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III. METODOLOGÍA

3.2. MODELOS DE ECUACIONES ESTRUCTURALES

3.2.4.4. EVALUACIÓN DEL MODELO

581 [VX-326]. White wins with 18 Bf7+

Kf8 19 e6, e.g., 19...Bxe6 20 Bxe6 with

582 [VX-326]. White wins with 18 Bxf7+ Kf8 19 e6 Bxe6 20 Bxe6 Qe8 21 Qh7, threatening 22 Qg8, mate, which Black can avoid only by giving up his Queen with 21...Qf7.

583 [VX-343]. 26 Qh8 is mate. Note that the e7 square is blocked.

584 [VX-332]. 23 Qh8 is mate. Note that the e7 square is blocked.

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585 [VX-339]. White wins with 15 Qh7+ Kf8 16 Bh6, threatening both 17 Qxg7 and 17 Qh8, mate.

586 [VX-341]. White wins with 22 f6, threatening 23 Qxg7, mate, e.g., 22...

Bxf6 23 Qf7/Bh6 is mate.

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587 [VX-343]. White wins with 24 Bxc5+, e.g., 24...Qe7 25 Rxf6+ Bxf6 26

588 [VX-328]. White wins with 19 Rxf6+ Ke7 20 Qxg7+ Kd6 21 Bf4, mate.

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589 [VX-343]. White wins with either 26 Rae1, threatening 27 Qh8, mate, or 26 Rxf6+ Ke7 27 Qxg7+ Kd8 28 Rf8, mate.

590 [VX-343]. White wins with 24 Rxf6+, e.g., 24...Bxf6 25 Bh6+ Bg7

591 [VX-332]. White wins with 23 Rxf6, e.g., 23...Rxf6 24 Qxg7, mate; 23...Bxh6 24 Qxf7, mate; or 23...Ke8 24 Rxf7, winning a Rook with multiple threats.

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592 [VX-344]. White wins with 17 Bh6, threatening both 18 Qxg7 and 18 Qh8, mate, e.g., 17...Bxh6 18 Qf7, mate, or

593 [VX-328]. White wins with 17 Bh6, threatening both 18 Qxg7 and 18 Qh8, mate, when 17...e6 defends the Bg7, but loses to 18 Qh8+ Ke7 19 Qxg7, mate. 19...Qf6, but 19 f6 wins, for example, 19...Nxf6 20 Bh6, threatening 21 Qxg7, mate, e.g., 20...Qe7/Re7 21 Qh8, mate, or 20...Qd7 21 Rxf6+ Ke7 22 Rf7+ wins

595 [VX-319]. White wins with 21 Rxg6+ Kf7 22 Qxh7+ Ke8 23 Rg8,

596 [VX-334]. White wins with 21 Qh7+ Kf7 22 Bg6+ Kf6 23 Ne4, mate.

597 [VX-337]. White wins with 20 Bh6 Re7 21 Qh7+ Kf8 22 Qh8+ Kf7 23 Qxg7+ Ke8 24 Qf8, mate.

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598 [VX-342]. White can take Black's Qf8 or mate with 23 Qg6+ Ke5 24 Bf4+,

599 [VX-336]. White wins with 17 Qh7+ Kf7 18 Bg6+ Kf6 19 Qh6, threat-ening 20 Bg5/Qg5, mate, when 19...e5 loses to either 20 Bh7+ Kf7 21 Qg6,

600 [VX-335]. White wins with 17 Qxg6+ Bg7 18 Qh7+ Kf7 19 Bg6+ Ke7 (19...Kf6 20 Bg5 is mate) and either 20 Qxg7+ or 20 Bg5+ and 21 Qxg7, when White has three pawns and an attack.

6. Miscellaneous Mates

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601 [VX-342]. White wins with 18 Qh7+ Kf8 19 Bh6/Qh8, mate.

602 [VX-330]. White wins with 22 Qh3+ Kg7 23 Qh7+ Kf8 24 Bh6/Qh8,

603 [VX-320]. White wins with 18 Qxg6+ Kh8 19 Rf7 and 20 Qxh7/Qg7, mate.

604 [VX-317]. White wins with 17 Qd2 Rfc8 18 Qh6 and 19 Qh8, mate.

605 [VX-336]. White wins with 16 Qh8+ Kf7 17 Ne5, mate.

606 [VX-334]. White wins with 18 Qh5+ Kf6 19 Qxf5, mate.

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607 [VX-335]. White wins with 18 Bh7+

Kh8 19 Bg6+ Kg8 20 Qh7+ Kf8 21

608 [VX-335]. White wins with 20 Qg6 Rg8 21 Nf7, mate. Note that 20 Nf7+

609 [VX-338]. White wins with 20 Qh6+ Kg8 21 Nh5, threatening Qg7, mate, and if 21...gxh5 then 22 Qh7 is

610 [VX-331]. White wins with 22 Qxg6+ Kh8 23 Qg7/Qh6/Qh5/ Rh5, mate.

611 [VX-331]. White wins with 20 Qxg6+ Kh8 21 Qg7/Qh6/Qh5/ Rh5, mate.

612 [VX-319]. White wins with 21 gxh7+ Kh8 22 Qg7, mate.

613 [VX-333]. White wins with 22 Bg5, threatening 23 Qh8, mate, and if 22...f6 then 23 Bh6 is mate.

614 [VX-314]. White wins with 21 Rxg6+ fxg6 22 Qxg6+ Kh8 23 Qxh7/Rxh7, mate.

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615 [VX-320]. White wins with 17 Rh3, threatening 18 Qh8, mate, when 17...Nh5 loses to 18 Qh7+ Kf8 19 Qxf7, mate.

