Enumerate the aldohexoses

You will list every pattern of OH groups in a Fischer projection, and then sort the patterns into D sugars and epimers. R means the OH is on the right and L means it is on the left.

The idea. A sugar with $n$ stereocentres has $2^n$ patterns. The last stereocentre decides D or L. Two patterns that differ in exactly one position are epimers.

Your tasks.

1. Complete stereoisomers(centres) so that it returns the number of stereoisomers.
2. Complete patterns(centres) so that it returns every R and L pattern as a string.
3. Complete d_sugars(all_patterns) so that it returns the patterns whose last letter is R.
4. Complete epimers(a, b) so that it is true when the two patterns differ at exactly one position.