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Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no captures and no pawn-moves.

Then is it possible to have a a pair of positions A and B, such that we can go from configuration A to B by legal moves, but not from B to A?

Minor addition: No stalemates or checkmates allowed, the game must be extendable atleast two moves in both direction from both A and B.

Two configurations are different also if the pieces are in the same places but it is a different player to move.

Edit: (t.b.) This question was also asked on mathoverflow.net. If you have something to say, please contribute it there instead of here, in order to collect the answers and remarks in one place.

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Depends. Say B is a stalemate position (no legal moves for one player, say player 2, but player 2 is not in check). Then player 2 cannot move at all, so you cannot go from B to A by legal moves beginning with player 2. But you could get from B to A if you start with the last-player-who-moved, since under your conditions all moves are necessarily reversible (the only pieces that have non-reversible moves are pawns). – Arturo Magidin Oct 22 '11 at 5:48
@Arturo All single moves aren't reversible in a single move, like a king moving from check – GM2001 Oct 22 '11 at 5:55
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Crossposted on MO: mathoverflow.net/questions/78827/irreversible-chess @GM2001, in the future, please wait some time before posting your question in multiple fora, and when you do, provide links to the other posts. – Zev Chonoles Oct 22 '11 at 14:47
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@Zev: I second quid's suggestion in a comment on MO to close the question here (I just voted to close). It seems to have attracted quite a bit of attention on MO, and it might be more useful to have the answers collected in one place. – t.b. Oct 22 '11 at 19:06
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@FoolForMath: actually I think the opposite is true, closed threads tend to have more views than open ones because people are curious what happened. I don't have a strong opinion on keeping this thread closed (I didn't really read the question). But I do have strong opinions about crossposting and do want to discourage that. – t.b. Oct 22 '11 at 20:16
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closed as too localized by t.b., Zev Chonoles Oct 22 '11 at 19:09

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1 Answer

up vote -1 down vote

Check out this blog posting for the solution. The answer is YES it's possible. He shows the position and how to get into it from standard chess.

http://www.alecjacobson.com/weblog/?p=1559

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Which were the positions A and B again? So that you can get from A to B, but not from B to A? – Jyrki Lahtonen Oct 22 '11 at 8:48
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Never mind it requires a pawn move. Consider this answer rescinded. – Neal Tibrewala Oct 22 '11 at 9:17

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