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?

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

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

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 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?

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?

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

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

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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

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?

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?

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 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.

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?

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?

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?

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

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?

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?

Investigate the different ways you could split up these rooms so that you have double the number.

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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

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?

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

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

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

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?

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

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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?

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?

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

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.

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

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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.

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?