Mate in 8 moves. can you find a faster way to victory ?

@ xman720: True; White's defense after Nxc2 wasn't so good (he probably should have tried putting the Rook on a different square, e.g. f1), but it doesn't really matter...it's still a won game for Black. Thanks for helping to verify that Nd4 is sound.

In a real game any smart player would just play Nd4.  It is irrelevant how many moves it takes to win or mate. what matters is the surety with which it is done.  Better a certain win in 30 more moves than a mate in 5 (6,7,8,9, ...) with a risk of a miscalculation.

Plus, white's moved against the mate in 8 are pretty forced and straightforward. But after Nd4 there are a lot of ways white can go wrong to lose even faster, as I showed with the fairly logical mate in 7.

Of course, after Rf1, I may have wished I just went for the mate in 8.

This is a puzzle, and the task is to find Black's quickest mate, not to offer opinions about what might be the best move in a game.

Against the best moves by White, I don't think Black can do better than a mate in 9. One way among many is the mate in 9 the OP gave as the solution in #1 (and called a mate in 8).

31...Rxe3 doesn't look particularly stupid, and I cannot see a way to stop quick mate.

Both Rxe3 and Nd4 look fine/winning to me. Though I found the challenge of trying to find a faster mate fun, as ModestAndPolite implied, a win is a win. :)

True, a win is a win, and a game is a game, and a puzzle is a puzzle. It seems to be fairly common in this forum for people to want to treat puzzles as if they were games.