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.

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

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?

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.

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?

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?

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

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.

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

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

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!

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.

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

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

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

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

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

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

Number problems at primary level that may require resilience.

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?

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

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

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

The clues for this Sudoku are the product of the numbers in adjacent squares.

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!

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

This Sudoku requires you to do some working backwards before working forwards.

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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?

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?

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

This task combines spatial awareness with addition and multiplication.

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

In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.

Related resources supporting pupils' understanding of multiplication and division through playing with numbers.

Resources to support understanding of multiplication and division through playing with number.

More resources to support understanding multiplication and division through playing with numbers