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7

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,...


7

New answer I found a new solution that is 2 moves better than my previous one! Big thanks to the answer by Retudin for the new pawn structure idea! Pieces: Moves: Position: Old answer Pieces: Moves: Position:


5

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


4

Pieces Correction (thanks to Rewan's remark): The king has a 3rd move (castling) Moves Position:


4

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): ...


3

Partly based on @Vepir's 19-move answer (Most similarity is due to convergence but I admit I borrowed the Bf1.) Proof game: Final position:


3

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


3

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


3

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


2

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


2

I'll start the fun: Proof:


2

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


1



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