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.

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?

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

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

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?

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

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 Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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

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

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?

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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.

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

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

This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

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

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

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

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?

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?

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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 a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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.

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?

Number problems at primary level that require careful consideration.

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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

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?

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

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.

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

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

Number problems at primary level that may require determination.

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

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

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?

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.