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A tournament in the planet Pymm pitted each elf contestant against every knight and Minotaur contestant, each knight contestant against every elf and Minotaur contestant and, each Minotaur contestant against every elf and knight contestant in three contests of skill: wrestling, archery and knife throwing. In other words, each type of being- elf, knight and Minotaur- competed against everyone in the other groups of beings in three different contests.

These facts are known:

1. The number of Minotaurs in the tournament was one fewer than the number of elves.

2. The total number of knight and Minotaur contestants is nine.

3. The number of elf vs. knight competitions in the three skills was seventy-two and, there were more knights than elves.

4. Twenty-seven contests were held each day.

How many days did the competition last?

Edited by K Sengupta

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6 days here is my work:

#3 says E*K*3=72 so E*K=24 so E,K => 4,6 or 3,8 or 2,12 or 1,24 but K<9 (#2)

so 4,6 or 3,8; but also by #1 and #2 E-1+K=9 so it must be:

Minotaurs=3

Elves = 4

Knights = 6

and total number competitions is 3*4*3+3*6*3+4*6*3 = 162

and by # 4 162/27= 6 days

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