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Black can resign after white plays 1.Rd8+ since mate can’t be prevented.
Rd8
Sacrificial banishment for the sin of the father…
1.Rd8+ Bxd8
1….. Bf8 2.Rxf8#
2.Qf7#
1Rd8+ win
1.Rd8+! Mate in 3!
A>1….Bxd8.2.Qf7#!
B>1….Qe8.2.Rxd8+.Bf8.3.Rxf8/Qf7#
C>1….Bf8.2.Rxf8/Qf7#!
more elegant is
1.Rd8+ Bxd8 or Bf8
(1…. Qe8 2.Rxe8+ Bf8 3.Qf7#)
2.Qf7#
A/ 1.Rd8+ Bxd8
2.Qf7#
B/1.Rd8+ Bf8
2.TRxf8#
C/1.Rd8+ Qe8
2.Rxe8+ Ff8
3.Rfxf8#
Rook to D8
This one is easy. 1. Rd8 Bxd8(forced)
2. Qf7#
Black is threatening Qxb2. So, white needs checks.
1. Rd8+
If 1 … Bxd8, 2. Qf7+ mate.
If 1 … Bf8, 2. Qf7+ or Rxf8+ mate.
Cute.
Black threatens Qxg2#.
But white would also have Qb8 mating if it wasnt for black’s double (Q+R) in c file.
Furthermore:
White should have a direct Qf7# if black’s bishop wasn’t on 7th rank!!!
Nothing more to discuss, it’s mate in 2 moves, almost, let’s say 3 then:
1. Rd8+! Qe8 (Bxd8 Qf7#)
2. Rxe8+ Bf8
3. Qf7#
pht,
That is what I meant by elegance.Whatever be the variation mate is by Qf7.