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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?

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    Suggestion: If Bobby gives it as an example it "must" be doable. He would not have intended it not to be guaranteed one or other way. Given that, trying very long and hard to see how it can be will probably help you more long term than asking the fine folks here - no matter how painful the quest may be. [[FWIW - my ability at chess is abysmal - consider doing what I say - not what I'd do :-) !!!}. – Russell McMahon Jan 18 at 10:33
  • I wonder what move black previously made to get the board to that position... its seems highly unlikely that white queen is just sitting there for the taking, but black did something else instead. – musefan Jan 18 at 13:36
  • perhaps this should be on meta, but can't OP just plug this into a computer? i guess a computer doesn't answer everything, but i think it's still in that range in like how maths se would consider like insufficient effort (i don't want to say low effort though!). i think OP should've plugged into computer and then could ask questions about what computer says. otherwise this page will be flooded with 'trivial' (see round bracket remark next!) puzzles like these (trivial in the sense that it's easily answered by computers, not that it's necessarily easy to answer) – BCLC Jan 18 at 13:59
  • @BCLC can you outline how to do that? I'm just starting to learn chess and would appreciate any info on that! – BruceWayne Jan 18 at 15:06
  • @RussellMcMahon agree 100%, I did stare at it and think for a while... But it was after reading the book straight for like an hour so should have probably just taken a break and come back with fresh eyes :) – BruceWayne Jan 18 at 15:08
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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

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    Ah! Thanks, don't know how I didn't see that. I bet that's the "proper" answer too, instead of wasting the extra moves the other way. – BruceWayne Jan 15 at 20:59
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    @BruceWayne: black tries to delay mate, even if it is unavoidable. – Razvan Socol Jan 16 at 4:40
  • @RazvanSocol and Brian Towers♦ perhaps this should be on meta, but can't OP just plug this into a computer? i guess a computer doesn't answer everything, but i think it's still in that range in like how maths se would consider like insufficient effort (i don't want to say low effort though!). i think OP should've plugged into computer and then could ask questions about what computer says. otherwise this page will be flooded with 'trivial' (see round bracket remark next!) puzzles like these (trivial in the sense that it's easily answered by computers, not that it's necessarily easy to answer) – BCLC Jan 18 at 13:59
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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?

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    Or, the goal is to eliminate the book from the action. Eliminating them from the board is in service of that, not the ultimate goal in itself. – Acccumulation Jan 16 at 22:33
  • @Acccumulation and Mateen Ulhaq perhaps this should be on meta, but can't OP just plug this into a computer? i guess a computer doesn't answer everything, but i think it's still in that range in like how maths se would consider like insufficient effort (i don't want to say low effort though!). i think OP should've plugged into computer and then could ask questions about what computer says. otherwise this page will be flooded with 'trivial' (see round bracket remark next!) puzzles like these (trivial in the sense that it's easily answered by computers, not that it's necessarily easy to answer) – BCLC Jan 18 at 14:00
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    @BCLC That might be worth posting on meta. There's a large number of questions posted here that can be answered with an engine. That seems to be accepted, so it seems people see value in a human-to-human exchange rather just an engine answer. For instance, in this case, answers consist of not just giving the answer to taking with the knight, but discussion of larger principles. – Acccumulation Jan 18 at 21:22
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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.

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