Answers.Body: <p>Position #1 - Black has a strong attack starting with Rxb3+, except the White Queen spoils the fun with Qxb3. However 1... Rh2! decoys the White Q to <code>h2</code>, leaving <code>b3</code> insufficiently defended. ex: <code>2... Rxb3+ 3. axb3 Qa1+ 4. Kc2 Nb4#</code>.  Or, if White refuses the Rook sacrifice and plays <code>2. Qd3</code>, black exploits the double attack on <code>a2</code> to force mate in 2: Qxa2+ followed by Qb2#.</p>
  
  <p>If White defends by interposing a Bishop or Rook, black just takes it, and White has the same dilemma but with fewer pieces. Once the Queen is decoyed from the defense of <code>b3</code>, Rxb3+ carries the day.</p>
  
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Answers.Body: <p>I believe that I can answer about position two, but I don't have time to analyze the others at the moment. After the rook goes in as a sacrifice, do QxF6 instead or BxF6. The only move the king has is to retreat to G8. White plays BH6 to set up for QG7 mate. To survive, Black must play either QF7 or QG6 in order to capture something. If QG6, white can play QF8 mate. If QG6, then white plays QD8 and it is not great for black. He must block with the queen, and will lose her either of the two squares she can block at (E8 or F8). E8, white captures for mate.</p>
  
  <p>EDIT: Position four doesn't look like much, perhaps it just wants you to win the knight?</p>
  
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Answers.Text: Whoops, I was not paying attention to the queen. Sorry!
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Answers.Body: <p>I will answer for position 1 and let you do the rest yourself.  The quickest way to figure these out is with an engine... there are several free engines you can find online that will answer all of your questions for you.  That said, I'm going to try and answer your questions on Position 1 without an engine. :)</p>
  
  <p>Well, 1. ... Rh2 looks really powerful.  The white Q is hit and white has no checks against the Black K, so white needs to address the threat.  The only ways to address the attack on the white Q are (a) move the Q or (b) block via Rg2, Be2, or Rd2.  Any Q move other than Qxh2 is bad since Black will take Qxa2+ and will soon mate.  So let's consider 2. Qxh2.  The only reasonable followup is 2. ... Rxb3+ as you noted.  If 3. axb3 Qa1+ 4. Kf2 we notice Qb2+ wins the white Q, but it cost us 2 rooks, which isn't great. So look for a better move... 4. ... Nb4 mate!  Ok, so after 2. ... Rxb3+ white cannot take the R.  But he's still up a R, so maybe he can run?  Both c2 and c1 are available after Rxb3+.  Both options look horrible though since the Black Q comes in with check and white's Q on h2 cannot get back to help.</p>
  
  <p>Specifically, 1. ... Rh2! 2. Qxh2 Rxb3+! 3. Kc1 Qa3+ 4. Kc2 Nb4#.  Or 3. Kc2 Qxa2+  4. Kc1 Rb1#.</p>
  
  <p>Ok, so after 1. ... Rh2! the rook cannot be taken, so white can try to block with 2. Rg2 or 2. Be2 or the horrible 2. Rd2.  But in every case, black just takes with the rook since the whole point is to distract the Q from guarding b3.  So white is just toast.</p>
  
  <hr>
  
  <p>Note: you want to try and visualize all of this without moving pieces.  Feel free to set up on a real board, but don't move anything.  This will make you stronger much faster.</p>
  
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Answers.UserDisplayName: Fixee
Answers.Body: <p>This is a very long question. And you can use Stockfish to check tactical solutions.</p>
  
  <p>Solutions of all positions except the 5th ends with mate or huge material gain. In position 5, Black plays a positional sacrifice, to turn that cramped position into a nice attacking one.</p>
  
  <hr>
  
  <h1>Position 1 - Black to play, why Rh2?</h1>
  
  <pre><code>[FEN "1r2k2r/p4pp1/2n1p3/q2pP1N1/3P1PB1/1Pb5/P1Q5/1K1R2R1 b - - 0 1"]
  
