What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

An investigation that gives you the opportunity to make and justify predictions.

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?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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?

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Find out about Magic Squares in this article written for students. Why are they magic?!

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

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 order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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

Can you make square numbers by adding two prime numbers together?

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!

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!

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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?

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.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

This dice train has been made using specific rules. How many different trains can you make?

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

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

What happens when you round these three-digit numbers to the nearest 100?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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