A game that tests your understanding of remainders.

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

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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?

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

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?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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?

Find the highest power of 11 that will divide into 1000! exactly.

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.

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

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

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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?

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

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

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.

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

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

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

Can you complete this jigsaw of the multiplication square?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

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?

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?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Can you find what the last two digits of the number $4^{1999}$ are?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

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

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

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

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?

Number problems at primary level that may require determination.

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

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!

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?

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.