  1... Rh2 2. Qxh2 Rxb3 3. Kc2 (3.Kc1 Qa3 4. Kc2 Nb4#) (3. axb3 Qa1 4. Kc2 Nb4#) Qxa2 4. Kc1 Qb1#
  </code></pre>
  
  <hr>
  
  <h1>Position 2 - White to play, why Re8?</h1>
  
  <pre><code>[FEN "r1bq4/1p4kp/3p1n2/p4pB1/2pQ4/8/1P4PP/4RRK1 w - - 0 1"]
  
  1. Re8 Qe8 2. Qf6 Kg8 3. Bh6 Qf7 4. Qd8 Qf8 5. Qf8#
  </code></pre>
  
  <hr>
  
  <h1>Position 3 - White to play, why Nd7?</h1>
  
  <pre><code>[FEN "2rq1rk1/1b2bppp/p1n5/1p1BN3/5B2/P7/1P3PPP/R2Q1RK1 w - - 0 1"]
  
  
  1. Nd7 Re8 2. Bxf7+ Kxf7 3. Qd5+ Kg6 4. g4 Bg5 ( 4... h6 5. Qf5# ) 5. Qf5+ Kh6
  6. h4 g6 7. Bxg5+ Kg7 8. Bf6+ Kf7 9. Qd5+ Re6 10. Bxd8  
  </code></pre>
  
  <hr>
  
  <h1>Position 4 - Black to play, why Bf6?</h1>
  
  <pre><code>[FEN "r4rk1/p6p/2q5/1p2pnB1/3p2Q1/P2P4/1P5P/R4RK1 w - - 0 1"]
  
  
  1. Bf6+ Kf7 2. Rxf5 Ke6 3. Rxe5+ Kd6 4. Re6+ Kc7 5. Qg7+ Kb6 6. Rxc6+ Kxc6 7.
  Rc1+ Kb6 8. Qc7+ Ka6 9. Rc6#  
  </code></pre>
  
  <hr>
  
  <h1>Position 5 - Black to play, why e5?</h1>
  
  <pre><code>[FEN "1nr5/2rbkppp/p3p3/Np6/2PRPP2/8/PKP1B1PP/3R4 b - - 0 1"]
  
  
  1... e5 $1 { Black has a cramped position. White rooks are dominating d-file,
  bishop and knight pressing hard on queenside. Black can't move.
  
  With ...e5,
  sacrificing pawn, Black vacates e6 square for bishop and doubles  and isolates
  White's pawns in the center. After fxe5, White's pawns are not threatening any
  more.}  2. fxe5 Be6 { Now it's the Black is attacking the c4 pawn, and c2 pawn
  with doubled rooks. Black turned a cramped position into attacking one with a
  very clever pawn sacrifice, which ruined White's pawn formation.}  
  </code></pre>
  
  <hr>
  
  <h1>Position 6 - Black to play, why Qh6?</h1>
  
  <pre><code>[FEN "2r2rk1/pp2pp1p/2np2p1/q4P2/2PBP1b1/2N5/PP1Q2PP/R4RK1 w - - 0 1"]
  
  
  1. Qh6 Nxd4 2. Nd5 Qd8 ( 2... Rfe8 3. f6 Ne6 4. fxe7 Qc5+ 5. Kh1 Qd4 6. Nf6+
  Qxf6 7. Rxf6 ) 3. Nxe7+ Qxe7 4. f6 Qxf6 5. Rxf6  
  </code></pre>
  
  <hr>
  
  <h1>Position 7 - Black to play, why Bxf3?</h1>
  
  <pre><code>[FEN "2rr2k1/p4p1p/2n3pb/2Ppp3/3Pb3/P1R1PNqP/4Q1P1/B3RB1K b - - 0 1"]
  
