In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Can you find the chosen number from the grid using the clues?

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

My coat has three buttons. How many ways can you find to do up all the buttons?

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

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

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Can you find out in which order the children are standing in this line?

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

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?

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?

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

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.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Find out what a "fault-free" rectangle is and try to make some of your own.

An investigation that gives you the opportunity to make and justify predictions.

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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?

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?

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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?

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.

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?

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

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