Easy Puzzle
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Easy Puzzle, white to moves. mate in three
Easy Puzzle 2. Black loses 1 rook by sacrificing one white piece
The first puzzle is not a mate-in-three. 1...gxf5 is a blunder. I don't think white can force mate in under 10.
I also don't think that 1. Bxd5 in the second puzzle is a sacrifice. 1...Qxd5 is a blunder. If the Queen recaptures, the compensation is immediate and overwhelming. So it is not a true sac in my book. The obvious reply is 1...c6. Also, after 1...Qxd5, I think 2. Qxd5 is the best move for white in view of the following line.
1. Bxd5 Qxd5 2. Qxd5 Rxd5 3. Re8+ Bf8 4. Bxf8 h6 5. Bd6+ Kg7 6. Bxc7
4. Bxf8 threatens 5. Bh6# of course. After 6. Bxc7, there is no way to save the knight. So the best continuation for black should probably be 6...Na6 7. Rxa8 Nxc7 8. Rxa7.