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The simplest solution is
1. Bg6+ hxg6
2. Qxg6+ Ke7
3. Bb4+ Nd6
4. Bxd6 checkmate.
The artificial one is based on the permutation of the first and second moves.
1.B (or Q)g6+ hxg6 2.B(or Q)x g6+
K e7 3.Bb4+ Nd6 4.Bxd6#
I love queen sacs!
1. Qg6+!! hxg6
2. Bxg6+ Ke7
3. Bb4+ Nd6
4. Bxd6#!
Looks simple.
1. Bg6+ hxg6
2. Qg6+ Ke7
3. Bb4+ Nd6
4. Bd6#
either Bg6+ or Qg6+ as first move.. I would prefer sacrificing the queen as it look cool. 😛
Then Bb4+ with mate next move.
This one is relatively easy.
1.Bg6+ hxg6
(1…Ke7 2.Bb4+ Nd6 3.Bxd6#)
2.Qxg6+ Ke7
3.Bb4+ Nd6
4.Bxd6#
1.Qg6+ or Bg6+
1…Ke7 2.Bb4+ Nd6 3.Bxd6 mate
A check on g6 seems to do it!
1. Qg6+ hxg6 (Ke7 was one move faster)
2. Bxg6+ Ke7
3. Bb4+ Nd6
4. Bxd6#
The less dramatic 1. Bg6+ also works fine, but 1. Qg6+ is more fun:-)
1.Bg6+ hxg6
2.Qxg6+ Ke7
3.Bb4+ Nd6
4.Bxd6#