[math-fun] Peg Solitaire question

Robin Houston asks ( https://twitter.com/robinhouston/status/1272564182098075652?s=21 ) : “The game of Solitaire has an unusual symmetry. If you interchange filled and unfilled places, and *also reverse time*, the game is unchanged. Is it known whether there is a “palindromic” solution, i.e. a solution that is invariant under this symmetry?” There is a known solution that is symmetric in a different sense: https://www.youtube.com/watch?v=z9nkGgxcT-w Jim Propp