  
  1... Bxf3 2. gxf3 exd4 3. exd4 ( 3. Rcc1 Bxe3 4. Qg2 Qxg2+ 5. Kxg2 Bxc1 6. Rxc1
  ) 3... Nxd4 4. Qe7 ( 4. Qd1 Bf4 5. Re2 Nxe2 6. Qxe2 Re8 7. Qg2 Re1 8. Qxg3 Bxg3
  9. Kg2 Rxa1 10. Kxg3 Rxf1 ) 4... Bf4 5. Re2 Nxe2 6. Qxe2 Rb8 7. Rc2 Rb1 8. Qg2
  Qxg2+ 9. Kxg2 Rxa1  
  </code></pre>
  
Answers.ContentLicense: CC BY-SA 3.0
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Answers.Text: Thank you for taking the long time to write this answer. The only remaining doubt is on Position 3, what would be the follow-up after `1. Nd7 Re8 2. Bxf7+ Kxf7 3. Qd5+ Kg6 4. g4 Bg5`? Other than that, I was able to understand everything, thank you very much.
Answers.UserDisplayName: Pedro A
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Answers.Text: @Hamsteriffic: `5.h4` seems like a winning move...
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Answers.Text: @Hamsteriffic Updated the solution of position 3, Bg5 is the best defense of Black, it's good that you see it, actually I missed it :)
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Answers.UserDisplayName: ferit
Body: <p>I was using a phone-app called <strong>Chessrating</strong> to get an estimation of my ELO rating. It gives me 16 chess positions and I have four attempts to find the best move. There were some positions that I did not understand the app's move choice. <strong>Why are those the best moves in the given positions? Is the app correct on all of them?</strong></p>
  
  <p>These are the 7 positions that I didn't understand, out of about 50 positions I played. They are all about sacrifices, except positions 4 and 7.</p>
  
  <ul>
  <li>I realize that if the sacrifice is accepted, some attacking chances show up, but I can't find a winning follow-up, and in the end, to me it looks like the player is just down the sacrifice.</li>
  <li>Of course, it is not obligatory to accept the sacrifice, and for that reason I don't see some of those sacrifices as winning. For the moves to be really winning, they must be winning in both cases (if either the sac is accepted or declined).</li>
  </ul>
  
  <hr>
  
  <h1>Position 1 - Black to play, why Rh2?</h1>
  
  <pre><code>1r2k2r/p4pp1/2n1p3/q2pP1N1/3P1PB1/1Pb5/P1Q5/1K1R2R1 b - - 0 1
  </code></pre>
  
  <p>My thoughts: after Qxh2, maybe black could play Rxb3+, but I don't see a checkmate follow-up, so it looks like black will be down a Rook.</p>
  
  <hr>
  
  <h1>Position 2 - White to play, why Re8?</h1>
  
  <pre><code>r1bq4/1p4kp/3p1n2/p4pB1/2pQ4/8/1P4PP/4RRK1 w - - 0 1
  </code></pre>
  
  <p>My thoughts: I think there is no problem with black accepting the rook sacrifice, by Qxe8. Of course black can then take the Knight on f6 with check, but I don't see a checkmate follow-up, so it seems to me that white would be down an exchange.</p>
  
  <hr>
  
  <h1>Position 3 - White to play, why Nd7?</h1>
  
  <pre><code>2rq1rk1/1b2bppp/p1n5/1p1BN3/5B2/P7/1P3PPP/R2Q1RK1 w - - 0 1
  </code></pre>
  
  <p>My thoughts: This time, I realize that if black accepts the knight sacrifice, they will lose their Queen in a follow-up tactic. But black could just decline the sacrifice with Re8, and I don't see a winning follow-up for white.</p>
  
  <hr>
  
  <h1>Position 4 - White to play, why Bf6+?</h1>
  
  <pre><code>r4rk1/p6p/2q5/1p2pnB1/3p2Q1/P2P4/1P5P/R4RK1 w - - 0 1
  </code></pre>
  
  <p>My thoughts: after black plays Kf7, I don't see any special follow-up for white, and this check doesn't seem to have anything special.</p>
  