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616 [VX-337]. White wins with 19 Qxg6+ Kf8 20 Qxf6+, e.g., 20...Kg8

617 [VX-327]. White wins with 20 Be5+, e.g., 20...Kf7 21 Qh7+ Bg7

618 [VX-333]. White wins with either 22 Qh8+ Ke7 23 Bg5+ f6 24 Qxf6, mate, or 22 Bg5, threatening Qh8, mate, when 22...f6 loses to 23 Bh6+ Qg7 24 Qxg7,

619 [VX-315]. White wins with 23 Rc3, e.g., 23...Qf8 24 Rh3 Qh6 25 Qxh6+

Kg8 26 Qh8/Qg7, mate or 23...Ng8 24 Rh3+ Nh6 25 Qxh6+ Kg8 26 Qh8/Qg7,

620 [VX-331]. White wins with 20 Qxg6+ Kf8 21 Bxf6, threatening both 22 Qg8, mate and 22 Bxd8 with 23 Qxf7, mate, and if 21...Rxf6 22 Qxf6+ Ke8 then 23 0-0 gives White a strong attack.

621 [VX-329]. White wins with 22 Bxf6 Qxf6 23 Re8+ Qf8 and either 24 Rxf8+

Kxf8 25 Re1 with 26 Re8, mate, or 24 Rae1, intending 25 Rxf8+ Kxf8 26 Re8, mate.

622 [VX-316]. White wins with 21 Rxf7, removing a defender of g6 and putting Black's Rook on f7, which will prevent Black's King from escaping. 21...Rxf7 22 Qxg6+ Kg8 23 Qh7+ Kf8 24 Qh8,

623 [VX-342]. White wins with 17 Bh6+, e.g., 17...Kf6 18 Qg5, mate;

17...Kg8 18 Qg6+ Kh8 19 Qg7, mate; or 17...Kh7/Kh8 18 Bxf8+ Kg8 19 Qxf7+

Kh8 20 Qg7/Qg8/Qh5, mate.

624 [VX-330]. White wins with 22 Bxe8+ Kf8 23 Bxd7, when 23...Nxd7 drops the Qc7; 23...Qxd7 loses to 24 Bh6+ Ke8 25 Qg8+ Bf8 26 Qxf8, mate;

and not taking the Bd7 leaves Black down a Rook and a pawn.

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625 [VX-335]. White wins with 17 Qh8+ Kf7 18 Ne5+ fxe5 (18...Ke8 19

626 [VX-338]. White wins with 21 Qxg6+ Kh8 22 Nh5, threatening 23 Qg7, mate, when 22...Rg8 23 Qh6 is mate, and 22...Qe7 23 Rxf8+ Qxf8 loses to 24 Nf6, e.g., 24...Qg7 25 Qh5+ Qh7 26 Qxh7,

627 [VX-336]. White wins with 16 Qh6+, e.g., a) 16...Kf6 17 Ne5, mate; b) 16...Kg8 17 Qh8+ Kf7 18 Ne5, mate, or c) 16...Kf7 17 Qh7+ Kf6 18 Bg5+ Kxg5 19 Ne5, threatening 20 Qg6+, e.g., 20...

Kf4 21 Qg3, mate, or 20...Kh4 21 Nf3,

628 [VX-335]. White wins with 16 Bxg6+, e.g., 16...fxg6 17 Qxg6+ Kh8 18 Qg7/Nf7, mate; 16...Kg8 17 Bxf7+ Kh8 18 Bg7+ Kxg7 19 Qg6+ Kh8 20 Qh6+

629 [VX-342]. White wins with 19 Qg6+ Kh8 (19...Kf8 20 Qxf7, mate) 20 Bxf7 (White's threat is 21 Qh6, mate) Qf8 21 Qh5+ Kg7 22 Bh6+, winning Black's Queen, unless White wants to mate in four -- 22...Kf6 23 Qg6+ Ke5 24 Bf4+ and now: 24...Ke4 25 Bd5+ Kd4 26 0-0-0, mate, or 24...Kd4 25 0-0-0+

Ke4 26 Bd5/f3, mate.

7. Miscellaneous Tactics

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630 [VX-327]. White wins material with 19 Bxg6 (threatening 20 Qh7, mate) fxg6 20 Qxg6+, winning Black’s Re8.

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631 [VX-323]. White wins with 22 Qxg6+ Qg7 (22...Bg7 23 Qh7 is mate) 23 Rxf8+ Kxf8 24 Bh6, winning Black’s Queen.

632 [VX-305]. White is down a piece for a pawn, but wins back the piece with 20 Qxg6+ Kf8 21 Rxh7, when White is up two pawns.

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633 [VX-308]. White is down a piece for a pawn, but now wins two pieces with 14 Qxh5, when there's no way to save the Bh6, e.g., 14...Kg8/Kg7 15 Qxh6.

634 [VX-322]. White is down a piece for two pawns, but wins material with 24 Bxe8+ Qg7 (24...Kf8 25 Qxf6+) 25

635 [VX-340]. After 13 Bh6 Rxg6, White should avoid winning Black's Qd8 with 14 Qh8+ Kf7 15 Qxd8, since after 15...Rxh6 16 Qxc7 Rh8 White's Queen gets trapped after 17...Na6 and 18...

Nxc7. Better is simply 14 Qxg6, when White has a Rook and pawn for two

637 [VX-322]. White wins with 22 Qh6 with Qg7, mate.

638 [VX-317]. White wins with 16 Qxg6, intending 17 h6 and 18 Qxg7.

639 [VX-311]. White wins material with 21 Bxg6.

640 [VX-311]. White wins the exchange with 21 Bg5 Rf7 22 Bxg6. but White can add another attacker with 18 Nxf6+ Nxf6 19 Qxg6+ Qg7 20 Qxf6.