This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Given the products of adjacent cells, can you complete this Sudoku?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Here is a chance to play a version of the classic Countdown Game.

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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

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

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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.

56 406 is the product of two consecutive numbers. What are these two numbers?

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

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?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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?

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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 four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

Use the information to work out how many gifts there are in each pile.

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

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?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

A game that tests your understanding of remainders.

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Can you complete this jigsaw of the multiplication square?

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

How would you count the number of fingers in these pictures?