Because the blue eyed person see 99 blue eyed people and the brown eyed person sees 100 blue eyed people. So, every brown eyed person was one day away from lea

Because the blue eyed person see 99 blue eyed people and the brown eyed person sees 100 blue eyed people. So, every brown eyed person was one day away from leaving when all the blue eyed people spontaneously left. However, now everyone left knows they have brown eyes. Update: To herge's point they probably don't know there are only two possibilities.