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Nurturing young mathematicians: teacher webinars

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There are **138** NRICH Mathematical resources connected to **Combinations**, you may find related items under Decision mathematics and combinatorics.

Problem
Primary curriculum
Secondary curriculum
### Fruity Pairs

Which two items of fruit could Kate and Sam choose? Can you order the prices from lowest to highest?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Button-up Some More

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Button-up

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Elevenses

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Domino Sorting

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangle Animals

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

Age 5 to 7

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Cuisenaire Environment

An environment which simulates working with Cuisenaire rods.

Age 5 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Three Ball Line Up

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Twelve Pointed Star Game

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cuisenaire Counting

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Finding Fifteen

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Robot Monsters

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Break it Up!

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Shape and Colour?

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Take Three from Five

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Six Times Five

How many six digit numbers are there which DO NOT contain a 5?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ladybirds in the Garden

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sealed Solution

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 1 Step 2 Step

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Prison Cells

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chances Are

Which of these games would you play to give yourself the best possible chance of winning a prize?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Teams

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Puzzling Sweet Shop

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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Round Up

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.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Buying a Balloon

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A City of Towers

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mixed-up Socks

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Dice

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Five Coins

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

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Noah

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Let's Investigate Triangles

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Cuboids

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sweets in a Box

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plants

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Age 5 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Room Doubling

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Train Carriages

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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### New House

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dice and Spinner Numbers

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sending Cards

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 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Street Party

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Calcunos

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Newspapers

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Little Boxes

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 3 Rings

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Homes

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tiles on a Patio

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tea Cups

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.

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cereal Packets

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Multilink Cubes

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polydron

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

Age 7 to 11

Challenge Level