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?

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

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

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?

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?

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?

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

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

Number problems at primary level that may require resilience.

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?

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?

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

This task combines spatial awareness with addition and multiplication.

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?

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?

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

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?

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

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.

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

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

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

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.

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

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?

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?

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?

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

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

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

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!

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

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.

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?

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

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?

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.

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

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

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

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?

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.

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

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

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?

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?