### Have You Got It?

Can you explain the strategy for winning this game with any target?

### Counting Factors

Is there an efficient way to work out how many factors a large number has?

### Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

##### Age 11 to 14 ShortChallenge Level

Which of the following statements is false?

A An octagon has $20$ diagonals

B A hexagon has $9$ diagonals

C A hexagon has $4$ more diagonals than a pentagon

D A pentagon has the same number of diagonals as it has sides

E A quadrilateral has twice as many diagonals as it has sides

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.