user12377: In a recent Youtube video, the black player reaches the following position
[White "NN"]
[Black "Chess Simp"]
[FEN "r2r4/ppp2p1k/2n4P/4p3/P3n3/B1P1P2P/P1qPK2P/R6R b - - 0 1"]

1... Rxd2+ 2.Kf3 Rf2+ (2.Kf1 Rxh2 3.Rxh2 Qxh2 {And mate to follow on the second rank.}) (2.Ke1 Rf2 {White cannot stop checkmate on d2.}) 3.Kg4 Qd2 {The queen joins the attack via e3 or d8}

Now, obviously black is completely winning and under normal circumstances has mate in 4. However, due to the constraints of a self-imposed challenge, black is only allowed to move pieces and pawns to dark squares. Nevertheless, the overwhelming material advantage should lead to checkmate soon. I've put what I think are the best continuations for black, but I'm having trouble finding a forced checkmate in the Kf3 line. Any help?

user32420: It looks that your variation should follow with Kh6 first, other than any Queen move.
See some variations:
[Title "Variations after 1...Rxd2+"]
[FEN "r2r4/ppp2p1k/2n4P/4p3/P3n3/B1P1P2P/P1qPK2P/R6R b - - 0 1"]

1...Rxd2+ 2. Kf3 Rf2 3. Kg4 Kxh6 4. Bc1 Nf6+ 5. Kh4 Rf4+ 6. exf4 (6. Kg3 Qf2#) Qf2#
(4. Bf8+ Rxf8 5. a3 Ne7 6. Rad1 Rf4+ 7. exf4 Qf2 8. Rdf1 Nf6#)
(4. Kh4 Rf4+ 5. exf4 Qf2+ 6. Kg4 Qf4#)
(4...Ne7 5. a3 Rf4+ 6. exf4 Qf2 7. fxe5+ Kg7 8. Rg1 Rh8 9. Bh6+ Rxh6 10. c4 Rh4#) 

I have been checking this for a few hours, it looks that after King to g4, ...Kxh6 gives the best chances. Black can also put a8-Rook into game from the d8-square, it can be sacrificed from d4 to open the position.
EDITED for 4. Raf1 variations:
4. Raf1 Qd2, 5. Kh4 Qd8+, 6. Be7 Qxe7+, 7. Kg4 Qg5#
4. Raf1 Qd2, 5. Rxf2 Qxf2, 6. Bf8+ Rxf8, 7. h4 Qxe3, 8. Rf1 Ne7, 9. Rxf7 Nf6+, 10. Rxf6+ Rxf6 11. a3 Rf5#
4. Raf1 Qd2, 5. Rxf2 Qxf2, 6. Bf8+ Rxf8, 7. h4 Qxe3, 8. Rf1 Ne7, 9. h5 Nf2+ 10. Kh4 Qf4#
4. Raf1 Qd2, 5. Rxf2 Qxf2, 6. Bf8+ Rxf8, 7. h4 Qxe3, 8. Rf1 Ne7, 9. h5 Nf2+ 10. Rxf2 Qxf2 11. a3 Rd8 12. a5 Rd2 13. c4 Qf4+ 14. Kh3 Rxh2#
4. Raf1 Qd2, 5. Rhg1 Qxe3 6. Bc1 Qxc1 7. Rxc1 Rf4#
4. Raf1 Qd2, 5. Rhg1 Qxe3 6. Bc1 Qxc1 7. Rxf2 Qxg1+ 8. Kf3 Qxf2+ 9. Kxe4 Rd8 10. a3 Qf4# 


12377: <p>In a <a href="https://www.youtube.com/watch?v=k_XXjjunU58" rel="nofollow noreferrer">recent Youtube video</a>, the black player reaches the following position</p>
<pre><code>[White &quot;NN&quot;]
[Black &quot;Chess Simp&quot;]
[FEN &quot;r2r4/ppp2p1k/2n4P/4p3/P3n3/B1P1P2P/P1qPK2P/R6R b - - 0 1&quot;]

1... Rxd2+ 2.Kf3 Rf2+ (2.Kf1 Rxh2 3.Rxh2 Qxh2 {And mate to follow on the second rank.}) (2.Ke1 Rf2 {White cannot stop checkmate on d2.}) 3.Kg4 Qd2 {The queen joins the attack via e3 or d8}
</code></pre>
<p>Now, obviously black is completely winning and under normal circumstances has mate in 4. However, due to the constraints of a self-imposed challenge, black is only allowed to move pieces and pawns to dark squares. Nevertheless, the overwhelming material advantage should lead to checkmate soon. I've put what I think are the best continuations for black, but I'm having trouble finding a forced checkmate in the Kf3 line. Any help?</p>
 32420: <p>It looks that your variation should follow with Kh6 first, other than any Queen move.
See some variations:</p>
<pre><code>[Title &quot;Variations after 1...Rxd2+&quot;]
[FEN &quot;r2r4/ppp2p1k/2n4P/4p3/P3n3/B1P1P2P/P1qPK2P/R6R b - - 0 1&quot;]

1...Rxd2+ 2. Kf3 Rf2 3. Kg4 Kxh6 4. Bc1 Nf6+ 5. Kh4 Rf4+ 6. exf4 (6. Kg3 Qf2#) Qf2#
(4. Bf8+ Rxf8 5. a3 Ne7 6. Rad1 Rf4+ 7. exf4 Qf2 8. Rdf1 Nf6#)
(4. Kh4 Rf4+ 5. exf4 Qf2+ 6. Kg4 Qf4#)
(4...Ne7 5. a3 Rf4+ 6. exf4 Qf2 7. fxe5+ Kg7 8. Rg1 Rh8 9. Bh6+ Rxh6 10. c4 Rh4#) 
</code></pre>
<p>I have been checking this for a few hours, it looks that after King to g4, ...Kxh6 gives the best chances. Black can also put a8-Rook into game from the d8-square, it can be sacrificed from d4 to open the position.</p>
<p>EDITED for <code>4. Raf1</code> variations:</p>
<pre><code>4. Raf1 Qd2, 5. Kh4 Qd8+, 6. Be7 Qxe7+, 7. Kg4 Qg5#
4. Raf1 Qd2, 5. Rxf2 Qxf2, 6. Bf8+ Rxf8, 7. h4 Qxe3, 8. Rf1 Ne7, 9. Rxf7 Nf6+, 10. Rxf6+ Rxf6 11. a3 Rf5#
4. Raf1 Qd2, 5. Rxf2 Qxf2, 6. Bf8+ Rxf8, 7. h4 Qxe3, 8. Rf1 Ne7, 9. h5 Nf2+ 10. Kh4 Qf4#
4. Raf1 Qd2, 5. Rxf2 Qxf2, 6. Bf8+ Rxf8, 7. h4 Qxe3, 8. Rf1 Ne7, 9. h5 Nf2+ 10. Rxf2 Qxf2 11. a3 Rd8 12. a5 Rd2 13. c4 Qf4+ 14. Kh3 Rxh2#
4. Raf1 Qd2, 5. Rhg1 Qxe3 6. Bc1 Qxc1 7. Rxc1 Rf4#
4. Raf1 Qd2, 5. Rhg1 Qxe3 6. Bc1 Qxc1 7. Rxf2 Qxg1+ 8. Kf3 Qxf2+ 9. Kxe4 Rd8 10. a3 Qf4# 
</code></pre>
