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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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?

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

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.

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.

There are lots of different methods to find out what the shapes are worth - how many can you find?

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

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?

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

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

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

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?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

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?

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

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

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?

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?

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

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

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

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

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

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

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?

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.

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?

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

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

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

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

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

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

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?

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

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?

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

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?

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

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

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