Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

The pages of my calendar have got mixed up. Can you sort them out?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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

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.

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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

How long does it take to brush your teeth? Can you find the matching length of time?

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

Can you draw a square in which the perimeter is numerically equal to the area?

How many ways can you find of tiling the square patio, using square tiles of different sizes?

These practical challenges are all about making a 'tray' and covering it with paper.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

Find out about Magic Squares in this article written for students. Why are they magic?!

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

How many different triangles can you make on a circular pegboard that has nine pegs?

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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?

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?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

Two sudokus in one. Challenge yourself to make the necessary connections.