Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
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?
What is the best way to shunt these carriages so that each train can continue its journey?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
How many different triangles can you make on a circular pegboard that has nine pegs?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Two sudokus in one. Challenge yourself to make the necessary connections.
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
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?
Can you find all the different ways of lining up these Cuisenaire rods?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
A Sudoku with clues as ratios.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?