### Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

### Retracircles

Four circles all touch each other and a circumscribing circle. Find the ratios of the radii and prove that joining 3 centres gives a 3-4-5 triangle.

### A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

# Snookered

##### Stage: 4 and 5 Challenge Level:

At a recent snooker competition, one player found herself faced with the situation below:

Her next shot was the brown ball which was nicely positioned on the lip of the pocket. Unfortunately she was unable to hit the brown ball directly as the black ball was in the way.

• Could she pot the brown ball by playing the white ball off only one cushion?
• Could she pot the brown ball by playing the white ball off two cushions?
• What are the coordinates of any points on the cushion that she could aim for to pot the brown ball?