  <hr>
  
  <h1>Position 5 - Black to play, why e5?</h1>
  
  <pre><code>1nr5/2rbkppp/p3p3/Np6/2PRPP2/8/PKP1B1PP/3R4 b - - 0 1
  </code></pre>
  
  <p>My thoughts: to me it looks like white can just take with the pawn (fxe5) and I don't see nothing special going on.</p>
  
  <hr>
  
  <h1>Position 6 - White to play, why Qh6?</h1>
  
  <pre><code>2r2rk1/pp2pp1p/2np2p1/q4P2/2PBP1b1/2N5/PP1Q2PP/R4RK1 w - - 0 1
  </code></pre>
  
  <p>My thoughts: after the queen goes to h6, if I was playing black I would immediately capture the bishop with the Knight, that is, Nxd4. Now I don't see any compensation for white.</p>
  
  <hr>
  
  <h1>Position 7 - Black to play, why Bxf3?</h1>
  
  <pre><code>2rr2k1/p4p1p/2n3pb/2Ppp3/3Pb3/P1R1PNqP/4Q1P1/B3RB1K b - - 0 1
  </code></pre>
  
  <p>My thoughts: to me it just looks like a simple exchange, exchanging the bishop for the knight. Of course white should take back with the pawn, because taking back with the queen leads to losing the rook. Why is this exchange considered good/useful?</p>
  
  <hr>
  
  <p><strong>So why are those considered the best moves on those positions? Do you see a better move in each position?</strong> In my opinion, a sacrifice can only be considered good if independently of the opponent accepting or declining the sacrifice, there is a good outcome. I don't want to hope that my opponent will play poorly.</p>
  
  <p><em>(I know this is a long question, should I split it in several (seven) questions instead?)</em></p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-01-03T22:36:12.717Z
Comments.Text: Yes, I think it is better to split into several questions as there are many positions to discuss.
Comments.UserDisplayName: Dag Oskar Madsen
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-01-04T13:05:33.730Z
Comments.Text: Of these, I find position 5 most interesting. The others are relatively straightforward tactical exercises.
Comments.UserDisplayName: Dag Oskar Madsen
Tags: <tactics><middlegame><sacrifice>
Title: Why are these sacrifices good moves? What are the winning follow-ups?
ThreadText: # Why are these sacrifices good moves? What are the winning follow-ups?
  
  (Asked by: username_0 on 2016-01-03)
  
  I was using a phone-app called **Chessrating** to get an estimation of my ELO rating. It gives me 16 chess positions and I have four attempts to find the best move. There were some positions that I did not understand the app's move choice. **Why are those the best moves in the given positions? Is the app correct on all of them?**
  
  These are the 7 positions that I didn't understand, out of about 50 positions I played. They are all about sacrifices, except positions 4 and 7.
  
  * I realize that if the sacrifice is accepted, some attacking chances show up, but I can't find a winning follow-up, and in the end, to me it looks like the player is just down the sacrifice.
  * Of course, it is not obligatory to accept the sacrifice, and for that reason I don't see some of those sacrifices as winning. For the moves to be really winning, they must be winning in both cases (if either the sac is accepted or declined).
  
  ---
  
  # Position 1 - Black to play, why Rh2?
  
  ```
  1r2k2r/p4pp1/2n1p3/q2pP1N1/3P1PB1/1Pb5/P1Q5/1K1R2R1 b - - 0 1
  
  ```
  
  My thoughts: after Qxh2, maybe black could play Rxb3+, but I don't see a checkmate follow-up, so it looks like black will be down a Rook.
  
