user19702: I am working through Bobby Fischer Teaches Chess and #134 asks

If White plays Rook-takes-Rook-check, can he mate?

The answer is Yes, the mate is delivered by the white Queen.  However, can't it be prevented?
Here's the board:
[title "Bobby Fischer #134"]
[fen "1r1r2k1/6pp/2n4q/2p1p2Q/pp2N2P/5P2/PPPR2P1/1K1R4 w - - 0 1"]

I can see how to get mate, with the Queen: 1. Rxd8 Rxd8 2. Rxd8 Nxd8 3. Qe8  for mate.
However, if 1. Rxd8 Nxd8 2. Rxd8 Rxd8 .  This prevents the Qe8 mate, doesn't it?
So when the question asks "can he mate", yes but it's not guaranteed.  Do I understand the board correctly?

user7657: White wants to play Qe8 for a back rank mate (since the Black king has no escape square).  To do so, he must eliminate Black's protection of the e8 square. Capturing both rooks accomplishes that by 1. Rxd8+, Rxd8 2. Rxd8+ Rxd8 3. Qe8 mate. But if he plays 1..., Nxd8 instead of 1..., Rxd8, he interrupts the other Black rook's protection of the e8 square, and White is able to mate a move sooner by 2. Qe8 mate.

user1090: The objective is not to eliminate the rooks.
The objective is to remove black's defense of the e8 square so that Qe8# can be played.
After Nxd8, does black still control e8?

user4418: 
However, if black takes with Rook, then Knight takes' white's rook,
white rook to take knight, then black rook to take white rook. This
prevents the Qe8 mate, doesn't it?

No, it accelerates it. Let's look at what happens if black takes with the knight instead of the rook
[fen "1r1r2k1/6pp/2n4q/2p1p2Q/pp2N2P/5P2/PPPR2P1/1K1R4 w - - 0 1"]

1. Rxd8 Nxd8 2. Qe8# {oops!}

Black gets checkmated in 2 moves instead of 3

19702: <p>I am working through <em>Bobby Fischer Teaches Chess</em> and #134 asks</p>
<blockquote>
<p>If White plays Rook-takes-Rook-check, can he mate?</p>
</blockquote>
<p>The answer is Yes, the mate is delivered by the white Queen.  However, can't it be prevented?</p>
<p>Here's the board:</p>
<pre><code>[title &quot;Bobby Fischer #134&quot;]
[fen &quot;1r1r2k1/6pp/2n4q/2p1p2Q/pp2N2P/5P2/PPPR2P1/1K1R4 w - - 0 1&quot;]
</code></pre>
<p>I can see how to get mate, with the Queen: 1. Rxd8 Rxd8 2. Rxd8 Nxd8 3. Qe8  for mate.</p>
<p>However, if 1. Rxd8 Nxd8 2. Rxd8 Rxd8 .  This <em>prevents</em> the Qe8 mate, doesn't it?</p>
<p>So when the question asks &quot;can he mate&quot;, yes but it's not guaranteed.  Do I understand the board correctly?</p>
 7657: <p>White wants to play Qe8 for a back rank mate (since the Black king has no escape square).  To do so, he must eliminate Black's protection of the e8 square. Capturing both rooks accomplishes that by 1. Rxd8+, Rxd8 2. Rxd8+ Rxd8 3. Qe8 mate. But if he plays 1..., Nxd8 instead of 1..., Rxd8, he interrupts the other Black rook's protection of the e8 square, and White is able to mate a move sooner by 2. Qe8 mate.</p>
 1090: <p>The objective is <em>not</em> to eliminate the rooks.</p>
<p>The objective is to <strong>remove black's defense of the <code>e8</code> square</strong> so that <code>Qe8#</code> can be played.</p>
<p>After <code>Nxd8</code>, does black still control <code>e8</code>?</p>
 4418: <blockquote>
<p>However, if black takes with Rook, then Knight takes' white's rook,
white rook to take knight, then black rook to take white rook. This
prevents the Qe8 mate, doesn't it?</p>
</blockquote>
<p>No, it accelerates it. Let's look at what happens if black takes with the knight instead of the rook</p>
<pre><code>[fen &quot;1r1r2k1/6pp/2n4q/2p1p2Q/pp2N2P/5P2/PPPR2P1/1K1R4 w - - 0 1&quot;]

1. Rxd8 Nxd8 2. Qe8# {oops!}
</code></pre>
<p>Black gets checkmated in 2 moves instead of 3</p>
