garfield's Proof

Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.

### For What?

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

# Screen Shot

##### Stage: 4 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?