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You are right! 14.0.7.16.3 will fall on this date, if we follow the most accepted and popular correlation between the calendars.
This Kata challenge is completely wrong in its very basic assumptions - explaining nothing.
Still, even if the original thing applied a very different correlation, it's simply impossible to have 20 as a coefficient in the Maya Long Count at all, as their math is based on digits from 0 to 19. Couldn't have a 13 "baktun" (PIK) coefficient in the early 2000's, unless you use another correlation - still, a 20 coefficient makes it invalid anyway.
I've done some research that leads to me to believe this description of the mayan long calendar is wrong.
13 20 7 16 3 should be 14 0 7 16 3 and it lies on January 6 2415.
The 13 baktun started on December 21 2012