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?

(In reply to An unlikely, but possible interpretation by Dej Mar)

Why not (a single solution!)?  In any case, archery and knife throwing (each against a target at a specified distance) could easily be seen as a group contest (e.g. all humans and all elves)but still ranking all in both groups so that each member could be credited with wins for each from the opposite group with a poorer score.  Not quite sure how many "competitions" that represents.  I'm not sure how wrestling would be conducted or scored, but perhaps something like a scrum (I'd leave that question to the Rugby fans.)  I am not a big fan of vagueness in specifications, unless the problem is clearly so marked in the heading. 

Posted by ed bottemiller on 2010-07-27 13:00:53