  ---
  
  # Position 2 - White to play, why Re8?
  
  ```
  r1bq4/1p4kp/3p1n2/p4pB1/2pQ4/8/1P4PP/4RRK1 w - - 0 1
  
  ```
  
  My thoughts: I think there is no problem with black accepting the rook sacrifice, by Qxe8. Of course black can then take the Knight on f6 with check, but I don't see a checkmate follow-up, so it seems to me that white would be down an exchange.
  
  ---
  
  # Position 3 - White to play, why Nd7?
  
  ```
  2rq1rk1/1b2bppp/p1n5/1p1BN3/5B2/P7/1P3PPP/R2Q1RK1 w - - 0 1
  
  ```
  
  My thoughts: This time, I realize that if black accepts the knight sacrifice, they will lose their Queen in a follow-up tactic. But black could just decline the sacrifice with Re8, and I don't see a winning follow-up for white.
  
  ---
  
  # Position 4 - White to play, why Bf6+?
  
  ```
  r4rk1/p6p/2q5/1p2pnB1/3p2Q1/P2P4/1P5P/R4RK1 w - - 0 1
  
  ```
  
  My thoughts: after black plays Kf7, I don't see any special follow-up for white, and this check doesn't seem to have anything special.
  
  ---
  
  # Position 5 - Black to play, why e5?
  
  ```
  1nr5/2rbkppp/p3p3/Np6/2PRPP2/8/PKP1B1PP/3R4 b - - 0 1
  
  ```
  
  My thoughts: to me it looks like white can just take with the pawn (fxe5) and I don't see nothing special going on.
  
  ---
  
  # Position 6 - White to play, why Qh6?
  
  ```
  2r2rk1/pp2pp1p/2np2p1/q4P2/2PBP1b1/2N5/PP1Q2PP/R4RK1 w - - 0 1
  
  ```
  
  My thoughts: after the queen goes to h6, if I was playing black I would immediately capture the bishop with the Knight, that is, Nxd4. Now I don't see any compensation for white.
  
  ---
  
  # Position 7 - Black to play, why Bxf3?
  
  ```
  2rr2k1/p4p1p/2n3pb/2Ppp3/3Pb3/P1R1PNqP/4Q1P1/B3RB1K b - - 0 1
  
  ```
  
  My thoughts: to me it just looks like a simple exchange, exchanging the bishop for the knight. Of course white should take back with the pawn, because taking back with the queen leads to losing the rook. Why is this exchange considered good/useful?
  
  ---
  
  **So why are those considered the best moves on those positions? Do you see a better move in each position?** In my opinion, a sacrifice can only be considered good if independently of the opponent accepting or declining the sacrifice, there is a good outcome. I don't want to hope that my opponent will play poorly.
  
  *(I know this is a long question, should I split it in several (seven) questions instead?)*
  
  **Tags:** tactics, middlegame, sacrifice
  
  > **Comments:**
  > **username_1**: Yes, I think it is better to split into several questions as there are many positions to discuss.  
  > **username_1**: Of these, I find position 5 most interesting. The others are relatively straightforward tactical exercises.  
  
  ---
  
  ## 4 answers
  
  ### Answer by username_5 on 2016-01-03. Score: 8 | Accepted answer
  
  This is a very long question. And you can use Stockfish to check tactical solutions.
  
  Solutions of all positions except the 5th ends with mate or huge material gain. In position 5, Black plays a positional sacrifice, to turn that cramped position into a nice attacking one.
  
  ---
  
  # Position 1 - Black to play, why Rh2?
  
  ```
  [FEN "1r2k2r/p4pp1/2n1p3/q2pP1N1/3P1PB1/1Pb5/P1Q5/1K1R2R1 b - - 0 1"]
  
  1... Rh2 2. Qxh2 Rxb3 3. Kc2 (3.Kc1 Qa3 4. Kc2 Nb4#) (3. axb3 Qa1 4. Kc2 Nb4#) Qxa2 4. Kc1 Qb1#
  
  ```
  
