Quote from Lobster:
Let us assume that it's three people, and only two of them have the disease. On the first night each one of the diseased monks will see only one monk with a dot and one monk without a dot. If he returns on the next day and the one guy wiith the dot returns as well, then he knows that that other guy must have seen someone with a dot, and since it cannot have been the third guy, it must be he himself. Therefore he kills himself after the second day. So does the other one. The one who was not ill has always seen two guys with a dot, so he knew that they would kill themselves after the second day if they were the only two with a dot. If they are dead after the second day, he knows that actually was the case and lives happily ever after. If they both return after the second day, he knows that each one of them must have seen two guys with a dot, so he knows that they all have the dot and they will all kill themselves after the third night.