Position #130 - in the 3.Bc8 line, after 3... Kg3 4.Be6 Rh2 why not 5.Bf7?

Good question.

I am considering 5. ..., Rh7 and when the bishop moves (what else?), 6. ..., Rc7.

Because of 6.Rh7 Bd5 7.Rh4+ Be4 8.Bxc5+

Agree - no way to cover ... Rc7 also.

This week's solution is quite funny.

1.Kc3 seems to win a piece. 1... Ne5 2.Kxc2 Ng4 doesn't help after 3.Bc4+ freeing to bishop.

1...Ne1 is tricky, because 2.Kd2 Nf3+ 3.Kxc2 Nd4+ wins the bishop.

2.Bc4+ Ke7! 3.Kd2 finally wins a piece.
But 3...Ng2! 4.Kxc2 Ne3+ followed by Nf5 and Nxh6 leads to a draw after. 5.Kc3 Nf5 (Note that Ke7 controls f8) 6.Bd3 Nxh6 7.gxh6 Kf7 8.Bh7 Kf6=

Now is white's turn to be cunning: 5.Kd3! Nf5 6.Ke4 Nxh6 7.Kf4!! and the knight is in bad shape. 7...Nf7 8.g6 Nh6 9.Kg5 wins.

Willems solutions looks convincing and beautiful. But there is something I do not understand:

1. Kc3, Ne1 2. Bc4+, Kg6! 3. Kd2 (what else?), Nf3 4. Kxc2, Nxg5 5. Bf8 Nh7! attacking the bishop. I do not see how white is going to prevent Nf6-h5-g7 or Nf6-e8-g7 in this case. I thought this ending is drawn if the knight reaches one of the squares b2-b7-g2-g7 covered by the king. I remember my surprise after I read this, because mostly these squares are quite awkward for nights :)

In a tournament game it might not win due to the 50 moves rule however for the validity of the study the tablebase verdict that 6.Bd6 (in Richard's suggestion) mates in 65 moves is sufficient.

Thanks Mr. Afek! You teached me something new! I should start using the database :) Ludek Pachman in Endspielpraxis im Schach (1977, 1981) calls positions like the one after 6. Bd6 'garantiert sicher' and he maintains that white can not break the defense. I read this just today before I saw the study (coincidentally). As I said, I was surprised, since in so many chess positions the knight is badly placed at those squares. There are many studies also where knights on b2, g2, g7, b7 are ignored, trapped, in the way, casually passed by by rook pawns, etc. And Kasparov once sacked the exchange on b7 with compensation due to... the badly placed knight. There are also known positions where a white knight on g7 does nothing for a kingside king attack, etc. I was just planning to write an article on this, starring this B+B vs N endgame as a notable exception. Alas :) FIDE should once again make an exception for this ending and some others to the fifty moves rule! Compliments on a wonderful study.

Thank you Richard for your kind words. Fide is right not to make any exceptions as there are too many such positions (numerous O+P vs. Q and R+B vs. 2 Kts for example) and there will be more in the future with the tablebase discoveries . In some cases the winning process lasts well over 200 moves. No arbiter can handle all this within the current time control.

Ok, that's a good argument, I guess, an arbiter does not have to have knowledge then of all the possible endgames and when someone is trying to win or not. After I learned this yesterday I visited Ken Thompson's page at Bell Labs, with the endgames, end if I understood it correctly I saw one endgame where the shortest path to mate was well over 6000 moves. (two bishops and a knight against a bishop). It took me almost ten moves before I realized the two white bishops were both dark-square bishops :)

Correction: I wasn't sure about the 6000 moves, and it appears to mean something else indeed, but anyway here is the link:
http://www.cs.bell-labs.com/who/ken/chesseg.html
So forget about the 6000 moves thing, sorry ...

For the problem 131,i could see all the routes leads to the DRAW only.Could any one help me.1. Kc3, Ne1 2. Bc4+, Kg6 3. Kd2, Nf3 4. Kxc2, Nxg5 5. Bf8 Nh7

This position is won according to endgame databases, so you might stop analysing and consider this line as a win for white.

Why still solution not published for the problem 131?