So I purchased a standard french bike, that has 3 blades in front and 7 at the rear - which makes 21 gears. It's not hard to find out which positions are the lightest or the hardest, but the order in between requires some arithmetic.
After 2 years, I finally decided to count the number of teeth on each blade, and to calculate the transmission ratio.
Only then did I discover that 2 combinations gave the same result: so I only have 20 gears at my disposal !
In any case, I wrote a small programme for this (I wanted to learn Java anyway) and you're invited to have a look.
You can enter the sizes of your own blades (if you bother to count them).