# Chapter 8: Strategies and problem solving

## Combinations

• You might need to find strategies for counting the total number of possible combinations

• One way of finding combinations is to make a systematic list

• Here are al the possible three-digit numbers that can be made from the number cards shown on the right

## Counting with calculation

• Sometimes it’s impossible to write down every possible combination

• You can count combinations by multiplying the numbers of choices for each opion

• Here is a four-character password for a website

• The total number of possible passwords is 26x20x26x2=27040

## Problem solving

• Work out how many choices there are for each dial

• Dial 1-letter = 26 choices

• Dial 2-digit from 0 to 9=10 choices

• Dial 3-digit from 0 to 9 = 10 choices

• The numbers of choices for each fia; has changed sometimes so 26 choices would increase to 25 if a letter was used

## Factors and Primes

• You have to use a whole number of building blocks in each row, so the length of each row has to be a multiple of the length of one block

• The answer will be the lowest common multiple

• Top tip

• If you are not sure how to start draw a sketch and this might help you see that the lengths are multiples of the numbers

## Fractions

• There are lots of steps in this question so makes sure you keep track of your working and write it down clearly

• Top tip

• Write words with each calculations to explain what you are doing

## Recurring decimals

• Start by writing x = the amount if you work out 1000x and 10x you can keep all your working in whole numbers

• Top tip

• If a question says ‘show that’ or ‘prove that’ you have to show every step of your working clearly and neatly

• If a question says ‘shows that’ or ‘prove that’ you have to show every step of your working clearly and neatly