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Final position: Lower bound for shortest proof game : Proof game with minimal number of moves:



A non symmetric entry with Will add proof game when/if required.


Okay.... I googled "A game that doesn't exist" and wound up with "Polybius (square)" which also came up in the commentary below. Hadn't heard of that before. A game that has existed for over 1500 years" presumably refers to Chess. I thought that might be the 'key' for a simple version of the square or an 8x8 square but it didn't work,...


First note that With that in mind, here is a position that can be proved to take


Let's open the challenge (without a proof game, since I already know a solution with more pieces is possible)


With the new hints this has become much simpler. In fact, OP has (unintentionally?) changed the character of the puzzle. At least some solutions can be step-by-step (like a sudoku for want of a better simile) reconstructed from the hints. For example number 8 (I'll only do one, so people still have a chance to earn the bounty by solving one of the others): ...


Proof game: Correctly formatted FEN (for copy'n'paste)


I'll start the fun: Proof:


Here is another solution with Position: Proof game: Alternative proof game: the pawns do all the work.

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