Many people don't realise that the mystery of Twin Peaks was in fact wrapped up very quickly in Video Stores all over Europe and the UK. (Australia as well) This home video release was a version of the Pilot episode re-edited with additional footage to become a self contained feature, and in fact had an ending.
Whats even better is that it had the correct ending, the mystery was solved in what would be the same way it was eventually in the series.
The additional sequences do make it into the Televised version, and do indeed contain the solution to the mystery. Yup, that's right it was BOB.
The international video release of the Twin Peaks Pilot is a strange thing, it has an ending that is technically the correct answer, and if you want to get really picky Cooper is even told who BOB used as a vessel... We the Audience just can't hear what Laura tells him. But essentially to make the Pilot a full feature they added the Dream Sequences from Episode 2 as an ending of sorts. For fans of the show this is the only place you can see the full version of the BOB and MIKE dream Cooper relates to the others, and this dream is used as the solution to the mystery. MIKE shows Cooper and Truman how to find BOB, they enter BOB's lair and are taunted by him. MIKE then shoots BOB.
Interestingly, here you probably get the best view you will ever see of BOB's tattoo, which reads "Fire Walk with me" and the full version of BOB's rhyme.
Then the action shifts the the "Twenty Five Years Later" dream, which plays out exactly the same as in Episode two, complete with Laura Whispering in Cooper's ear. (The Name of the Killer as we find out later)
I have watched this version several times, as it was the only version of the Pilot available on Home Video in Australia. I had the whole first season on VHS, but the official release did not include the Pilot episode, so borrowing this from the local Video Store was my only source of the Pilot Episode. As a stand alone, it's ok. The ending is pretty unsatisfactory to be honest when taken in isolation from the series, the mystery is solved basically by an anonymous tip. The Red Room is just an oddity, a dead end.
But the so call "Alternative ending" is an interesting curiosity, and the MIKE and BOB sequence is very atmospheric. It can be seen posted on Youtube or as part of the Blue Ray "Missing Pieces" box set of the series.
And as I said... Technically it is a correct solution :p (April Fools)