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 this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

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

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

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

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

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.

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?

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

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?

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

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

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?

This problem is designed to help children to learn, and to use, the two and three times tables.

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?

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

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

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

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

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

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

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?

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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

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. . . .

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

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?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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?

Can you work out some different ways to balance this equation?

Have a go at balancing this equation. Can you find different ways of doing it?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?