Timeline for Checkmate in $\omega$ moves?
Current License: CC BY-SA 3.0
14 events
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| Oct 2, 2017 at 21:21 | comment | added | jeq | The link to your image seems to be broken. | |
| Feb 24, 2013 at 18:53 | comment | added | Joel David Hamkins | For the perpetual, we would seem to need to supplement the five-check-square argument by an explanation of why such a check could never be blocked by a cross check, that is, a check by the white queen on the black king which is blocked by a black rook that simultaneously gives check to the white king. This would in effect give control back to black for a forced checkmate. | |
| Feb 20, 2013 at 21:02 | comment | added | Joel David Hamkins | Ah, I see. | |
| Feb 20, 2013 at 5:21 | comment | added | Noam D. Elkies | I didn't just remove the b3 pawn; I also moved the Queen from e3 to f4 and the White King from e6 to e5. | |
| Feb 19, 2013 at 23:39 | comment | added | Joel David Hamkins | If the pawn is removed, could you explain why white cannot move the queen west, rather than east, and go for the perpetual from the left side. It seems this would ruin black's forking/skewer plan. | |
| Jan 6, 2012 at 7:24 | comment | added | Johan Wästlund | That's very nice! White should also make sure his king doesn't get in the way of any of those five checks, but consistently going N-E already takes care of this. I guess this means that Noam's modification brings the solution down to seven pieces with the losing side to move. | |
| Jan 6, 2012 at 1:28 | comment | added | Philip Engel | Good observation; removing the pawn surely goes a long way in proving the existence of a perpetual. A queen sufficiently far away always has at least 5 possible check squares. They can't all be blocked, since there are only 4 rooks. | |
| Jan 6, 2012 at 0:45 | comment | added | Noam D. Elkies | Yes, this is nice, though indeed the perpetual would have to be verified (already in Q+P vs. Q on an 8x8 board there are positions that are won after a long near-perpetual). A full perpetual is not needed, only that for each $N$ the Queen can move where it can check for at least $N$ moves if the Rooks stop checking. Under the same assumption, we can remove the pawn (which serves only to stop Westwards Queen moves) by moving the Queen one square NE and her husband one square South. This gives the Queen a check, but a Rook can safely block while giving check and then the Queen is soon lost. | |
| Jan 5, 2012 at 20:42 | comment | added | Johan Wästlund | Great! The white king's strategy should be to go North-East. I can't see immediately how to get the perpetual, but it seems to work. This looks like the simplest example so far on an edgeless board. | |
| Jan 5, 2012 at 11:01 | history | edited | Philip Engel | CC BY-SA 3.0 |
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| Jan 5, 2012 at 10:56 | history | edited | Philip Engel | CC BY-SA 3.0 |
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| Jan 5, 2012 at 10:49 | history | undeleted | Philip Engel | ||
| Jan 5, 2012 at 10:49 | history | deleted | Philip Engel | ||
| Jan 5, 2012 at 10:49 | history | answered | Philip Engel | CC BY-SA 3.0 |