FEN Puzzle.

Originally posted by ilywrin
i've always suspected criminal intentions in me. Anyway, a Mate in 4 (white to move).
[fen]8/8/5Bp1/8/R7/7k/8/7K [/fen]

This one I can do. Forced moves make things easier.

1. Bh4 g5 2. Kg1
a) 2. ... gxh4 3. Kf2 Kh2 4. Rxh4#
b) 2. ... g4 3. Bg5 g3 (3. ... Kg3 4. Ra3# ) 4. Rh4#

From Sokolsky - Ravinsky
White to move and win

I'm not asking for a full variation list. Finding the first move and showing why other alternatives don't work is fine.

Obviously 1.a8Q or 1.Rb8 fail after 1...Rc2+ 2.Ka3 Ra2+ 3. Kb4 Rxa8 = or 3...Ra4+ 4.Kc5 Rc4+ with perpetual check.
So 1.b4 Rc8 /1...Rd(e5)? 2.a8Q Rd(e)2 + 3.Kc3 Rc2+ 4. Kd4 Rd2 +5. Ke5 Re2+ 6.Qe4 + -/
2.b5 Ra8 /2... Bd7 3. Rb7 Be8 4. b6 Ra8 5. Rxf7 ~ 6. b7 + -/ 3. Rb8 Rxb8 4. axb8N! Bxb5 5. Ka3 and the knight makes its way to e7 mating.
Unless I have missed something 🙂. A nice puzzle in any case.
Very well... The famous end of the Mitrofanov's study:

White to play and win.

Originally posted by ilywrin
Obviously 1.a8Q or 1.Rb8 fail after 1...Rc2+ 2.Ka3 Ra2+ 3. Kb4 Rxa8 = or 3...Ra4+ 4.Kc5 Rc4+ with perpetual check.
So 1.b4 Rc8 /1...Rd(e5)? 2.a8Q Rd(e)2 + 3.Kc3 Rc2+ 4. Kd4 Rd2 +5. Ke5 Re2+ 6.Qe4 + -/
2.b5 Ra8 /2... Bd7 3. Rb7 Be8 4. b6 Ra8 5. Rxf7 ~ 6. b7 + -/ 3. Rb8 Rxb8 4. axb8N! Bxb5 5. Ka3 and the knight makes its way to e7 mating.
Unless I have miss ...[text shortened]... nd of the Mitrofanov's study:
[fen]kb4Q1/P7/1PP5/K6q/8/8/8/4n3 [/fen]
White to play and win.

I've always had the solution as 1. a8=B being the only winning move. But I'll have to look into your lines and see if there is a mistake there or if I've misremembered the puzzle.

The Mitrofanov study is famous for the seemingly illogical 1. Qg5 leading to mate.

yes, the solution is indeed 1.a8B! I failed to see that after 1.b4 Rc8 2.b5 Black can play 2...Bxb5 and now 3.Rxb5 Rc2+ leads to perpetula check 🙁. Ah, well, and to think I discarded 1.a8B as too long to analyze... Anyway:
a very nice and not too long study:

White to play and win

Originally posted by ilywrin
yes, the solution is indeed 1.a8B! I failed to see that after 1.b4 Rc8 2.b5 Black can play 2...Bxb5 and now 3.Rxb5 Rc2+ leads to perpetula check 🙁. Ah, well, and to think I discarded 1.a8B as too long to analyze... Anyway:
a very nice and not too long study:
[fen]1N6/8/K7/3k4/3p3B/p7/2PP4/8 [/fen]
White to play and win

You can find the analysis (I agree it is very long) at the bottom of this page. http://www.xs4all.nl/~timkr/chess2/minor.htm

Still unanswered:

White to play and win