In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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?

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?

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?

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

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?

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?

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

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?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Investigate the different ways you could split up these rooms so that you have double the number.

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Can you fill in the empty boxes in the grid with the right shape and colour?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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

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.

How many models can you find which obey these rules?

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?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

What is the best way to shunt these carriages so that each train can continue its journey?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

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?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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.

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

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

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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?

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

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?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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....?