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

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

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

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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?

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?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

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?

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

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?

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?

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

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?

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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?

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.

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

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!

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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?

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?

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.

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

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!

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.

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.

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?

Can you make square numbers by adding two prime numbers together?

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.

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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?

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

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

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

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?

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

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

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

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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?

This challenge is about finding the difference between numbers which have the same tens digit.

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

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?