  ---
  
  # Position 2 - White to play, why Re8?
  
  ```
  [FEN "r1bq4/1p4kp/3p1n2/p4pB1/2pQ4/8/1P4PP/4RRK1 w - - 0 1"]
  
  1. Re8 Qe8 2. Qf6 Kg8 3. Bh6 Qf7 4. Qd8 Qf8 5. Qf8#
  
  ```
  
  ---
  
  # Position 3 - White to play, why Nd7?
  
  ```
  [FEN "2rq1rk1/1b2bppp/p1n5/1p1BN3/5B2/P7/1P3PPP/R2Q1RK1 w - - 0 1"]
  
  1. Nd7 Re8 2. Bxf7+ Kxf7 3. Qd5+ Kg6 4. g4 Bg5 ( 4... h6 5. Qf5# ) 5. Qf5+ Kh6
  6. h4 g6 7. Bxg5+ Kg7 8. Bf6+ Kf7 9. Qd5+ Re6 10. Bxd8  
  
  ```
  
  ---
  
  # Position 4 - Black to play, why Bf6?
  
  ```
  [FEN "r4rk1/p6p/2q5/1p2pnB1/3p2Q1/P2P4/1P5P/R4RK1 w - - 0 1"]
  
  1. Bf6+ Kf7 2. Rxf5 Ke6 3. Rxe5+ Kd6 4. Re6+ Kc7 5. Qg7+ Kb6 6. Rxc6+ Kxc6 7.
  Rc1+ Kb6 8. Qc7+ Ka6 9. Rc6#  
  
  ```
  
  ---
  
  # Position 5 - Black to play, why e5?
  
  ```
  [FEN "1nr5/2rbkppp/p3p3/Np6/2PRPP2/8/PKP1B1PP/3R4 b - - 0 1"]
  
  1... e5 $1 { Black has a cramped position. White rooks are dominating d-file,
  bishop and knight pressing hard on queenside. Black can't move.
  
  With ...e5,
  sacrificing pawn, Black vacates e6 square for bishop and doubles  and isolates
  White's pawns in the center. After fxe5, White's pawns are not threatening any
  more.}  2. fxe5 Be6 { Now it's the Black is attacking the c4 pawn, and c2 pawn
  with doubled rooks. Black turned a cramped position into attacking one with a
  very clever pawn sacrifice, which ruined White's pawn formation.}  
  
  ```
  
  ---
  
  # Position 6 - Black to play, why Qh6?
  
  ```
  [FEN "2r2rk1/pp2pp1p/2np2p1/q4P2/2PBP1b1/2N5/PP1Q2PP/R4RK1 w - - 0 1"]
  
  1. Qh6 Nxd4 2. Nd5 Qd8 ( 2... Rfe8 3. f6 Ne6 4. fxe7 Qc5+ 5. Kh1 Qd4 6. Nf6+
  Qxf6 7. Rxf6 ) 3. Nxe7+ Qxe7 4. f6 Qxf6 5. Rxf6  
  
  ```
  
  ---
  
  # Position 7 - Black to play, why Bxf3?
  
  ```
  [FEN "2rr2k1/p4p1p/2n3pb/2Ppp3/3Pb3/P1R1PNqP/4Q1P1/B3RB1K b - - 0 1"]
  
  1... Bxf3 2. gxf3 exd4 3. exd4 ( 3. Rcc1 Bxe3 4. Qg2 Qxg2+ 5. Kxg2 Bxc1 6. Rxc1
  ) 3... Nxd4 4. Qe7 ( 4. Qd1 Bf4 5. Re2 Nxe2 6. Qxe2 Re8 7. Qg2 Re1 8. Qxg3 Bxg3
  9. Kg2 Rxa1 10. Kxg3 Rxf1 ) 4... Bf4 5. Re2 Nxe2 6. Qxe2 Rb8 7. Rc2 Rb1 8. Qg2
  Qxg2+ 9. Kxg2 Rxa1  
  
  ```
  
