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I don’t see an alternative to QxE6…
1Qxe6+ Kh8
[1… Qf7 2Qxc8+ Qf8 3Qxf8#]
2Bc5 (keep cool)
This is a multitask move
(i)It prepares for Bd4# albeit delaying tactics.
(ii) It tries to divert Q from control of g7 square.
(iii)It prevents black Q checks from c2.
2…. Qa7 [Let me control g7 as well as d4 even at the cost of my life]
3Qxc8# [Not interested in your life,queen.]
Other possibility is
2…. Rg8
3Bd4+ Qg7[3… Rg7 4Qe8#]
4hxg7+ Rxg7
5Qe8#
1.Qxe6+ Kh8 forced 2.Bc5! deadly !
1. Qxe6+ Kh8 (1. .. Qf7 2. Qxc8+ Qf8 3. Qxf8#) 2. Bc5 Qxc5 (2. .. Rg8
3. Bd4+ Rg7 4. Qe8#) 3. Qf6+ Kg8
4. Qg7#
Qe6+, Qxc8+, Qxf8#
Oh, wondered where the whole was. Well then, 1.Qe6+ Kh8 2. Bc5 should do the trick, a diversion that prevents 2. …Qc2+ and mate coming
can get a draw I think by Qxf6+
… Kh8
Qg6+ Kg8
Qf6+ and so on
The black queen has just one too many tasks to perform in guarding the king:
1. Qe6 Kh8 (Qf7 2.Qc8 Qe8 3.Qe8#)
2. Bc5!
Threatens both Bd4 followed by mate, and if black takes at c5, white plays Qf6 followed by Qg7#. The best black can do is to block the checks from the bishop at e5 with the queen, and or with the rook at either f6 or g7.
I like this puzzle. the key seems to be the second move of Bc5!
1.Qxe6+ Kh8
2.Bc5 Qxc5
3.Qf6+ Kg8
4.Qg7#
– High skills of MR KO (Malaysian)