This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

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.

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?

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

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

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

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

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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?

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?

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?

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

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

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

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 working in a systematic way will ensure none are left out.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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

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

Number problems at primary level that require careful consideration.

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

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?

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

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

This task follows on from Build it Up and takes the ideas into three dimensions!

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

Can you replace the letters with numbers? Is there only one solution in each case?

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.

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?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

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?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.