This has to be the worst puzzle I have ever attempted. There's at least ten logical solutions, none of which I have found to be correct. You shouldn't have to make 'Assumptions' in a logic puzzle.
I did as the hint said, found a pretty and logical solution and got a "beeep". If it's not obious, then it must be one of the other (2 to the power of 17 ~ 128.000) solutions... thanks. But again, Sparrow did it in 55 seconds...