Exploring and noticing

problem
Napkin

Age

14 to 16

Challenge level

A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.
problem
Of all the areas

Age

14 to 16

Challenge level

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
problem
Sitting pretty

Age

14 to 16

Challenge level

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?
problem
Plus minus

Age

14 to 16

Challenge level

Can you explain the surprising results Jo found when she calculated the difference between square numbers?
problem
Alphabet soup

Age

11 to 14

Challenge level

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.
problem
How old am I?

Age

14 to 16

Challenge level

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
problem
Differences

Age

11 to 14

Challenge level

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
problem
Quad in quad

Age

14 to 18

Challenge level

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
problem
Tet-trouble

Age

14 to 16

Challenge level

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?
problem
Dozens

Age

7 to 14

Challenge level

Can you select the missing digit(s) to find the largest multiple?