Seven colleges and universities are competing to recruit six high school footbal

Question

Seven colleges and universities are competing to recruit six high school football players to play for their varsity teams. Each school is only allowed to sign one more player, and each player is only allowed to commit to a single school. The table below lists the seven institutions and the students they are trying to recruit, have been admitted, and are also interested in playing for that school. (There's no point in assigning a school a player who cannot meet academic requirements or doesn't want to be part of that team.) The players are identified by the integers 11 through 6.6. Find a way of assigning the players to the schools that maximizes the number of schools who sign one of the six players.

4. Seven colleges and universities are competing to recruit six high schoo football players to play for their varsity teams Each school is only allowed to sign one more player, and each player is only allowed to commit to a single school. The table below lists the seven institutions and the students they are trying to recruit, have been admitted, and are also interested in playing for that school. IThere's no point in assigning a school a player who cannot meet academic requirements or doesn't want to be part of that team.)The players are identified by the integers 1 through 6. Find a way of assigning the players to the that maximizes the number of schools who sign one of the six players School Player numbers Boston College 1, 3, 4 Clemson University 1 3, 4, 6 Georgia Institute of Technology 2,6 University of Georgia None interested University of Maryland 2, 3, 5 University of North Carolina 1, 2, 5 Virginia Polytechnic Institute and State University 1, 2, 5, 6

Explanation / Answer

Method:

Georgia refers to "Georgia Institute of Technology" and not "University of Georgia".We won't be assigning anybody to the "University of Georgia".

We will be assigning players to school and not the other way around.After each assigning the school that has the least number of options should be assigned.(For example initially Georgia will be assigned as it has only 2 options).While assigning players a player should be assigned such that the decrease in number of options of all the other schools is minimum.(For example Georgia will be assigned player 6 as it will decrease the options of Clemson and Virginia by one each(total 2) while if we assign 2 to Georgia Maryland,North Carolina and Virginia will lose one option each i.e. 3 options in total).In the same way the process is to be repeated.

1st Round:

Boston- 1,3,4

Clemson-1,3,4,6

Georgia-2,6

Maryland-2,3,5

NC-1,2,5

Virginia-1,2,5,6

Assigning Player 6 to Georgia.

2nd Round:

Boston- 1,3,4

Clemson-1,3,4

Maryland-2,3,5

NC-1,2,5

Virginia-1,2,5

Assigning Player 4 to Boston.

3rd Round:

Clemson-1,3

Maryland-2,3,5

NC-1,2,5

Virginia-1,2,5

Assigning Player 3 to Clemson.

4th Round:

Maryland-2,5

NC-1,2,5

Virginia-1,2,5

Assigning Player 5 to Maryland.

5th Round:

NC-1,2

Virginia-1,2

Assigning Player 1 /Player 2 to NC(lets say 2).

6th Round:

Virginia-1

Assigning Player 1 to Virginia.

So after all assigning:

Boston: 3

Clemson: 4

Georgia: 6

Maryland: 5

NC: 2

Virginia: 1

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