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A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
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?
My coat has three buttons. How many ways can you find to do up all the buttons?
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?
How many models can you find which obey these rules?
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?
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?
Explore the different snakes that can be made using 5 cubes.
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?
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
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?
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.
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?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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?
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.
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.
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?
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?
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?
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.
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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?
Can you fill in the empty boxes in the grid with the right shape and colour?
Find all the numbers that can be made by adding the dots on two dice.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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?
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
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.?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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?
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 can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
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.
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.
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?