Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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.

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

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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.

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?

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!

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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 were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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

You have 5 darts and your target score is 44. How many different ways could you score 44?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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!

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?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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

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?

The pages of my calendar have got mixed up. Can you sort them out?

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 work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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?

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

Can you substitute numbers for the letters in these sums?

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

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?