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

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

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

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .

Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .

This challenge combines addition, multiplication, perseverance and even proof.

This task combines spatial awareness with addition and multiplication.

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

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

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

This Sudoku, based on differences. Using the one clue number can you find the solution?

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

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

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

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

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.

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?

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.

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

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

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

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.

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?

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

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

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?

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?

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

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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?

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

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?

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.

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?