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?
(In reply to
Answer by K Sengupta)
If there is a 1x1 grid then it trivially follows that A and B are the same person -and, accordingly, they have the same height.
If A and B are situated in the same column, then we observe that B is the shortest in his column. Hence, if A is situated in the same column - then A must be taller than B
If A and B are situated in the same row, then A is the tallest in his row. So, if B is located in that row- then it trivially follows that A is taller than B.
If A and B are in different rows and columns, then let us consider an individual C who is located in the same row as B and the same column as B.
A and C are in the same row. So, A is taller than C, as A is the tallest in this row. B and C are in the same column, so that B is shorter than C, as B is the shortest in his column. Therefore, A is taller than C, and C is taller than B. Accordingly, A must be taller than B.
Consequently, without considering the trivial 1x1 grid, it follows that:
If A and B are two different individuals, then A is always taller than B.
Edited on August 30, 2022, 8:00 am
Explanation to Puzzle Answer
