user45: The following tactics problem comes from ChessTempo, and was taken from a game between Anatoly Karpov and Alexey Kuzmin. It's white's move.
The idea of the problem is to find white's best move from the shown position.
But my question is slightly different: If both players play perfectly from the position shown in the diagram, can white force a win, or can black force a draw?
[FEN "8/3Q2pk/5p1p/5P2/5K1P/p3r3/b2n2P1/8 w - - 0 1"]

I tried using a few chess engines to analyze the position, leaving them running for hours. White gets a very favorable evaluation (about +4 or +5 depending on the engine). I'd normally consider this to be enough for a certain win. But after looking at the computer's best line it seems that after initially winning some material, white's queen just goes round in circles without making any further progress while the black king sits safely behind the wall of pawns. 
I guess either the position is a draw, or the computer isn't able to plan far enough ahead to find the winning line. I can't see an easy way for white to win, but I'm no expert and it's possible I've overlooked something.
So what do you think: is it a theoretical win for white or can black escape with a draw?

user142: Actually, this looks like a win to me. 
Once you get the below sequence:  
[FEN "8/3Q2pk/5p1p/5P2/5K1P/p3r3/b2n2P1/8 w - - 0 1"]

1. Qxd2 Re5 2. Qxa2 Ra5

The computer engines get distracted because of all of the possibilities with the king moving over to assist the queen with that lone pawn, but really, if you mix things up and start trading pawns on the kingside, you're going to end up with a much more favorable position for White.
Look at:
[FEN "8/6pk/5p1p/r4P2/5K1P/p7/Q5P1/8 w - - 0 1"]

3. g4

Which starts the action on the kingside. In fact, with Stockfish, this move alone wasn't recommended even after looking at the position for quite some time (it wanted me to march the king over to assist the queen in defending the queenside against the pawn and rook), but after I made it, the score immediately jumped up to 7+.
Anyway, a couple moves in from here and I started getting "mate in 35" reports, so I think this is definitely winnable once you start trading off (or winning) some of the kingside pawns, while watching out for the pawn on A.
Update after a bit more analysis:
Most paths get to something like the following:
[FEN "7k/6p1/8/5PK1/8/8/Q7/7r b - - 0 1"]

1... Rh6 2. Kf4 Rb6 3. Qc4 Rd6 4. Ke5 Rh6 5. Qc8+ Kh7 6. Qe6 Kh8 7. Kd6 Rf6 8. Ke7 Kh7 9. Qxf6 gxf6 10. Kxf6 Kh6 11. Ke6 Kh5 12. f6 Kg5 13. f7 Kf4 14. Kd5 Kf3 15. Kd4 Kg3 16. Ke4 Kh3 17. f8=Q Kg3 18. Qf3+ Kh2 19. Qg4 Kh1 20. Kf3 Kh2 21. Qg2#

Where you have one white pawn left on the kingside, and the queenside pawn was taken care of. So, the fortress is gone once you push the pawn a bit more and trade them off. With perfect play, it is a loss in 20 moves according to this 6-man tablebase.

user45: I think that the position is a theoretical draw.
While Freeman's answer is quite good, but I think he has overlooked that 1. Qxd2 leads to a clearly drawn position because of Black's amazing response 1 ...Rb3!!
[FEN "8/3Q2pk/5p1p/5P2/5K1P/p3r3/b2n2P1/8 w - - 0 1"]

1. Qxd2 Rb3!! 2. Qxa2 Rb2!! 3. Qxa3 Rxg2

Now I don't see any way for White to win. Black has created an impenetrable fortress and white's queen can do nothing.
The 2400+ rated player Alexey Kuzmin missed the move 1... Rb3 in the game, playing instead 1... Re5? which gives a theoretically losing position. All the engines I tried also miss the sequence 1... Rb3 and 2... Rb2 and instead play a losing move.
I suggest that if there is a forced win for White then we must start looking at 1.Kxe3. This move doesn't win as much material as 1. Qxd2, but it leads to a more dynamic position. White can prevent Black from promoting thanks to black's wrong-colored bishop that is unable to protect the a1 square. White can also threaten to advance the g-pawn to attempt to disrupt Black's wall of pawns.
However a computer analysis of 1. Kxd3 seems to show that despite White's material advantage Black can still get a draw.
I'm no expert, so there may be a mistake in my analysis, so please correct me if I'm wrong.

