Can you explain the surprising results Jo found when she calculated the difference between square numbers?
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
A red square and a blue square overlap. Is the area of the overlap always the same?
Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
A 10×10×10 cube is made from 27 2×2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
The sums of the squares of three related numbers is also a perfect square - can you explain why?
