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 solution by Dej Mar)

The problem is posted as "just math" but this is misleading -- or a spelling mistake for "just myth" (can a good problem really have two solutions??).  The Minotaur is (or was) an individual, not a group or species (taurus).  The "competitions" do not make much sense, since some competitor might have to fight a large number of contests each day (let alone three contests each, at least one of which, wrestling, would be taxing) if the other group vastly outnumbered his.  Perhaps Ady is trying to help us, by forcing one Minotaur, and hence eight humans (hence a "total number" of nine).  The Minotaur could probably fight and defeat (and eat?) many opponents each day.  Follow this thread and Theseus may give you the answer (or at least another one). Who knows how "elves" would do, since they are mythical. Next...

Posted by ed bottemiller on 2010-07-27 10:53:35