45: <p>The following <a href="http://chesstempo.com/chess-problems/92441" rel="noreferrer">tactics problem</a> comes from ChessTempo, and was taken from a <a href="http://chesstempo.com/gamedb/game/183362/8/3Q2pk/5p1p/5P2/5K1P/p3r3/b2n2P1/8%20w%20-%20-%200%2042" rel="noreferrer">game between Anatoly Karpov and Alexey Kuzmin</a>. It's white's move.</p>

<p>The idea of the problem is to find white's best move from the shown position.</p>

<p>But my question is slightly different: If both players play <em>perfectly</em> from the position shown in the diagram, can white force a win, or can black force a draw?</p>

<pre><code>[FEN "8/3Q2pk/5p1p/5P2/5K1P/p3r3/b2n2P1/8 w - - 0 1"]
</code></pre>

<p>I tried using a few chess engines to analyze the position, leaving them running for hours. White gets a very favorable evaluation (about +4 or +5 depending on the engine). I'd normally consider this to be enough for a certain win. But after looking at the computer's best line it seems that after initially winning some material, white's queen just goes round in circles without making any further progress while the black king sits safely behind the wall of pawns. </p>

<p>I guess either the position is a draw, or the computer isn't able to plan far enough ahead to find the winning line. I can't see an easy way for white to win, but I'm no expert and it's possible I've overlooked something.</p>

<p>So what do you think: is it a theoretical win for white or can black escape with a draw?</p>
 142: <p>Actually, this looks like a win to me. </p>

<p>Once you get the below sequence:  </p>

<pre><code>[FEN "8/3Q2pk/5p1p/5P2/5K1P/p3r3/b2n2P1/8 w - - 0 1"]

1. Qxd2 Re5 2. Qxa2 Ra5
</code></pre>

<p>The computer engines get distracted because of all of the possibilities with the king moving over to assist the queen with that lone pawn, but really, if you mix things up and start trading pawns on the kingside, you're going to end up with a much more favorable position for White.</p>

<p>Look at:</p>

<pre><code>[FEN "8/6pk/5p1p/r4P2/5K1P/p7/Q5P1/8 w - - 0 1"]

3. g4
</code></pre>

<p>Which starts the action on the kingside. In fact, with Stockfish, this move alone wasn't recommended even after looking at the position for quite some time (it wanted me to march the king over to assist the queen in defending the queenside against the pawn and rook), but after I made it, the score immediately jumped up to 7+.</p>

<p>Anyway, a couple moves in from here and I started getting "mate in 35" reports, so I think this is definitely winnable once you start trading off (or winning) some of the kingside pawns, while watching out for the pawn on A.</p>

<p><strong>Update after a bit more analysis:</strong></p>

<p>Most paths get to something like the following:</p>

<pre><code>[FEN "7k/6p1/8/5PK1/8/8/Q7/7r b - - 0 1"]

1... Rh6 2. Kf4 Rb6 3. Qc4 Rd6 4. Ke5 Rh6 5. Qc8+ Kh7 6. Qe6 Kh8 7. Kd6 Rf6 8. Ke7 Kh7 9. Qxf6 gxf6 10. Kxf6 Kh6 11. Ke6 Kh5 12. f6 Kg5 13. f7 Kf4 14. Kd5 Kf3 15. Kd4 Kg3 16. Ke4 Kh3 17. f8=Q Kg3 18. Qf3+ Kh2 19. Qg4 Kh1 20. Kf3 Kh2 21. Qg2#
</code></pre>

<p>Where you have one white pawn left on the kingside, and the queenside pawn was taken care of. So, the fortress is gone once you push the pawn a bit more and trade them off. With perfect play, it is a loss in 20 moves according to <a href="http://www.k4it.de/index.php?topic=egtb&amp;lang=en" rel="nofollow noreferrer">this 6-man tablebase</a>.</p>
 45: <p>I think that the position is a <strong>theoretical draw</strong>.</p>

<p>While Freeman's answer is quite good, but I think he has overlooked that <code>1. Qxd2</code> leads to a clearly drawn position because of Black's amazing response <code>1 ...Rb3!!</code></p>

<pre><code>[FEN "8/3Q2pk/5p1p/5P2/5K1P/p3r3/b2n2P1/8 w - - 0 1"]

1. Qxd2 Rb3!! 2. Qxa2 Rb2!! 3. Qxa3 Rxg2
</code></pre>

<p>Now I don't see any way for White to win. Black has created an impenetrable fortress and white's queen can do nothing.</p>

<p>The 2400+ rated player Alexey Kuzmin missed the move <code>1... Rb3</code> in the game, playing instead <code>1... Re5?</code> which gives a theoretically losing position. All the engines I tried also miss the sequence <code>1... Rb3</code> and <code>2... Rb2</code> and instead play a losing move.</p>

<p>I suggest that <em>if</em> there is a forced win for White then we must start looking at 1.Kxe3. This move doesn't win as much material as <code>1. Qxd2</code>, but it leads to a more dynamic position. White can prevent Black from promoting thanks to black's wrong-colored bishop that is unable to protect the a1 square. White can also threaten to advance the g-pawn to attempt to disrupt Black's wall of pawns.</p>

<p>However a computer analysis of <code>1. Kxd3</code> seems to show that despite White's material advantage Black can still get a draw.</p>

<p>I'm no expert, so there may be a mistake in my analysis, so please correct me if I'm wrong.</p>
