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Find The Shortest Mate

I got this puzzle pretty easily- less than a minute- but the simple elegance of it was pleasing. White to move.

8/8/3p4/6QR/4b3/7P/5K1P/6Bk w - - 0 1

  1. Qg8!!!

a) 1...Bc6, 2. Rd5!! Bxd5, 3. Qxd5#!
b) 1...d5, 2. Qg4! (Black is in zugzwang) d4, 3. Qxe4#!

Yes, Loyd was deeply fond of zugzwang themes in mate in 3s.

c) 1.Qc8 Bf3
2.Kxf3 d5

It took 20 minutes to solve this puzzle.

Hey, Alena!! You mistyped 1. Qc8. It should be 1. Qg8

Yes, you are right Dave.

1.Qg8 Ba8
2.Rd5 Bxd5

Kg3! +-