Chess Calculation Exercise 1 - Solution

This is my thinking and solution to the calculation puzzle as posted here:

http://www.chess.com/blog/Benedictine/chess-calculation-exercise-1

If you are just looking for the solution without my thoughts it can be found in this video:

http://www.youtube.com/watch?v=9Kn15YfU8cU

If you want to read my calculations (and I'm really just noting them for my sake too) they can be found below.

Initial position:

OK, I gave myself about 20 minutes to look at the above position and to write down my calculations, without moving the pieces. Here was my thinking:

Clearly the black king is vulnernable and a forcing sequence leading to mate looked possible. The bishops looked particularly good and the rook has a nice open file, Rc6+ immediately sprang to mind, but I tried to look wider before analysing moves. The bishop on b4 is hanging so any non-check and that could fall. The black squared bishop was well placed for black potentially stopping some threats. White's king could be prone to checks but escape via h2 looks OK.

So I looked at the checks, obviously the most forcing moves. Rc6+, Nc5+, Nf4+ and Bf5 and Bd5+. I also looked at Rc7 trying to put the black king in a mating net. Out of all of these though Rc6+ appeared to be the move, as of course Bd5+ or Bf5+ doesn't seem to work, the king can take the bishop seemingly without any compensation, the rook can't even check on c5. I also looked at any possible king and queen fork but nothing seemed to be going to work in that regard, so I went about analysing my chosen Rc6+. My calculations as written below:

1. Rc6+

Two possible replies only:

1...Kd7 or 1...Kf7.

1...Kf7 2. Bg6+ Kg8 (only move) Rc8#

So 1...Kd7 2.Rd6+ four replies:

2...Kc7, 2...Ke7, 2...Ke8, 2...Kc8.

2...Ke7 would leave 3.Rxd8+ meaning a tempo save and a freeing move on the bishop on b4. This is a clear won endgame. So three other moves to consider 2...Ke8, 2...Kc7, 2...Kc8. However, I had calculated that of these moves I could still play 3.Rxd4 and then the line would run:

3. Rxd4 a5xb4 4. Rxb4 Qa5+ 5 Kh2 and is safe. So I figured that from here white would have a clear advantage in the endgame with Rook, bishop, Knight and three pawns vs Queen and three pawns, but with black's king more exposed and the black b5 pawn probably falling soon. I saw this as a default position for white, however I tried see if I could find anything better with the three remaining moves 2...Ke8, 2...Kc7, 2...Kc8.

2...Kc8 3 Bf5+, leaves three moves - 3...Kb8, 3...Kc7, 3...Kb7. To 3...Kc7 or 3...Kb7 white has 4. Rd7+ but what then? The knight can't get in on the action because of the bishop on d4 and seemingly the king can dance around in the corner and dodge checks from the bishop and rook. Of course if there are no checks the bishop on b4 falls. Similar thing with the other remaining king moves.

So at this point I would have been happy to return to my default position and to capture the black bishop if white doesn't blunder allowing mate with 1...Kf7. However, I decided to return to the starting position and have a quick look again at those remaining checks, though again I didn't find any joy.

Summary of moves here:

So then I looked at the solution and compared my notes.

Solution

See video link posted at the start.

I was pleased to note that the speaker in the video considered the same things I mentioned, the forcing checks, the bishop hanging on b4 etc and immediately starting analysing the Rc6+ line, which was so far so good. Again 1...Kf7 leads to mate. 1...Kd7 and the move given was 2.Rd6+, so far so good, though I didn't think these moves where hard to find, rather perhaps the most obvious, however I thought that was probably it, still a very good exercise. However, of course as you probably realised and I should have, I missed the immediate 3...Qa1+ winning the rook. An over-sight on my part. Of course I could have seen that in a game after playing 1.Rc6+ Kd7 2. Rd6+ (K moves but not to e7) then I might have looked for fresh at the then position, considering threats etc before playing 3. Rxd4. But I had missed it in calculating from scratch.

So that was a clear over-sight. However, if you have seen the video, then comes the brilliant bolt from the blue - 1. Bh7!

OK, so I have a bit of a headache after looking at all of that again, but I really like the Bh7 move, though the combinations that follow black avoiding losing the queen are also good.

So to conclude, there was clearly so much in that position that I didn't see. The 3. Rxd4 oversight was naughty, I should have seen that, so another reminder to look for alternatives, not to consider here axb4 only. I was pleased with my reading of 1.Rc6+ apart from that though. 1 Bh7 seems like something special, and when you have found that then all those other alternative lines become possible (though I'm not sure I would have found the knight sacrifice mate...) Though just going back to the starting position again with 1. Bh7 in mind:

Perhaps one obvious tactical question should spring to mind; the king and queen are on the same diagonal, are there any tactics? Then perhaps Bh7 might have been found.

Still, at least I can be comforted in the fact that the GM playing the game also missed it and played 1.Rc6+ and from the fact that I learned a great deal from looking at this position.