Junior Divisional 2013/2

Problem for Junior Group from Divisional Mathematical Olympiad will be solved here.
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tanmoy
Posts: 282
Joined: Fri Oct 18, 2013 11:56 pm
Location: Rangpur,Bangladesh

Junior Divisional 2013/2

Unread post by tanmoy » Sun Nov 09, 2014 10:27 pm

There are $200$ students in a school.Some teams need to be formed with these students,but the problem is,each
student dislikes exactly three other students(dislike is not always associative,that is if Sakib dislikes Zubaer,it does not necessarily mean that Zubaer dislikes Sakib).Now,at least how many teams should be formed so that it can be ensured that no team has any member who is disliked by a team-mate.(it's not necessary for each team to have the same number of students) :?:
"Questions we can't answer are far better than answers we can't question"

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Hasibul Haque Himel.
Posts: 2
Joined: Mon Oct 27, 2014 11:24 am
Location: Naogaon

Re: Regional Math olympiad,Rangpur,2014;P:10

Unread post by Hasibul Haque Himel. » Wed Nov 19, 2014 5:33 pm

2teams.................

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Raiyan Jamil
Posts: 138
Joined: Fri Mar 29, 2013 3:49 pm

Re: Regional Math olympiad,Rangpur,2014;P:10

Unread post by Raiyan Jamil » Thu Nov 20, 2014 7:35 pm

I think that the answer is 200.
Because , the lowest number of groups can be 1 consisting of 200(all the students) and the highest number of groups can be 200 consisting 1 student each . Now, it is said that "it's not necessary for each team to have the same number of students ". So,even if there are 199 groups in which, 198 groups contain 1 student each and a single group contains 2 students . But, even then, it cannot be ensured that , any one student or both the two students dislike each other in that single group . And so,I think the answer in 200 groups .
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Naheed
Posts: 20
Joined: Sun Dec 16, 2012 11:10 pm

Re: Junior Divisional 2013/2

Unread post by Naheed » Wed Jan 14, 2015 5:27 pm

I am fully agreed with the logic shown by Raiyan Jamil. I also think that the minimum and only number of teams that should be formed is 200, which means each team would contain a single student. It can also be ensured that no team has any member who is disliked by another team-mate (here's no option to be!).

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