Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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?
Shady Symmetry
Age 11 to 14
Challenge Level
How many different symmetrical shapes can you make by shading triangles or squares?
Hexy-metry
Age 14 to 16
Challenge Level
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
The Spider and the Fly
Age 14 to 16
Challenge Level
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
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?
On the Edge
Age 11 to 14
Challenge Level
If you move the tiles around, can you make squares with different coloured edges?
Square It
Age 11 to 16
Challenge Level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
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?
Quadrilaterals Game
Age 11 to 14
Challenge Level
A game for 2 or more people, based on the traditional card game Rummy.
Shapely Pairs
Age 11 to 14
Challenge Level
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
Property Chart
Age 11 to 14
Challenge Level
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
Semi-regular Tessellations
Age 11 to 16
Challenge Level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Transformation Game
Age 11 to 14
Challenge Level
Why not challenge a friend to play this transformation game?
Which Solids Can We Make?
Age 11 to 14
Challenge Level
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
Constructing Triangles
Age 11 to 14
Challenge Level
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
NRICH is part of the family of activities in the Millennium Mathematics Project.