Nine Colours
Age 11 to 16
Challenge Level
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Triangles to Tetrahedra
Age 11 to 14
Challenge Level
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Reflecting Squarely
Age 11 to 14
Challenge Level
In how many ways can you fit all three pieces together to make shapes with line symmetry?
Cuboids
Age 11 to 14
Challenge Level
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Same Length
Age 11 to 16
Challenge Level
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Isosceles Triangles
Age 11 to 14
Challenge Level
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Kite in a Square
Age 14 to 18
Challenge Level
Can you make sense of the three methods to work out what fraction of the total area is shaded?
NRICH is part of the family of activities in the Millennium Mathematics Project.