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Puzzle Statement:

Consider the game of chess, but with a slight modification of the rules as follows: all heavy pieces (i.e., the queens and rooks) are allowed to jump as far across the board as they want, regardless of any pieces (pawns/minors/heavies/kings) in the way.

More specifically, any vertical/horizontal/diagonal move by a queen and any vertical/horizontal move by a rook is legal (including captures), unless there is a piece of the same color on the destination square (or if the player trying to make the move is in check after the move is completed). Similarly, queens and rooks can also be used to check/checkmate the opponent's king from a distance, ignoring any pieces that lie in between.

With these modified rules, and beginning with the usual starting position of chess with white to move, the outcome of the game with best play by both sides can be provably determined. Does white win, does black win, or do they draw with best play?

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    $\begingroup$ provably determined you say? Wow I would have thought there would be even more states and higher branching factor to consider... $\endgroup$
    – Dmitry Kamenetsky
    Sep 24 at 15:07
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    $\begingroup$ Loved this idea! $\endgroup$
    – Jafe
    Sep 25 at 3:29
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    $\begingroup$ Was wondering why the bishops were excluded from jumping until I finally saw the outright silly 1. Bb5# :-) $\endgroup$
    – Bass
    Sep 25 at 6:30

1 Answer 1

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The result is a

win for white, by mate in 5.

The idea is to

back-rank mate black by moving a queen or rook there after having captured or lured away black's rooks and queen from that rank. By giving check every move, black's ability to respond is limited and the game tree is tiny.

Here's the line:

Capture the opponent's rook with 1. Rxa8+. Since black's king can't move out of check and blocking is ineffective, black must capture this rook. If black recaptures with their other rook 1...Rxa8, then 2. Qh5#. Otherwise, black must recapture 1...Qxa8. Now go 2. Qa4+. If black captures with their queen 2...Qxa4, then Rxh8#. So, black must move 2... Kd8.
Now continue with the forced line:
3. Qd4+ Ke8
4. Rxh8+ Qxh8
5. Qxh8#

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    $\begingroup$ rot13(Avpr nafjre. Lbh qba'g arrq gb pbafvqre Oynpx'f guveq zbir oybpxvat jvgu dhrra gb qrr svir orpnhfr, yvxr lbh fnvq, oybpxvat vf varssrpgvir, naq Juvgr pna fvzcyl pncgher gur Oynpx xvat.) $\endgroup$
    – Benjamin Wang
    Sep 24 at 20:08
  • $\begingroup$ rot13(Avpr! Gurer'f npghnyyl n pbhcyr bgure yvarf gung yrnq gb na rira snfgre zngr, ohg guvf nafjref gur dhrfgvba qrsvavgviryl.) $\endgroup$
    – acegikmoqsuwy2000
    Sep 25 at 0:40
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    $\begingroup$ V guvax gur yvar 1. Ekn8+ Dkn8 2. Dn4+ Dkn4 3. Ekn8# unf n glcb. Gurer'f ab cvrpr ba n8 gb pncgher, naq ab juvgr ebbx pna zbir gurer naljnl? V nffhzr lbh zrna 3. Eku8#? $\endgroup$
    – A. Rex
    Sep 25 at 1:31
  • $\begingroup$ ㅤㅤㅤㅤWㅤhat?ㅤㅤㅤㅤㅤㅤ $\endgroup$
    – OverLordGoldDragon
    Sep 25 at 13:24
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    $\begingroup$ @OverLordGoldDragon the scrambled comments are to prevent spoilers. You can decode them using rot13 $\endgroup$
    – Benjamin Wang
    Sep 25 at 16:35

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