2. Count-the-names calendars

The renowned Athenians of the classical era used the eponym system. They named the years of their calendar after the Chief Archon, the constitutional head of state chosen to preside for one year.

Similarly Roman calendar years were named after Consuls. By the end of the empire, the list of eponyms was nearly a thousand consuls long and working out a time interval could be tedious.

In the New World, the Brule of the North American plains employed a system of naming years after extraordinary events rather than administrative officials.