From the official's question and captain's answer, the 3 slaves would know that either 2 of them are blue and the other brown, or that 2 of them are brown and the other blue. Lets say Alan was blue and Ben and Chris were brown. Alan observes the other two have brown eyes, and hence deduces that his eyes must be blue, and therefore leaves. As Ben and Chris both have observed that Alan had blue eyes, and that he was not slain on boarding the boat. Therefore they conclude that they both have brown eyes, thus also earn the right to leave. The King then puts his official to death when he hears about the dumb arsed question that allowed 3 of his best slaves to walk free.
