# Resources tagged with: Combinations

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### There are 99 results

Broad Topics > Decision Mathematics and Combinatorics > Combinations

### Finding Fifteen

##### Age 7 to 11Challenge Level

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?

### Sealed Solution

##### Age 7 to 11Challenge Level

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?

### Penta Primes

##### Age 7 to 11Challenge Level

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

### Six Is the Sum

##### Age 7 to 11Challenge Level

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

### Calendar Cubes

##### Age 7 to 11Challenge Level

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

### Polo Square

##### Age 7 to 11Challenge Level

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

### Two Egg Timers

##### Age 7 to 11Challenge Level

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

### Bean Bags for Bernard's Bag

##### Age 7 to 11Challenge Level

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

### Elf Suits

##### Age 7 to 11Challenge Level

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

### Dice and Spinner Numbers

##### Age 7 to 11Challenge 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?

### Team Scream

##### Age 7 to 11Challenge Level

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?

### Octa Space

##### Age 7 to 11Challenge Level

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?

### Prison Cells

##### Age 7 to 11Challenge Level

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?

### Home City

##### Age 7 to 11Challenge Level

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

### Zargon Glasses

##### Age 7 to 11Challenge Level

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?

### Hubble, Bubble

##### Age 7 to 11Challenge Level

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

### It Figures

##### Age 7 to 11Challenge Level

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### On Target

##### Age 7 to 11Challenge Level

You have 5 darts and your target score is 44. How many different ways could you score 44?

### Room Doubling

##### Age 7 to 11Challenge Level

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

### More and More Buckets

##### Age 7 to 11Challenge Level

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?

### Cat Food

##### Age 7 to 11Challenge Level

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

### Sweets in a Box

##### Age 7 to 11Challenge Level

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?

### Making Cuboids

##### Age 7 to 11Challenge 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?

### Halloween Investigation

##### Age 7 to 11Challenge 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?

##### Age 7 to 11Challenge Level

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

### Magic Triangle

##### Age 7 to 11Challenge Level

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

### Sending Cards

##### Age 7 to 11Challenge 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?

##### Age 7 to 11Challenge Level

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?

### Chocs, Mints, Jellies

##### Age 7 to 11Challenge Level

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?

### 3 Rings

##### Age 7 to 11Challenge 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?

### Delia's Routes

##### Age 7 to 11Challenge Level

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

### The Puzzling Sweet Shop

##### Age 5 to 11Challenge Level

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?

### Wag Worms

##### Age 7 to 11Challenge 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.

### Two on Five

##### Age 5 to 11Challenge 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?

### Ice Cream

##### Age 7 to 11Challenge 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.

### Calcunos

##### Age 7 to 11Challenge Level

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

### Street Party

##### Age 7 to 11Challenge 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.

### Train Carriages

##### Age 5 to 11Challenge 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?

### Newspapers

##### Age 7 to 11Challenge 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?

### Plates of Biscuits

##### Age 7 to 11Challenge Level

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?

### The Money Maze

##### Age 7 to 11Challenge Level

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

### Throw a 100

##### Age 7 to 11Challenge Level

Can you score 100 by throwing rings on this board? Is there more than way to do it?

### Button-up Some More

##### Age 7 to 11Challenge Level

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

### Five Coins

##### Age 5 to 11Challenge Level

Ben has five coins in his pocket. How much money might he have?

### Penta Post

##### Age 7 to 11Challenge Level

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

### Three by Three

##### Age 5 to 11Challenge Level

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

### Map Folding

##### Age 7 to 11Challenge 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?

### A Rod and a Pole

##### Age 7 to 11Challenge Level

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

### Break it Up!

##### Age 5 to 11Challenge Level

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.

### Cereal Packets

##### Age 7 to 11Challenge Level

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