  > **Comments:**
  > **username_0**: Thank you for taking the long time to write this answer. The only remaining doubt is on Position 3, what would be the follow-up after `1. Nd7 Re8 2. Bxf7+ Kxf7 3. Qd5+ Kg6 4. g4 Bg5`? Other than that, I was able to understand everything, thank you very much.  
  > **username_6**: @Hamsteriffic: `5.h4` seems like a winning move...  
  > **username_5**: @Hamsteriffic Updated the solution of position 3, Bg5 is the best defense of Black, it's good that you see it, actually I missed it :)  
  
  ---
  
  ### Answer by username_2 on 2016-01-03. Score: 2
  
  Position #1 - Black has a strong attack starting with Rxb3+, except the White Queen spoils the fun with Qxb3. However 1... Rh2! decoys the White Q to `h2`, leaving `b3` insufficiently defended. ex: `2... Rxb3+ 3. axb3 Qa1+ 4. Kc2 Nb4#`. Or, if White refuses the Rook sacrifice and plays `2. Qd3`, black exploits the double attack on `a2` to force mate in 2: Qxa2+ followed by Qb2#.
  
  If White defends by interposing a Bishop or Rook, black just takes it, and White has the same dilemma but with fewer pieces. Once the Queen is decoyed from the defense of `b3`, Rxb3+ carries the day.
  
  
  ---
  
  ### Answer by username_3 on 2016-01-03. Score: 1
  
  I believe that I can answer about position two, but I don't have time to analyze the others at the moment. After the rook goes in as a sacrifice, do QxF6 instead or BxF6. The only move the king has is to retreat to G8. White plays BH6 to set up for QG7 mate. To survive, Black must play either QF7 or QG6 in order to capture something. If QG6, white can play QF8 mate. If QG6, then white plays QD8 and it is not great for black. He must block with the queen, and will lose her either of the two squares she can block at (E8 or F8). E8, white captures for mate.
  
  EDIT: Position four doesn't look like much, perhaps it just wants you to win the knight?
  
  > **Comments:**
  > **username_3**: Whoops, I was not paying attention to the queen. Sorry!  
  
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  ### Answer by username_4 on 2016-01-03. Score: 1
  
  I will answer for position 1 and let you do the rest yourself. The quickest way to figure these out is with an engine... there are several free engines you can find online that will answer all of your questions for you. That said, I'm going to try and answer your questions on Position 1 without an engine. :)
  
  Well, 1. ... Rh2 looks really powerful. The white Q is hit and white has no checks against the Black K, so white needs to address the threat. The only ways to address the attack on the white Q are (a) move the Q or (b) block via Rg2, Be2, or Rd2. Any Q move other than Qxh2 is bad since Black will take Qxa2+ and will soon mate. So let's consider 2. Qxh2. The only reasonable followup is 2. ... Rxb3+ as you noted. If 3. axb3 Qa1+ 4. Kf2 we notice Qb2+ wins the white Q, but it cost us 2 rooks, which isn't great. So look for a better move... 4. ... Nb4 mate! Ok, so after 2. ... Rxb3+ white cannot take the R. But he's still up a R, so maybe he can run? Both c2 and c1 are available after Rxb3+. Both options look horrible though since the Black Q comes in with check and white's Q on h2 cannot get back to help.
  
  Specifically, 1. ... Rh2! 2. Qxh2 Rxb3+! 3. Kc1 Qa3+ 4. Kc2 Nb4#. Or 3. Kc2 Qxa2+ 4. Kc1 Rb1#.
  
  Ok, so after 1. ... Rh2! the rook cannot be taken, so white can try to block with 2. Rg2 or 2. Be2 or the horrible 2. Rd2. But in every case, black just takes with the rook since the whole point is to distract the Q from guarding b3. So white is just toast.
  
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  Note: you want to try and visualize all of this without moving pieces. Feel free to set up on a real board, but don't move anything. This will make you stronger much faster.
  
  
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