AoA!
A group of 61 students is divided into 3 subgroups. Two students play a game of chess (only once) if and only if they are in the same subgroup. Find a partition such that the total number of games is a multiple of 61.
What do you say?
Chess Game!
Everybody is a genius; but if you judge a fish on its ability to climb a tree, it will live its entire life believing that it is stupid. - Albert Einstein
- nafistiham
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Re: Chess Game!
i think it should have been said that,no subgroup can be an empty set.
if it is not a condition then a solution is $[0,0,61]$
hint:
if it is not a condition then a solution is $[0,0,61]$
hint:
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: Chess Game!
Your answer being?
Everybody is a genius; but if you judge a fish on its ability to climb a tree, it will live its entire life believing that it is stupid. - Albert Einstein
- nafistiham
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Re: Chess Game!
the next thing is trial and error. i haven't completed it yet. whenever i do, i'll post.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: Chess Game!
You've written: \[\frac{x!}{2!(x - 2)!}= \frac{x^2 - 1}{2}\]
Shouldn't it instead be as follows?
\[\frac{x!}{2!(x - 2)!}= \frac{x^2 - x}{2}\]
Shouldn't it instead be as follows?
\[\frac{x!}{2!(x - 2)!}= \frac{x^2 - x}{2}\]
Everybody is a genius; but if you judge a fish on its ability to climb a tree, it will live its entire life believing that it is stupid. - Albert Einstein
- nafistiham
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- Joined:Mon Oct 17, 2011 3:56 pm
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Re: Chess Game!
oops.
I am really sorry about the mistake.
thanks a lot for the correction.
I am really sorry about the mistake.
thanks a lot for the correction.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: Chess Game!
There's no need to be sorry.
Everybody is a genius; but if you judge a fish on its ability to climb a tree, it will live its entire life believing that it is stupid. - Albert Einstein