In the last section, you worked out formulas that could be used in a spreadsheet. This section gives you more practice in deriving formulas both by looking at number tricks and rearranging existing formulas.

## Activity: Think of a Number

Try this number puzzle: “Think of a number. Add 5. Double it. Subtract 8. Divide by 2. Take away the number you first thought of. Add 4.” [ If you use your calculator, remember to press the Equals sign after each instruction. ]

Now if 1 represents the letter “A,” 2 represents the letter “B,” 3 represents the letter “C,” and so on, work out the letter represented by your answer and write down the name of an animal beginning with this letter.

Start by choosing 3 as the initial number. The instructions work out as follows.

Starting with 3
Double it:
Subtract 8:
Divide by 2:

You will find that you always get 5, whatever number you start with. This gives the letter E. Did you choose an elephant?

## Activity: How Does This Trick Work?

To see how this trick works, read through the instructions from before. Because you could have thought of any number, replace this unknown number by a thought bubble like this:  ### Comment

Keep the thought bubble as part of the new number that you get at each stage.  This shows that the numerical answer is always 5—it does not depend on which number was chosen first. So the letter of the alphabet chosen is E. There are not many animals with names beginning with E and most people do think of an elephant first, but you might be unlucky if someone chooses an emu or an eel!

Rather than using a cloud to represent the number and explaining the trick pictorially, you could write down expressions for the answer at each stage and use either a word (for example, number) or a letter (for example, n) to represent the number. Write out the trick again, expressing it with the unknown number n. 