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I just want to say that their are more possible (legal) chess positions than atoms in the known UNIVERSE. HYACHAHAHACHA. It hurts my brain comprehending that.
You know what, there are 64 squares on a chessboard. Each square can contain either a pawn, knight, bishop, rook, queen, king, of either colour, for 12 possibilities. Add in an empty square, which means that each square can have 13 possible units.
The total number of possible configurations would be 13^64. This would mean around 10^71 possible configurations. The vast majority of these would be nonsense illegal positions with 17 white kings and 33 black knights on the board, so this is an absolute upper bound to the number of positions.
There are around 10^80 atoms in the universe.
I think that just using elementary logic, and not knowing any hard math, it's possible to figure this out.