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Resources tagged with Combinations similar to Taking a Die for a Walk:

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Broad Topics > Decision Mathematics and Combinatorics > Combinations

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3 Blocks Towers

Age 5 to 7 Challenge Level:

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?

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Those Tea Cups

Age 7 to 11 Challenge Level:

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.

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Two Dice

Age 5 to 7 Challenge Level:

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

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Two on Five

Age 5 to 11 Challenge Level:

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?

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Sending Cards

Age 7 to 11 Challenge Level:

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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Semaphore Signals

Age 7 to 11 Challenge Level:

Semaphore is a way to signal the alphabet using two flags. You might want to send a message that contains more than just letters. How many other symbols could you send using this code?

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Snakes

Age 5 to 7 Challenge Level:

Explore the different snakes that can be made using 5 cubes.

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Polydron

Age 7 to 11 Challenge Level:

This activity investigates how you might make squares and pentominoes from Polydron.

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Calcunos

Age 7 to 11 Challenge Level:

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

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Mixed-up Socks

Age 5 to 7 Challenge Level:

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?

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Halloween Investigation

Age 7 to 11 Challenge Level:

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?

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Ice Cream

Age 7 to 11 Challenge Level:

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.

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Making Cuboids

Age 7 to 11 Challenge Level:

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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Add 3 Dice

Age 7 to 11 Challenge Level:

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

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Triangle Animals

Age 5 to 7 Challenge Level:

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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Multilink Cubes

Age 7 to 11 Challenge Level:

If you had 36 cubes, what different cuboids could you make?

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Hamilton's Puzzle

Age 7 to 11 Challenge Level:

I start my journey in Rio de Janeiro and visit all the cities as Hamilton described, passing through Canberra before Madrid, and then returning to Rio. What route could I have taken?

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Elf Suits

Age 7 to 11 Challenge Level:

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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Jumping Cricket

Age 5 to 7 Challenge Level:

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?

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Wag Worms

Age 7 to 11 Challenge Level:

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.

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Calendar Cubes

Age 7 to 11 Challenge Level:

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

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Map Folding

Age 7 to 11 Challenge Level:

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?

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Noah

Age 5 to 7 Challenge Level:

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

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Cereal Packets

Age 7 to 11 Challenge Level:

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

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Tiles on a Patio

Age 7 to 11 Challenge Level:

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

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Triangle Edges

Age 5 to 7 Challenge Level:

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

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Butterfly Cards

Age 7 to 11 Challenge Level:

Four children were sharing a set of twenty-four butterfly cards. Are there any cards they all want? Are there any that none of them want?

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Cuisenaire Counting

Age 5 to 7 Challenge Level:

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

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Nineteen Hexagons

Age 5 to 7 Challenge Level:

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?

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Play a Merry Tune

Age 7 to 11 Challenge Level:

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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Three Ball Line Up

Age 5 to 7 Challenge Level:

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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Combining Cuisenaire

Age 7 to 11 Challenge Level:

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

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Button-up

Age 5 to 7 Challenge Level:

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

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Button-up Some More

Age 7 to 11 Challenge Level:

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

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Dice and Spinner Numbers

Age 7 to 11 Challenge Level:

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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Penta Place

Age 7 to 11 Challenge Level:

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

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Home City

Age 7 to 11 Challenge Level:

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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Little Boxes

Age 7 to 11 Challenge Level:

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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Four-triangle Arrangements

Age 5 to 7 Challenge Level:

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

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Street Party

Age 7 to 11 Challenge Level:

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.

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New House

Age 7 to 11 Challenge Level:

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

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We'll Bang the Drum

Age 5 to 7 Challenge Level:

How many different rhythms can you make by putting two drums on the wheel?

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Newspapers

Age 7 to 11 Challenge Level:

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?

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A City of Towers

Age 5 to 7 Challenge Level:

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?

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Let's Investigate Triangles

Age 5 to 7 Challenge Level:

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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Briefcase Lock

Age 5 to 7 Challenge Level:

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?

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Red Express Train

Age 5 to 7 Challenge Level:

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

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The School Trip

Age 5 to 7 Challenge Level:

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?

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Train Carriages

Age 5 to 11 Challenge Level:

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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3 Rings

Age 7 to 11 Challenge Level:

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?