Queen sacrifice cool..

Attack the king directly is useless? I mean your variation is better than mine, but you could still mate this king in four moves by attaking directly. That's not useless.

1. Qd3 Rd8 2. Nc3+ Kc1 3. Nb4

Then if ...Rxd3, 4. Nxd3#   If ...Re8 (or any other move), 4. Qb1#

 this is ture,i cannot disagree, but it clearly says mate in 3.You have to mate in 3.And attacking the king is useless if you want to achieve a mate in 3....

If it was a white to play and win,then your variation will do,BUT THIS IS A MATE IN 3!!!

1. Nxe3 Rc8 2. Qxc8 3. bxc3 Qc1#

 i'm sorry???the black pawns are going down

or the black king will be in check in the beginning

and why does black mate in your solution...

Yeah right I'm one move late... Anyway nice puzzle ;)

how did the black king end up all the way across the board with only a rook and 3 pawns?

this is truly amazing, though