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A grid of people (Posted on 2002-07-09) Difficulty: 3 of 5
Imagine a "grid" of people: some number of people arranged in a number of rows and columns in a rectangular formation.

We designate person A as the shortest person in the group of the tallest people of each row. We then designate person B as the tallest person in the group of shortest people in each column.

Who is taller, A or B?

  Submitted by levik    
Rating: 3.5833 (12 votes)
Solution: (Hide)
There are 4 cases to consider:

A and B are the same person
(This is possible, if for example, the grid is a 1x1 grid). I this case A and B are the same height.

A and B are in the same row
Since A comes from a group of people who are the tallest in their rows, A must be the tallest person in his row. Thus, if B is in the same row, A is taller.

A and B are in the same column
Since B comes from a group of people who are the shortest in their respective columns, B must be the shortest in his column. Thus, if A is in the same column, A must be taller.

A and B are in different rows and columns
For this case, imagene a person C, who is in the same row as A, and in the same column as B. C must be shorter than A, since A is the tallest in his row. C must be taller than B since B is the shortest in his column. Thus, since A is taller than C who is taller than B, A must be taller than B.

As you see in all cases but the specialized case where A and B are the same person, A must be the taller of the two.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionMath Man2012-01-13 22:35:17
AnswerK Sengupta2008-02-29 06:33:40
Some Thoughtsre: Problem with Solutionsassy2004-05-18 11:01:03
SolutionThe crux of the matterRichard2003-12-13 23:51:03
Some ThoughtsQuestion.Barry Knapp2003-12-12 21:12:08
re: Problem with SolutionJack Squat2003-12-12 14:02:32
Problem with SolutionGamer2003-04-14 11:39:10
Hm...suna2002-11-11 15:36:46
SolutionMaybe....Dulanjana2002-07-10 05:40:46
SolutionMaybe it is this way....Dulanjana2002-07-10 05:39:44
re: Four line proof:TomM2002-07-10 03:42:40
SolutionFour line proof:G. Steve Arnold2002-07-09 08:18:59
re(2): Coordinate SystemTomM2002-07-09 02:40:03
Questionre: Coordinate Systemlevik2002-07-09 02:05:14
SolutionCoordinate SystemTomM2002-07-08 17:11:20
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