[borisp]

This should have been more clearly stated in the assumptions: They all know that there are only two possibilities for eye color. So, when they have ruled out blue as a possibility, then they know they are all brown - eyed, which means they know their own eye color, which means it's suicide time.

Was this what was unclear? This might also shed light: when the brown eyed people see N+1 folks not wake up, they know that there were not N+2 people with blue eyes (i.e. that none of them have blue eyes) because if there were, then the N+1 blue eyed people would have had no way to draw the suicidal conclusion. I.e. they are all perfectly rational, and they all know that everyone else is perfectly rational, which is another necessary assumption that I should have made clearer.