### Pythagorean Triples

How many right-angled triangles are there with sides that are all integers less than 100 units?

### Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

### The Old Goats

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't fight each other but can reach every corner of the field?

# Tennis

##### Stage: 3 Challenge Level:

On a given tennis court, the distance between the baseline and the net is $10$ metres and the distance between the service line and the net is $5$ metres. The net is $0.9$ metres high. A player serves the ball directly above the baseline (assume the ball travels in a straight line).

1. What is the minimum height that the ball can be hit at so as to ensure the ball lands in the service area?
2. How far does the ball travel before it hits the ground?
3. Assuming the player receiving the serve stays on the baseline and hits the ball as it crosses the baseline, how should the server hit the ball so that his opponent has the least time to receive the serve?
This problem was given by Mikael Brown.