One of the Most Famous Chess Puzzles

Here is a polished, richer Saavedra, by the legendary composer Mark Liburkin (actually my favorite composer).

White to play, and win.

I have never seen that one before. Interesting execution of the theme. Although knowing it was a Saavedra made the solving easier (not by much - it's a short study anyway.)

wow, that's a cooler one.

same idea of underpromotion.

The Liburkin study, which is famous, contains an additional underpromotion. I'm not sure if Remellion covered that, as I can't see the whole solution of post #22 on my phone. Anyway, it arises in the line 1. Nc1 Rd5+ 2. Kc2 Rc5+ after which 3. Kd2? only draws.

Of course, black doesn't have to cooperate with that forced mate pattern in the puzzle from post #1. He can simply allow the pawn to queen, and then there is a strong possibility of a draw due to the 50-move rule. K+Q can force mate against K+R, but it isn't easy to do if black plays well. With perfect play, it can take up to 31 moves to force a win, and even grandmasters have been known to fail at forcing a win within 50 moves (just ask Walter Browne).

Black's best option here is to allow the pawn to promote to queen. This gives him a good likelihood of a draw, and even the possibility of a win, which is far better than a guaranteed loss. This is what Chessmaster 9000 chose to do when I played this puzzle against it, i.e., on move 3, instead of going along with the forced mate pattern (which it could probably "see"), it chose 3...Kb2. I queened (4. c8=Q), and then I switched it to let the engine play against itself from that position. Of course, the engine knows exactly how to force mate in such an endgame, so white won, but it took 25 moves to do so:

quite nice stalemate after 3... Rxb5 4. c7 Rb2+ 5. Kd3 Rc2! and draw.

Yes. Now that I looked at Remellion's solution (which is correct), I can add the line with the second underpromotion (which is kind of trivial once you get that far, but adds to the value of the study):

bishop, rook, what comes next?

Have you ever seen that one? White to play and win.

That looks like a cool position but I can't solve it.

It is not NN vs.NN. It is a composition

Actually N.N. doesn't signify 'no name':

"The abbreviation "NN" is used to signify an unknown player, usually an amateur. Although NN is sometimes believed to stand for "no name", that is a misconception: it is in fact an abbreviation of the Latin nomen nescio which means 'I do not know the name.'"
-http://www.chessgames.com/perl/chessplayer?pid=12883

Einstein.

Cool puzzle! Took me a while

Mark Liburkin, Vechernaya Moscva, 1933

This is probably the most impressive endgame study I have ever seen.

According to http://timkr.home.xs4all.nl/chess/saavedra.htm, G.E. Barbier was the editor who published first the ending of the game Fenton-Potter and then the puzzle based on it.

Searched it up. That is amazing!

That's just sick.

Try this one everyone....White to move & checkmate in (2) moves.