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1.Ra3 Kb4 2.Qa8 Kc4 3.Qe4#
.. 2 ..c4 3.Qf8#
1.. b4 2.Qf1Kd4 3.Qd3#
1.. Kd4 2Qh4#
1.Ra3 isn’t an easy find- I went through several other moves first before realizing the rook on a3 could be protected from a8 followed by mate in the key line below from a8.
1. Ra3
Probably should have considered this move earlier than I did. First, it constrains black’s first moves to 3 variations- b4, Kb4, and Kd4, and 1. …Kd4 is mate after 2.Qd5. In addition after 1. …b4, black is down to one move:
1. ………….b4
2. Qf1! Kd4
3. Qd3#
Finally:
1. ………….Kb4
2. Qa8! Kc4
3. Qe4#
or, the prettiest of all:
2. ………….c4
3. Qf8#