Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

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?

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Investigate what happens when you add house numbers along a street in different ways.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Delight your friends with this cunning trick! Can you explain how it works?

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.

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

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

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.

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?

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?

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.

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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.

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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

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

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?

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

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

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?

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.

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

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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.

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?

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?

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!

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?