Here's a pretty puzzle, from Sam Loyd. It's actually surprisingly easy, if one applies a bit of reasoning to the subject.
On which square does the black king have to stand for white to achieve checkmate in three from white's starting position (all the pawns on the front rank, and all the rest of the pieces on the back rank), assuming no other black pieces are on the board?
Don't cheat!
The square on h4.
The mates in three are:
1. d4 Kg4
2. e4+ Kh4
3. g3#
1. d4 Kh5
2. Qd3 Kg4 or Kh4
3. Qh3#