In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

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

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?

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?

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?

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

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 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?

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

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.

There were 22 legs creeping across the web. How many flies? How many spiders?

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

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?

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!

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

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?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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

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 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?

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?

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

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?

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

Number problems at primary level that require careful consideration.

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

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?

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

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

Number problems at primary level that may require resilience.

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

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

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

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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

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?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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?

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?

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