my motiviation was intellectual curiosity and some random Lichess reading about chess engine authors wondering whether 8 bit e.g. numbers 0 to 255 (or 1 to 256), will be enough for storing the number of legal moves. Which triggered my brain: "I HAVE THE KNOWLEDGE TO SOLVET HIS FOR HUMANITY :O". It's not at all relevant practically, as you have elaborated, and there probably is a more elegant proof that 256 can't be exceeded.
my motiviation was intellectual curiosity and some random Lichess reading about chess engine authors wondering whether 8 bit e.g. numbers 0 to 255 (or 1 to 256), will be enough for storing the number of legal moves. Which triggered my brain: "I HAVE THE KNOWLEDGE TO SOLVET HIS FOR HUMANITY :O". It's not at all relevant practically, as you have elaborated, and there probably is a more elegant proof that 256 can't be exceeded.