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?

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

Number problems at primary level that may require resilience.

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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?

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

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

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.

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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?

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

This challenge combines addition, multiplication, perseverance and even proof.

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?

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

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

This task combines spatial awareness with addition and multiplication.

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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?

This number has 903 digits. What is the sum of all 903 digits?

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

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?

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

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?

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

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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

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

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?

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

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

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" .

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

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

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. . . .

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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

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.

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.

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?

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?