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

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?

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?

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.

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

Can you find different ways of creating paths using these paving slabs?

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?

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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 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!

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

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

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?

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

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

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?

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

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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 challenge combines addition, multiplication, perseverance and even proof.

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?

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

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?

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?

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

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

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.

This task combines spatial awareness with addition and multiplication.

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

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

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?

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?

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

Find the next number in this pattern: 3, 7, 19, 55 ...

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

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

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

How would you count the number of fingers in these pictures?

Number problems at primary level that require careful consideration.

Number problems at primary level that may require resilience.

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

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?