The Maya, a people living on and around the Yucatan Peninsula, had two calendars running simultaneously. Centuries ago, their civil calendar had 365 days, while their divine calendar had only 260 days. While the Maya celebrated their birthdays on the same day of each year according to the civil calendar, they considered themselves lucky if they could celebrate their birthdays on certain days in the divine calendar.

1. Mekel was born on civil date 26, which happened to be divine date 91. What was the divine date of his 10th birthday?

2. Show that Mekel one day celebrated his birthday on a divine New Year’s day, and give his age in civil years.

3. Lotaxh was born the day after Mekel. Determine whether Lotaxh ever celebrated her birthday on a divine New Year’s day.

4. Occasionally, a divine year passed during which Mekel’s birthday did not occur. Mekel and Lotaxh were married on her 20th birthday. Before their marriage, what age(s), in civil years, had Mekel been when an entire divine year elapsed without his birthday being celebrated?

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1. 10 civil years is equal to 3650 days. 3650 days is equal to 14 divine years and 10 days(3650 / 260 = 14 remainder 10), making his 10th birthday fall on divine day 101 (91+10).

2. on his 14th birthday it was a divine new year. Can come up with some work if you need it, but I really just guessed and checked. [91+365x - 1] / 260 until I got a whole number. The -1 is there because in the problem you're looking for day 1 of the year, however it's much easier to subtract a day off and look for day 0 of the year.

3. Lotaxh can never have a birthday on a divine new year because 92+365x - 1 will always result in a 1 or 6 as the first digit, and to be divided by 260 it needs to be a 0.

I'll do #4 when I wake up, it's like 3 am atm >_>.