A molecule with one stereocenter has one pair of stereoisomers: a pair of enantiomers.

A molecule with two stereocenters has 6 pairs of stereoisomers: 4 pairs of diastereomers and 2 pairs of enantiomers.

Given that, how many stereopairs does a molecule with 3 stereocenters have (assume no meso)? How many pairs of diastereomers? How many pairs of enantiomers?

Can you come up with formulas for the number of total stereopairs, diastereomer pairs, and enantiomer pairs given a molecule with n stereocenters?

First one with the right answer is the coolest!

For more fun, don’t just reply when you have the right answer. Reply with some initial guesses, first approximations, and thought process. A good discussion is more fun than one person posting the right answer 🙂

WARNING: The (a) correct answer is posted below. There are other correct general formulas I’ve seen. If you still want to play along, don’t read the comments. Try it on your own first, then read the comments. 🙂