Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Watch this animation. What do you see? Can you explain why this happens?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

What is the best way to shunt these carriages so that each train can continue its journey?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

Can you fit the tangram pieces into the outlines of the convex shapes?

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you fit the tangram pieces into the outline of Mah Ling?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Can you fit the tangram pieces into the outlines of the people?

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you find a way of counting the spheres in these arrangements?

Can you mark 4 points on a flat surface so that there are only two different distances between them?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Can you fit the tangram pieces into the outline of the house?

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.

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

How many moves does it take to swap over some red and blue frogs? Do you have a method?

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?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

How many different symmetrical shapes can you make by shading triangles or squares?

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

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?

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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.