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

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

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

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?

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

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?

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?

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

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?

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?

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

This challenge combines addition, multiplication, perseverance and even proof.

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

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?

This task combines spatial awareness with addition and multiplication.

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.

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.

Number problems at primary level that may require determination.

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.

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?

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?

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

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

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?

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

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

Here is a chance to play a version of the classic Countdown Game.

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

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?

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

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?

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

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

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

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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

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?

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

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.

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.

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

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

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

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.