The solution (to the paradox which the OP is about, not the xkcd version, which the OP is not about) is not about what each individual knows after the foreigner

The solution (to the paradox which the OP is about, not the xkcd version, which the OP is not about) is not about what each individual knows after the foreigner has imparted the fact that there are people with blue eyes, but what each individual knows about what the others know after that. For n=1, after the foreigner has spoken, any other islander would know that the islander who can see no blue eyes (i.e. the one with blue eyes) will kill himself. For n=2, after one day, by the logic in the OP, an islander will know if the one blue-eyed islander has not yet committed suicide, then he himself must have blue eyes and commit suicide. For n+1 it follows the OP. The solution to the paradox therefore is before the foreigner speaks, each islander knows there are some islanders with blue eyes, after the foreigner speaks, each islander knows that each other islander knows that there are islanders with blue eyes. (The existence of blue eyes has become common knowledge http://en.wikipedia.org/wiki/Common_knowledge_%28logic%29 http://en.wikipedia.org/wiki/Common_knowledge_%28logic%29 ) Aside: I am not sure an English language description really covers the contortions of this logical conundrum.