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

If you have only four weights, where could you place them in order to balance this equaliser?

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?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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.

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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 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 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.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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?

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

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?

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 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!

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?

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 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 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. . . .

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

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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?

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?

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

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

Got It game for an adult and child. How can you play so that you know you will always win?

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

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?

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

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?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

This task follows on from Build it Up and takes the ideas into three dimensions!

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?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?