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The 2004 British Informatics Olympiad - Round One question 1

Question 1
Mayan Calendar

The Mayan civilisation used three different calendars. In their long count calendar there were 20 days (called kins) in a uinal, 18 uinals in a tun, 20 tuns in a katun and 20 katuns in a baktun. In our calendar, we specify a date by giving the day, then month, and finally the year. The Maya specified dates in reverse, giving the baktun (1-20), then katun (1-20), then tun (1-20), then uinal (1-18) and finally the kin (1-20).

The Mayan date 13 20 7 16 3 corresponds to the date 1 January 2000 (which was a Saturday).

1 (a)
[24 marks]

Write a program which, given a Mayan date (between 13 20 7 16 3 and 14 1 15 12 3 inclusive), outputs the corresponding date in our calendar. You should output the month as a number.

You are reminded that, in our calendar, the number of days in each month is:

  Sample run
13 20 9 2 9
22 3 2001
2February28 / 29 (leap year)
  Within the range of dates for this question, every year divisible by 4 is a leap year.
1 (b)
[2 marks]
What are the Mayan dates for 1 February 2000 and 1 January 2001?
1 (c)
[3 marks]
The Maya believed the universe was destroyed and re-created every cycle of their calendar, which was 20 baktun in length. How many kins (days) are there in a cycle? What day of the week is the last day of the current cycle (20 20 20 18 20)?

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