A tournament in the planet Lynn pitted each elf contestant against every human and Minotaur contestant, each human contestant against every elf and Minotaur contestant, and each Minotaur contestant against every elf and human contestant in three contests of skill: wrestling, archery and knife throwing. In other words, each type of being- elf, human and Minotaur- competed against everyone in the other groups of beings in three different contests.
These facts are known:
1. The total number of human and Minotaur contestants is nine.
2. The number of elf vs. human competitions in the three skills was seventy-two.
3. Twenty-seven contests were held each day.
How many days did the competition last, given that it lasted for less than 30 days?