How many different rhythms can you make by putting two drums on the wheel?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
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....?
Use the clues to colour each square.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
What happens when you try and fit the triomino pieces into these two grids?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you find all the different ways of lining up these Cuisenaire rods?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Can you cover the camel with these pieces?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.
What is the best way to shunt these carriages so that each train can continue its journey?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
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?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
How many trains can you make which are the same length as Matt's, using rods that are identical?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.