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

A game that tests your understanding of remainders.

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?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

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

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?

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

Can you complete this jigsaw of the multiplication square?

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?

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

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?

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.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

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

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?

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?

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

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?

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

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?

Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.

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?

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

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.

Number problems at primary level that require careful consideration.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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?

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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

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

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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

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?

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!

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

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

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

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

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