Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Pythagorean Triples

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

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?

Overlapping Beer Mats

Stage: 3 Short Challenge Level:

Two beer mats, each the shape of a regular hexagon with area 36cm$^2$, are placed on top of each other, as shown below.

If they are placed so that the corner of the lower beer mat is in the centre of the higher beer mat, as shown below, what is the area of the overlap?

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

This problem is adapted from the World Mathematics Championships

You can find more short problems, arranged by curriculum topic, in our short problems collection.