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

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?

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

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

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.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

Ben has five coins in his pocket. How much money might he have?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Can you replace the letters with numbers? Is there only one solution in each case?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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.

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?

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?

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

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

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!

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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?