Interessanterweise werden in der Lösung alle vier unendlich entfernten Felder des projektiven Schachbretts benutzt.
A.Buchanan: In projective geometry, every family of parallel straight lines intersects at an infinitely distant point. Chess problem composers in the former Yugoslavia have adapted this idea for the chessboard, adding four special squares “at infinity.”

Now a queen on a bare board, for example, can zoom off to the west (or east) and reach a square “at infinity” from which she attacks every rank on the board simultaneously from both directions. She might also zoom to the north (or south) to reach a different square at infinity; from this one she attacks every file simultaneously, again from both directions. Finally she can zoom to the northwest or southeast and attack all the diagonals parallel to a8-h1, or zoom to the northeast or southwest and attack all the diagonals parallel to a1-h8. These four “infinity squares,” plus the regular board, make up the field of play. (2015-11-20)
Henrik Juel: Fine explanation, Andrew, but I still need to see the intended solution (if you know it); this may also clarify the weird stipulation (2015-11-20)
Alfred Pfeiffer: Diese Schachvariante wurde 1952 von Prof. Lav Rajcic und Nenad Petrovic erfunden (D.B.Pritchard: The Encyclopedia of Chess Variants) (2015-11-20)
A.Buchanan: The articulate explanation is not mine: I found it at http://www.futilitycloset.com/?s=chess
I think one needs to add that only line pieces have the privilege to leave the regular board in this way. Which suggests another variant with Nightriders. Now there are another 4 squares accessible only by Nightriders. (2015-11-21)
Henrik Juel: Thanks, Andrew and Alfred
Nice key, but too bad about the trial after 1... Kg3 (2015-11-21)
Henrik Juel: Andrew has pointed out that the flaw after 1... Kg3 is only a dual (2015-11-22)
A.Buchanan: Someone asks me: is there a cook? 1. D-PD2 Sc7a8,Sc7d5 can be answered by 2. Kh3# (2020-11-10)
A.Buchanan: By the way: the squares at infinity are on a straight line, but that cannot be navigated by the queen. For suppose the contrary: then the direction of movement along that line would have to be parallel to some direction of movement of the queen, i.e. by symmetry parallel to *all* directions of movement of a queen, i.e. since lines parallel to one line are parallel to one another, we conclude that all lines on the board are parallel to one another. This is absurd, so the queen cannot navigate the line at infinity (2020-11-10)
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