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Curious…Combinatorics?
I didn’t succeed in solving this problem. Now just curious :)
This story is told in one Arabian tale.
12 men (cutthroats) sat in a circle around the fire. Each of them bloody hated his neighbours from both sides. They needed 5 men to hide a treasure. In how many ways it is possible to make a group of 5 cutthroats for hiding treasure that they wouldn’t kill each other?
The answer given – 36.
Wow, it never came to my mind to separate odd and even numbers. Maybe it was meant in the book. Though why do you exclude such combinations as , for example
1, 3, 6, 8, 11 ?
But guys, why you multiplied 6 variants with odd numbers with 6 variants with even numbers???? We cannot mix them!
Total number of variants in your case should be then 6+6=12.
1 Answer
- M3Lv 71 decade agoFavorite Answer
suppose you number the men clockwise from 1-12
and put #1 in the group.
then 6 possible people are available for forming the gr. of 5
1-3-5-7-9-11, and 6 are left out, 2-4-6-8-10-12
thus from each of odd numbered and even numbered men,
6C5 = 6 groups can be formed
thus total ways = 6*6 = 36
EDIT ON ADD, NOT MULTIPLY
right, the above only gives 6+6 = 12 groups
multiplication was due to conditioned reflex !
there r 4 other groups of 6 each
for convenience, let them start with 1,3,5,7,9 &11
i) one odd no. e.g. 1-4-6-8-10 to 11-2-4-6-8
ii) 2 odd nos. e.g. 1-3-6-8-10 to 11-1-4-6-8
iii) 3 odd nos. e.g. 1-3-5-8-10 to 11-1-3-6-8
iv) 4 odd nos. e.g. 1-3-5-7-10 to 11-1-3-5-8
GRAND TOTAL: 36
