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?

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

How many different shapes can you make by putting four right- angled isosceles triangles together?

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

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

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

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

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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

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

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Can you find all the different triangles on these peg boards, and find their angles?

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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

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

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?

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Find all the numbers that can be made by adding the dots on two dice.

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?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

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

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?

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

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

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Can you find all the different ways of lining up these Cuisenaire rods?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

What happens when you try and fit the triomino pieces into these two grids?

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

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.