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?

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?

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

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?

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 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 many different triangles can you make on a circular pegboard that has nine pegs?

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

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?

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.

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.

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?

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

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?

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?

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

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?

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?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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 create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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'.

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

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?

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.

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.

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

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

An activity making various patterns with 2 x 1 rectangular tiles.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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....?

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?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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?

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?

How many trapeziums, of various sizes, are hidden in this picture?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?