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?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Can you use the information to find out which cards I have used?

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?

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

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

An investigation that gives you the opportunity to make and justify predictions.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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

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

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

Have a go at balancing this equation. Can you find different ways of doing it?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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?

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

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Can you work out some different ways to balance this equation?

What happens when you round these three-digit numbers to the nearest 100?

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

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

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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

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?

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?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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.

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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

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?

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 make square numbers by adding two prime numbers together?

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

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.

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