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Three Skill Settlement (Posted on 2010-07-26) Difficulty: 2 of 5
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?

No Solution Yet Submitted by K Sengupta    
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What am I missing? (spoiler?) | Comment 1 of 7
let e = # of elves, h = # of humans, m = # of minotaurs

then
a) h + m = 9
   eh = 24
   eh+em+mh=9d, where d < 30
   
b) eh = 24, but h <9, so possible values are

h m e  eh+em+mh
- - -- --------
1  8 24 224  not divisible by 9
2  7 12 122  not divisible by 9
3  6  8  90  10 days
4  5  6  74  not divisible by 9
6  3  4  54  6 days
8 1 3 24  not divisible by 9

So, at first blush,
I seem to have two possible answers, 6 and 10 days.
Both seem possible.


  Posted by Steve Herman on 2010-07-26 14:01:59
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