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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?

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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?

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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?

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

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

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This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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

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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?

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

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

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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?

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

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Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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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.

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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?

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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?

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

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Use these head, body and leg pieces to make Robot Monsters which are different heights.

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

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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.

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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?

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If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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

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

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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?

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If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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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.

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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?

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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?

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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?

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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?

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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?

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

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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.

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

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Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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

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Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?

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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?

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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?

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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?

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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?

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Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

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Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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

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I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

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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?

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These two group activities use mathematical reasoning - one is numerical, one geometric.