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Broad Topics > Decision Mathematics and Combinatorics > Combinations

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Domino Sorting

Stage: 1 Challenge Level: Challenge Level:1

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

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Cuisenaire Environment

Stage: 1 and 2 Challenge Level: Challenge Level:1

An environment which simulates working with Cuisenaire rods.

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The Twelve Pointed Star Game

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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What Shape and Colour?

Stage: 1 Challenge Level: Challenge Level:1

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

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Ladybirds in the Garden

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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Sealed Solution

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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Prison Cells

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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The Puzzling Sweet Shop

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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Number Round Up

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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Buying a Balloon

Stage: 2 Challenge Level: Challenge Level:1

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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A City of Towers

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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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Mixed-up Socks

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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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Noah

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Let's Investigate Triangles

Stage: 1 Challenge Level: Challenge Level:1

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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Making Cuboids

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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Sweets in a Box

Stage: 2 Challenge Level: Challenge Level:1

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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More Plant Spaces

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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More Children and Plants

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This challenge extends the Plants investigation so now four or more children are involved.

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Those Tea Cups

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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Button-up Some More

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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Button-up

Stage: 1 Challenge Level: Challenge Level:1

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

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More and More Buckets

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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We'll Bang the Drum

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Play a Merry Tune

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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Sounds Great!

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

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Move a Match

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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Four-triangle Arrangements

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Triangle Animals

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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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Creative Approaches to Mathematics Across the Curriculum

Stage: 1

Suggestions for teachers about exploring maths in different contexts: art, history and so on

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Combining Cuisenaire

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Three Ball Line Up

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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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Two and One

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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Nineteen Hexagons

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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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Cuisenaire Counting

Stage: 1 Challenge Level: Challenge Level:1

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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Butterfly Cards

Stage: 2 Challenge Level: Challenge Level:1

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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The Money Maze

Stage: 2 Challenge Level: Challenge Level:1

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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Finding Fifteen

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Sorting Symmetries

Stage: 2 Challenge Level: Challenge Level:1

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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Chocoholics

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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Robot Monsters

Stage: 1 Challenge Level: Challenge Level:1

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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Polo Square

Stage: 2 Challenge Level: Challenge Level:1

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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Here to There 1 2 3

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Triangle Edges

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Hamilton's Puzzle

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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Break it Up!

Stage: 1 and 2 Challenge Level: Challenge Level:1

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

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The Secret World of Codes and Code Breaking

Stage: 2, 3 and 4

When you think of spies and secret agents, you probably wouldn’t think of mathematics. Some of the most famous code breakers in history have been mathematicians.

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Semaphore Signals

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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Chocs, Mints, Jellies

Stage: 2 Challenge Level: Challenge Level:1

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?

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Rod Measures

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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Beads

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?