Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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?

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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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?

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?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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?

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?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

What happens when you try and fit the triomino pieces into these two grids?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Try this matching game which will help you recognise different ways of saying the same time interval.

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?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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?

This challenge is about finding the difference between numbers which have the same tens digit.

Find all the numbers that can be made by adding the dots on two dice.

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?

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Can you fill in the empty boxes in the grid with the right shape and colour?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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?

Can you find all the different triangles on these peg boards, and find their angles?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Try out the lottery that is played in a far-away land. What is the chance of winning?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

My coat has three buttons. How many ways can you find to do up all the buttons?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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. . . .

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.