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?

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?

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?

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?

What is the best way to shunt these carriages so that each train can continue its journey?

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?

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

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 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?

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

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

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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 to have an ordered approach.

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

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

In this matching game, you have to decide how long different events take.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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

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

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....?

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

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

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

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

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

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

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'.

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

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?

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?

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

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.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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

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

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.

These practical challenges are all about making a 'tray' and covering it with paper.

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?