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?

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.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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

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

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

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

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.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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?

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?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

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.

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 use this information to work out Charlie's house number?

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

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

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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.?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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

What could the half time scores have been in these Olympic hockey matches?

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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

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

In how many ways can you stack these rods, following the rules?

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

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

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

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

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do 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?

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.