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 A grid of people (Posted on 2002-07-09)
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.

 Subject Author Date Solution Math Man 2012-01-13 22:35:17 Answer K Sengupta 2008-02-29 06:33:40 re: Problem with Solution sassy 2004-05-18 11:01:03 The crux of the matter Richard 2003-12-13 23:51:03 Question. Barry Knapp 2003-12-12 21:12:08 re: Problem with Solution Jack Squat 2003-12-12 14:02:32 Problem with Solution Gamer 2003-04-14 11:39:10 Hm... suna 2002-11-11 15:36:46 Maybe.... Dulanjana 2002-07-10 05:40:46 Maybe it is this way.... Dulanjana 2002-07-10 05:39:44 re: Four line proof: TomM 2002-07-10 03:42:40 Four line proof: G. Steve Arnold 2002-07-09 08:18:59 re(2): Coordinate System TomM 2002-07-09 02:40:03 re: Coordinate System levik 2002-07-09 02:05:14 Coordinate System TomM 2002-07-08 17:11:20

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