# 2 Your own formulas

Let’s start this section by looking at a number trick and seeing if a formula can derived, or built, for it. The aim of the trick is to end up with the name of an animal.

To do this follow the instructions listed below. The final number represents a letter of the alphabet, numbered in ascending order from A to Z. So, A is 1, B is 2, C is 3 etc. Then write down the name of an animal beginning with that letter.

The instructions for the trick are:

- Think of a number.
- Add 5.
- Double this.
- Subtract 8.
- Divide by 2.
- Take away the number you first thought of.
- Add 4.
- The final number represents a letter of the alphabet, numbered in ascending order from A to Z. So, A is 1, B is 2, C is 3 etc.
- Now write down the name of an animal beginning with that letter.

## Activity 4 What animal?

Carry out the number trick, starting with the number 3 and then any other number you would like to start with. What do you notice about the result in both cases?

### Answer

Starting with 3, the instructions work out as follows

Instruction | Expression |
---|---|

Add 5 | |

Double it | |

Subtract 8 | |

Divide by 2 | |

Take away the number you first thought of | |

Add 4 |

You will find that you always get 5, whatever number you start with! This gives the letter E. Most people will then think of elephant, although you cannot always guarantee that. The odd eel or emperor penguin may sneak in!

What is really interesting here though, to a mathematician, is how the trick works. The activity in the next section will help you to work this out.