Mayan Pyramid

Cuboids are used to form a Mayan cross. Scaled copies of the cross are stacked one on top of the other to form a Mayan pyramid.

Mayans are known for their precise and sophisticated calendars. The Mayans used two calendars: the Haab calendar, which consisted of 365 days grouped into 20 months of 18 days each plus a five-day month, and the Tzolkin calendar which consisted of 260 days grouped into 13 months of 20 days each. The Tzolkin calendar was used for religious purposes and can be represented by a geometric shape called the Mayan cross. Each layer of the pyramid in this Demonstration is a Mayan cross. The cross made of 13 squares represents the months, and has 20 sides representing the days.

Suppose that New Year's Day of both calendars coincide and that you start building the pyramid one layer at a time each New Year's Day of the Tzolkin calendar. How many levels will the pyramid have when New Year's Day coincides once more?