Twenty-six villages are ranged around the coastline of an island. Their names, in order, are A, B, C, …, Z. At various times in its history, the island has been visited by 26 missionaries, who names are also A, B, C, …, Z. Each missionary landed first at the village that bore his name and began his work there. Each village was pagan to begin with but became converted when visited by a missionary. Whenever a missionary converted a village he would move along the coastline to the next village in the cycle A–B–C-…-Z–A. If a missionary arrived at an uncoverted village he’d convert it and continue along the cycle, but there was never more than one missionary in a village at a time. If a missionary arrived at a village that had already been converted, the villagers, feeling oppressed, would kill him and revert to a state of paganism; they would do this even to a missionary who had converted them himself and then traveled all the way around the island. There’s no restriction as to how many missionaries can be on the island at any given time. After all 26 missionaries have come and gone, how many villages remain converted?