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?

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

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

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

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

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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

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?

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

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

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

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 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.

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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?

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

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

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

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

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

Can you substitute numbers for the letters in these sums?

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!

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?

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.

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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.

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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.

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

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!

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

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?

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?

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

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?

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?

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

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

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

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

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