in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

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?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

To avoid losing think of another very well known game where the patterns of play are similar.

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.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

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.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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.

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

Can you beat the computer in the challenging strategy game?

Can you explain the strategy for winning this game with any target?

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Here is a chance to play a fractions version of the classic Countdown Game.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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?

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Here is a chance to play a version of the classic Countdown Game.

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

How good are you at finding the formula for a number pattern ?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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.

Can you find the pairs that represent the same amount of money?

Use Excel to explore multiplication of fractions.

A game in which players take it in turns to choose a number. Can you block your opponent?

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

Use Excel to investigate the effect of translations around a number grid.

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

Use an interactive Excel spreadsheet to explore number in this exciting game!

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

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.