As a logic puzzle it is very tenuous. The proposed solution (which is lower down the blog post) is that because any blue eyed Islander is able to count the number of blue eyed people (99), if on day 99 those people do not kill themselves it means that there is one further blue eyed Islander, and it is them.
Brown eyed Islanders see 100 blue eyes, and so know that if mass suicide occurs on day 100 then they are not blue eyed.
It's only a short reprieve though; because either the browns know that only two colours exist (and so on day 100 immediately know they are brown) or they face the same conundrum as blue, and commit suicide on day 900.
The problem with the puzzle is not really the logical reasoning (which is sound, as described in the puzzle). The problem is that the Islanders, who are described as very logical, should know this information already. That they are still alive when the foreigner arrives is illogical.
EDIT: to downvoters; consider the problem & solution very very carefully (or read my subsequent comment). Initially it seems a little illogical that the browns would die too, but it is ultimately the same basic problem that the blues face :)
Brown eyed Islanders see 100 blue eyes, and so know that if mass suicide occurs on day 100 then they are not blue eyed.
It's only a short reprieve though; because either the browns know that only two colours exist (and so on day 100 immediately know they are brown) or they face the same conundrum as blue, and commit suicide on day 900.
The problem with the puzzle is not really the logical reasoning (which is sound, as described in the puzzle). The problem is that the Islanders, who are described as very logical, should know this information already. That they are still alive when the foreigner arrives is illogical.
EDIT: to downvoters; consider the problem & solution very very carefully (or read my subsequent comment). Initially it seems a little illogical that the browns would die too, but it is ultimately the same basic problem that the blues face :)