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

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?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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

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?

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?

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?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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?

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?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Can you make square numbers by adding two prime numbers together?

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?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

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?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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.

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

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!

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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!

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

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?

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

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

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