I'm not normally a chess guy, but this puzzle is cool.
Black's knight has to sit on d7, threatening to go to f6, but can't do it until white's knight moves off of e8. Thus, black has to get his king over to help, but he literally cannot. There's too many squares he can't walk onto.
d8, d7, d6 are illegal/occupied.
All spaces 2 moves from white's knight are also blocked, so that blocks d5, d4, e4, f4, g4, and h5 (also b5, which is important later). c5 is blocked by white's knight moving to e4 in two moves. (g5 is also blocked by that, but black can't get there fast enough anyways)
White's king also has a large number of trap spaces, but unlike black, he has a way in, and until he gets in, he can just leave the knight deadlock. White just needs to avoid any spaces that are a knight's move from e5 as well as e4 (don't technically need to worry about the e4 moves as long as you don't need to be able to spring the trap on black king to c5).
So white's king moves b3, c2, d1, e1, f1, g2, h3, h4, g5, and then it's set. Black can't get his king over fast enough to block that, because his first move has to be back to the a-file, as b5 and c5 both lead to losses. His fastest route is a5, b4, c3, d3, e3, but that's when white's king moves to g2, cutting him off.
Edit: oops, more work to do. I didn't think allowing black to check with the knight on the initial move to b3 would matter, but it does, because black can move the knight to e4 to take up the deadlock again, but now black's king can move in to help.
Edit Edit: Ok, I think white can move his king a3, b2, c2. Black can try to shadow to a5, then b4, but c4 is bad, and c5 is bad unless the white king steps onto d2. So the black king can't shadow white onto the c-file, and that lets the white king move d1, e1, f1, g2 before the black king can make it to f3.
(September 10th, 2013, 11:29)Zargon Wrote: I'm not normally a chess guy, but this puzzle is cool.
Black's knight has to sit on d7, threatening to go to f6, but can't do it until white's knight moves off of e8. Thus, black has to get his king over to help, but he literally cannot. There's too many squares he can't walk onto.
d8, d7, d6 are illegal/occupied.
All spaces 2 moves from white's knight are also blocked, so that blocks d5, d4, e4, f4, g4, and h5 (also b5, which is important later). c5 is blocked by white's knight moving to e4 in two moves. (g5 is also blocked by that, but black can't get there fast enough anyways)
White's king also has a large number of trap spaces, but unlike black, he has a way in, and until he gets in, he can just leave the knight deadlock. White just needs to avoid any spaces that are a knight's move from e5 as well as e4 (don't technically need to worry about the e4 moves as long as you don't need to be able to spring the trap on black king to c5).
So white's king moves b3, c2, d1, e1, f1, g2, h3, h4, g5, and then it's set. Black can't get his king over fast enough to block that, because his first move has to be back to the a-file, as b5 and c5 both lead to losses. His fastest route is a5, b4, c3, d3, e3, but that's when white's king moves to g2, cutting him off.
Edit: oops, more work to do. I didn't think allowing black to check with the knight on the initial move to b3 would matter, but it does, because black can move the knight to e4 to take up the deadlock again, but now black's king can move in to help.
This is wrong.
I'll spoiler the solution as I have to go away for awhile.
1. Ka3 !! (other king moves run into knight forks sometime or later) 1...Kc6 (the main line; black has other moves that loose faster for example 1...Ka5 Nc7 2. Nc6 Nf6 3. Kb3 or are useless like going backward and black cannot get to the d-pawn while the white king can by making a loop) 2. Ka2 !! (The only move to avoid knight forks again) 2...Kc5 (if 2...Kb6 white can use the original idea of 3. Nc7 Nf6 4. Nd5+) 3. Nd6 Nf6 4. Ne4+
I don't see how white gets trapped doing Ka3, Kb2, as per my revised solution, rather than Ka3, Ka2 (presumably Kb1, to avoid Kb2). It seems like Ka3, Ka2, Kb1 will get pinned to the 1-row by black doing Ka5, Kb4, Kb3, since it seems to me that the 3-row is safe for black's king.
think I solved it on the train (MJW, you really should credit the study composer)
the first thing I tried was 1. Nc7 Nf6 2. Nd5+ to deflect the knight but that fails because black's Nxd5+ is check
the white squares are dangerous to both kings. The white king can't move to c4, d3 etc because of Ne5+ followed by Nc6. Although the black king can't use d5 because of white's Nf6+, there's no way to exploit that. 1. Kc3 Kc5 2. Kd2 Kd4 is the only flanking maneuver white could try but that accomplishes nothing, and if black gets to walk his kind c5-d4-e5 it's a draw.
in that 1. Kc3 Kc5 line, white can try 2. Nd6 again, but after Nf6 3. Ne4+ Nxe4+ is again check
At this point it becomes apparent that the white king is mostly just a liability as it allows black to gain a turn by checking. 1. Kb3 also doesn't work. Nc5+ 2. Kc4 Ne6 3. Kd5 Nf4+ and Ng6 draws.
by process of elimination that leaves 1. Ka3!
Now black can't move the knight or move his king to a6/b5/b7 which lose to obvious checks, so that leaves
a) 1... Kc5 2. Nd6 Nf6 3. Ne4+! Nxe4 4. e8Q
b) 1... Ka7 (Ka5 is similar) 2. Kb3. Since black moved his king away from the action white can now threaten to attack with the king. Nc5+ 3. Kc4 Ne6 4. Nd6! Ng7 (avoiding the fork after Nc7 Nb5+) 5. Kb5, and white wins with Kc6, Kd7, Nf5. If black tries 2. ...Kb6 instead, then the original try 3 Nc7 Nf6 4. Nd5+ works.
c) 1... Kc6
now c6 is a safe square but the black king is running out of squares there (Kb5/b7/d5 immediately checkable, Kb6 losing to Nc7, Kc5 losing to Nd6)
White has to pass the move to put black in zugzwang with 2. Ka2! 2. Kb2 doesn't work because after 2... Ne5 3. Nf6 and black has yet another obnoxious check Nc4+ followed by Nd6 drawing. The solution is hilarious because the white king has to run as far away as possible to avoid being checked, and the knight just dominates the black king on its own! After Ka2, all black moves lose as above.
Ok, now I understand why the given solution works.
(September 10th, 2013, 19:17)uberfish Wrote: Kb2 doesn't work because after 2... Ne5 3. Nf6 and black has yet another obnoxious check Nc4+ followed by Nd6 drawing.
Ok, now I understand why the given solution works.
(September 10th, 2013, 19:17)uberfish Wrote: Kb2 doesn't work because after 2... Ne5 3. Nf6 and black has yet another obnoxious check Nc4+ followed by Nd6 drawing.
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