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)

## Junior Divisional 2013/2

**Forum rules**

Please

**don't post problems (by starting a topic)**in the "Junior: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.

### Junior Divisional 2013/2

"Questions we can't answer are far better than answers we can't question"

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

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

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

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

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

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 .

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 .

**A smile is the best way to get through a tough situation, even if it's a fake smile.**

### Re: Junior Divisional 2013/2

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!).