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.

Can you work out some different ways to balance this equation?

Can you replace the letters with numbers? Is there only one solution in each case?

Have a go at balancing this equation. Can you find different ways of doing it?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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

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?

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?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

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?

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

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?

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.

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!

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

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

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 a great variety of ways of asking questions which make 8.

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

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

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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?

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

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

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

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?

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.

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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?

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

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.

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

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?

Can you complete this jigsaw of the multiplication square?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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?

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

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

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

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