Is there a memorable solution to Kirkman's School Girl Problem?
I do not know about photographic memory, but I found this quite appealing way to describe it:
The girls are represented as points and the groups as paths. Each group contains three girls and no two girls belong to the same group on different days. I found the description of it on this website and made the above animation of it.
BTW: Just a few thoughts. The link goes into details about enumerating the points and states that the pattern should be rotated counterclockwise. The enumeration is only necessary if we are to write down the groups, and any initial enumeration may be chosen. If the girls can sort it out among themselves, they can even choose with whom they want to be on the first day.
Rotating counterclockwise is only one possible choice: Let the $7$-cycle $\tau=(1234567)$ represent the rotation by one step counterclockwise each day as in the animation. Then we have a cyclic subgroup of order $7$ in $S_7$ with generators $\tau,\tau^2,...,\tau^6$ $$ \mathbb Z_7\simeq\langle\tau\rangle=\langle\tau^2\rangle=...=\langle\tau^6\rangle\subseteq S_7 $$ where $\tau^k$ corresponds to rotating $k$ steps counterclockwise. Then $\tau^6$ still generates the entire group and corresponds to rotating one step clockwise instead (it should come as no surprise that this works as well).