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

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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?

Are these statements always true, sometimes true or never true?

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

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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

Fill in the numbers to make the sum of each row, column and diagonal equal to 15.

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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

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?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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.

There were 22 legs creeping across the web. How many flies? How many spiders?

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

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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?

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

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

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?

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

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!

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

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?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

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

You have 5 darts and your target score is 44. How many different ways could you score 44?

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?

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

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!