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The compound given is camphor:

1,7,7-trimethylbicyclo[2.2.1]heptan-2-one

We have to find the total number of stereoisomers for this compound. Now I can see two chiral carbons so I thought the number would be $4$ but it turns out that there are only $2$.

I can't quite see why. I realize that it is a bridgehead compound which would make it non-planar but how does that affect stereochemistry? Any help would be appreciated.

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    $\begingroup$ The bridgehead atoms have to be inverted simultaneously. You can't have a hydrogen or methyl group pointing inside. Technically, we should ask how many stereoisomers are reasonable. $\endgroup$
    – Zhe
    May 3, 2020 at 12:50
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    $\begingroup$ To follow-up on @Zhe's answer, the enantiomer arises by inverting both stereoisomers. However, you are correct conceptually. Inverting only one stereocenter at a time gives a pair of "trans" enantiomers that are too unstable to exist. $\endgroup$
    – user55119
    May 19, 2020 at 23:53

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