Stumped by Sam Loyd

White to Mate in two moves:

White can only mate on two squares e7 and h8, but if 1.Qa3 black has 1...c5 or 2...O-O-O. If 1.Qa1 then 1...O-O-O. At least that's what I thought, but after 1.Qa1 black can't castle because he made the last move and it must have been with either the King or Rook, so castling is not legal.

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Solution to Retrograde Problem

Black to move

1... Bxd5+

This only draws, but that is not the task. After  1... Rxd5 2.Kxb4 Rd4+ 3.c4+ Kd2 4.Ka5 Bxc4 white has a B vs. R and B and will lose in 15 moves at most.

2. c4 bxc3+ 

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Fischer Story

OK, so I'm a day early!