Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
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?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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....?
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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 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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
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?
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?
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
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.
How many triangles can you make on the 3 by 3 pegboard?
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?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
In this matching game, you have to decide how long different events take.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
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?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
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.
Can you find all the different triangles on these peg boards, and find their angles?
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
Investigate the different ways you could split up these rooms so that you have double the number.