user20092: [FEN "4r3/pq3k2/1p4p1/2p1Qn1p/2PpN3/3P4/PP3PPP/R5K1 w - - 0 1"]

It is White to move the above position.
After Ng5 check, the Black king can go only to g8 or f8.
If the Black king goes to g8, they lose their rook. After Kf8 by Black, what is White's best move?

user15543: White is easily winning in this position. Here is the best continuation according to Stockfish. I would trust Stockfish on this one since it should be pretty easy for a good tatictal player to figure out themselves.
 [FEN "4r3/pq3k2/1p4p1/2p1Qn1p/2PpN3/3P4/PP3PPP/R5K1 w - - 0 1"]

1. Ng5+ Kf8 2. Qh8+ Ke7 3. Re1+ Kd6 4. Qxe8 Qd7 5. Qxg6+ Kc7 6. Ne6+ Kb8 7. Qxf5 a5 8. Nxd4 Qxf5 9. Nxf5 a4

White is now two pawns and two pieces up. It is an easy stroll to victory lane from here.

user12873: Best is 2.Qh8+ Ke7, after which White has a choice:

Go for 3.Qh7+ Kf6 4.Qxb7 Kxg5, when White has won a queen for a knight with a completely winning position.
Go for 3.Re1+, which is slightly more complicated but leads to a forced mate according to Stockfish:


 [FEN "4r2Q/pq2k3/1p4p1/2p2nNp/2Pp4/3P4/PP3PPP/R5K1 w - - 0 3"]

3.Re1+ Ne3 4.Qg7+ Kd6 5.Qxb7 Re7 6.Qb8+ Kc6 7.fxe3 Rb7 8.Qa8 a5 9.exd4 cxd4 10.Qc8+ Rc7 11.Re6+ Kc5 12.Qf8+ Re7 13.Qxe7#.


20092: <pre><code>[FEN "4r3/pq3k2/1p4p1/2p1Qn1p/2PpN3/3P4/PP3PPP/R5K1 w - - 0 1"]
</code></pre>

<p>It is White to move the above position.</p>

<p>After Ng5 check, the Black king can go only to g8 or f8.</p>

<p>If the Black king goes to g8, they lose their rook. After Kf8 by Black, what is White's best move?</p>
 15543: <p>White is easily winning in this position. Here is the best continuation according to Stockfish. I would trust Stockfish on this one since it should be pretty easy for a good tatictal player to figure out themselves.</p>

<pre><code> [FEN "4r3/pq3k2/1p4p1/2p1Qn1p/2PpN3/3P4/PP3PPP/R5K1 w - - 0 1"]

1. Ng5+ Kf8 2. Qh8+ Ke7 3. Re1+ Kd6 4. Qxe8 Qd7 5. Qxg6+ Kc7 6. Ne6+ Kb8 7. Qxf5 a5 8. Nxd4 Qxf5 9. Nxf5 a4
</code></pre>

<p>White is now two pawns and two pieces up. It is an easy stroll to victory lane from here.</p>
 12873: <p>Best is 2.Qh8+ Ke7, after which White has a choice:</p>

<ol>
<li>Go for <code>3.Qh7+ Kf6 4.Qxb7 Kxg5</code>, when White has won a queen for a knight with a completely winning position.</li>
<li>Go for <code>3.Re1+</code>, which is slightly more complicated but leads to a forced mate according to Stockfish:</li>
</ol>

<hr>

<pre><code> [FEN "4r2Q/pq2k3/1p4p1/2p2nNp/2Pp4/3P4/PP3PPP/R5K1 w - - 0 3"]

3.Re1+ Ne3 4.Qg7+ Kd6 5.Qxb7 Re7 6.Qb8+ Kc6 7.fxe3 Rb7 8.Qa8 a5 9.exd4 cxd4 10.Qc8+ Rc7 11.Re6+ Kc5 12.Qf8+ Re7 13.Qxe7#.
</code></pre>
