Can you find the chosen number from the grid using the clues?

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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?

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

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?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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?

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

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?

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

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?

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

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

How many possible necklaces can you find? And how do you know you've found them all?

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

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?

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?

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.

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

This dice train has been made using specific rules. How many different trains can you make?

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?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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.

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

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

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.

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 make square numbers by adding two prime numbers together?

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?

Can you find all the ways to get 15 at the top of this triangle of numbers?

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!

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?