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ke2
A truly beautiful puzzle. Most (including me) would try the check to cover the h1 square immediately, but that fails, though it takes work to demonstrate this:
1. Bc6 Kg1!
Here, Nf3 blocking will be a draw after the white king plays e2 attacking the pinned knight a second time. Also, Kh2 will draw after white plays Bd7 attacking the pawn which now can’t move off the white square in time. The last of the king moves, Kg3 is also a draw: [1. …Kg3 2.Kf1 h2 (or 2. …Ng2 3.Bb7!=) 3.Bh1! Nf3 4.Ke2 Nd4 5.Kf1= as black can make no progress.] Continuing:
2. Ke2 h2
And now white can do nothing to stop Ng2 followed by h1Q if the bishop doesn’t just go to h1 immediately since the white king can only attack g2 from f3 which blocks the bishop’s access to that same square, but black has a reply to win against 3.Bh1:
3. Bh1 Ng2!
Black can also win with Ng6, though that is a less direct route for the coming knight maneuver. Here, the bishop is immune at move 3: [3. …Kh1? 4.Kf2! and you will not find a line where the knight can ever control either f1 or f2 with the white king on the other square and having to move, but if white tries 4.Kf1?? black can make this zugzwang arise (4.Kf1?? Nf5 5.Kf2 Nd6 6.Kf1 Ne4 and the white king will have to let the black king out of jail since the knight now controls f2 with white to move from f1)]. Continuing from 3. …Ng2 above:
4. Kf3
If the king goes to the d-file, black just captures at h1 and has time to get back to g2 before the white king hems him in on h1. Continuing:
4. …..Kh1
5. Kf2 Ne3! and now white can’t go to f1 and must allow black to play Kg1 followed by h1Q winning the game. No, at the first move, white must force black into one of the above positions, but with the other player to move. There is only one move that can change the move order this way:
1. Bd7!!
Black’s reply on move 1 is forced of course:
1. …..h2
2. Bc6!
The only drawing move. If white plays Ke2, black wins with Kg1 followed by Ng2 as in the previous line. If the white king doesn’t move to the second rank, or white doesn’t check with the bishop, black just queens with check instead. Continuing:
2. …..Kg1
If Kg3 or Kh3, white can play Bh1 on either move and draw, or Kf2 on the second of those for a draw, too. Continuing:
3. Bh1! Kh1 (alternatives below)
4. Kf2!
And, again, you will not find a line that allows black to cover f1 or f2 with the white king on the other square and having to move. However, now, black can’t even win with alternative moves at move 3:
3. …..Ng2
4. Ke2
And notice how this position is different from what we saw earlier. In that earlier position, the white king was already on e2 and had to move to f3. Here, he has just arrived at e2 and it is black that must now move. Now, white will just wait for black to take at h1, and will move to either f1 or f2 depending on where the knight is at that moment. For example:
4. …..Nf4
5. Ke1
Also draws with Ke3 or Kf3 since, at this moment, he would need to go to f2 if black capture at h1. Continuing:
5. …..Nd3
6. Ke2! and now, if black takes at h1, white now plays to f1 and black won’t be able to force him into zugzwang.
Again, a beautiful example of zugzwang.
Bd7-c6-h1
1.Bd7 h2
2.Bc6+ Kg1
3.Bh1!
It’s Lloyd. Sam Lloyd with two l’s. Have some respect for the man.
1.Fd7 h2 2.Fc6 Rg1 3Fh1 Rxh1 4Rf2 =
Anonymous,
You can probably expect a visit by Cortex. It appears, according to his son, it is spelled “Loyd”.
1. Bd7 h2
2. Bc6+ Kg1
3. Bh1 Kh1:
4. Kf2! draws
White’s King will slip between f1 & f2. Black’s knight can only give check, not control the square to which White’s King must move.
First I tried
1 Bc6+ Kg1
(1… Nf3 2Ke2 draws)
2Bh1 (Necessary since … Ng2 will block white B’s control on h1)
2…. Ng2+
3Ke2 h2
4Kf3 Kxh1
5Kf2 Ne3!! and white is in zwugzwang.
Correct is
1Bd7 h2
2Bc6+ Kg1
3Bh1 Ng2+
4Ke2 Kxh1
5Nf3+ Kf2 and black is in zwugzwang as N can not gain a tempo.
Dear Yancey,
The theme is really beautiful.Bishop usually can make a waiting move,but here after going to h1 it is immobilised. Even with 1Bc6 Kg1 I would try 2Bh1 whether successful or not as otherwise 2… Ng2(instead of your 2… h2)would arise. If you assure me that that black will play 2… h2 for any white move I would play
1Bc6 Kg1 2Bb7. Now 2…h2 will be replied by 3Bh1 and white can draw.
One of the points to this study is that a knight on a given square can only reach another square in a sequence of moves that is either always even, or always odd, regardless of the path taken. So, if a knight on a board can get to a particular square in 1, 3, or 5 moves, then he can never reach it in 2, 4, or 6 moves etc. This, of course, follows directly from one easily observable fact about knights- they can only move from dark squares to light squares in a single move, and vice versa.
Dear Yancey,
that is true about N but here B is also under handicap.the threat of … Ng2 forces Bh1.B on the side that is a8 to f3 part of the diagonal it can provide a waiting move but forced on h1 it can not provide a waiting move and that is Lloyd