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

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

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?

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

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.

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?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

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

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

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

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

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

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

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?

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

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

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?

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

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

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

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?

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

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

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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

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

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

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!

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?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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.

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?

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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.

In how many ways can you stack these rods, following 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.

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.

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

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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

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

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

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

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?