Imagine you were given the chance to win some money... and imagine you had nothing to lose...

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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.

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

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

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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

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

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

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

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

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

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?

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

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?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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.

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

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

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?

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?

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?

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

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

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?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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?

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

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?

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

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?

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?

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

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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?

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?