Err - this could get a little convoluted but i'll try and explian my logic - hopefully it is correct and i didn't just get lucky

- Imagine I am a blue eyed person on the Island
- I can see 99 people with blue eyes, 101 with brown eyes and 1 with green eyes
- There are therefore either 99 Blue eyed people or there are 100, depending on my own eye colour.
- Since the Blue eyed people didn't leave on the 99th night, then those 99 people must still not have been sure that they were blue eyed themselves which means I must have been confusuing them
- Therefore on the 100th night, I will know I have blue eyes for certain since there can't be 101 of us, so I will leave along with all the other blue eyed people who realise the same thing at the same time