Use the information about Sally and her brother to find out how many children there are in the Brown family.

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!

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?

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 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?

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

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

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?

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

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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

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?

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

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.

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.

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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

Play this game and see if you can figure out the computer's chosen number.

It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

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

Number problems at primary level that require careful consideration.

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

How would you find out how many football cards Catrina has collected?

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

How will you work out which numbers have been used to create this multiplication square?

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

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?

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

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?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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?

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?

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

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