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QUESTION

# How many stereoisomers can exist for cortisone?

Cortisone can be found on wikipedia. I've redrawn the structure below, with standard steroid numbering. Noting that sp^3 carbons are potential chiral centers, I've marked them.

Carbon-8: S Carbon-9: S Carbon-10: R Carbon-13: S Carbon-14: S Carbon-17: R

So, we see six stereocenters. We also don't see any carbons that can allow any cis-trans geometric isomers. Finally, there is no plane of symmetry anywhere here. So, with that in mind, the number of stereounits (stereocenters + cis-trans centers) is still six.

The number of stereoisomers is known to be 2^n - "meso structures", but since there is no plane of symmetry, it is just 2^n, where n is the number of stereounits.

Thus, 2^6 = color(blue)(64) stereoisomers.