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?

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

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?

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?

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.

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

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.

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?

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.

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?

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?

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

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?

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?

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

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

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

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!

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?

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

This task combines spatial awareness with addition and multiplication.

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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?

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!

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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?

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

Number problems at primary level that may require resilience.

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?

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

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

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?

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?

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?

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.

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?

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. . . .

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

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?

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

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 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?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?