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

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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!

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

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 find the chosen number from the grid using the clues?

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

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

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

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

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

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?

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!

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

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

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?

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?

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.

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?

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

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

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?

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

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.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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

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?

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?

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

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

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

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.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

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

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

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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.

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

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

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

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?

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