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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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 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?
What happens when you try and fit the triomino pieces into these two grids?
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?
Can you cover the camel with these pieces?
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?
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?
Use the clues to colour each square.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
These practical challenges are all about making a 'tray' and covering it with paper.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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....?
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. . . .
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
How many different rhythms can you make by putting two drums on the wheel?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
Can you find all the different triangles on these peg boards, and find their angles?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
How many triangles can you make on the 3 by 3 pegboard?
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 activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
In this matching game, you have to decide how long different events take.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?