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

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?

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?

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.

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.

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?

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

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

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?

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 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.

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

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

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?

Number problems at primary level that may require resilience.

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

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

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?

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!

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 find different ways of creating paths using these paving slabs?

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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?

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

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

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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?

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.

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?

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?

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

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

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

This task combines spatial awareness with addition and multiplication.

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?

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!

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

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

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?

What is the least square number which commences with six two's?

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.

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

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?

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?