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

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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

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?

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?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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?

Number problems at primary level that may require determination.

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

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.

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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?

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?

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?

Are these statements always true, sometimes true or never true?

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

This task combines spatial awareness with addition and multiplication.

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?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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

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?

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

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?

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.

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?

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?

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

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

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?

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

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?

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

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

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

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?

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

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?

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

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!

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?