To clarify, what is the chess-board configuration that would maximize the number of valid moves one player could make on his or her turn? I thought of this question while playing chess, how apropos. I doubt there is a unique configuration, but I am not sure. The problem seems difficult because one must consider every single piece's movement, and the limitations on that piece's movement by other pieces. At any rate, I appreciate any thoughts, hints, or solutions.

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    $\begingroup$ Is promoting to a knight considered a different move from promoting to a queen? $\endgroup$ – Karl Kroningfeld Mar 31 '13 at 2:58
  • $\begingroup$ I think it can't be unique, because you could swap the color of all pieces(and also which player will move next) to get a configuration with the same number of moves available. $\endgroup$ – Michael Burge Mar 31 '13 at 2:59
  • $\begingroup$ I agree, I think we could forget the uniqueness...but I would consider all promotion as one move (if you don't like that we can add those at the end) $\endgroup$ – Coffee_Table Mar 31 '13 at 3:03
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    $\begingroup$ Curious question. But could you clarify what the conditions on the board are? Must the position be reachable in a legal chess game? Or can we just place pieces anywhere on an 8x8 board (e.g. 30 white queens and nothing else)? $\endgroup$ – Douglas S. Stones Apr 3 '13 at 17:20
  • $\begingroup$ @DouglasS.Stones : I meant in accordance with the unfolding of a legal game on an 8x8 board, assuming no pieces get captured. However, I like your second variation as well (just placing pieces randomly on the board). $\endgroup$ – Coffee_Table Apr 3 '13 at 19:27

If just the major white pieces are placed on the board, there is an almost-unique 100 move solution. There are many variations, and a couple of dozen of them are given in Guide to Fairy Chess by Anthony Dickins. Some of these are also given in Martin Gardner's Sixth book.

These are known as construction tasks.

  • $\begingroup$ Some of those positions from Dickins's Guide to Fairy Chess were posted in answer to this question on chess.stackexchange, e.g., a legal position with all 32 men and 99 possible moves. Also, a position from actual play with 79 possible moves. $\endgroup$ – bof Feb 2 '14 at 22:27

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