# Who is taller A or B?

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500 men are arranged in an array of 10 rows and 50 columns according to their heights.

Tallest among each row of all are asked to come out. And the shortest among them is A.
Similarly after resuming them to their original positions, the shortest among each column are asked to come out. And the tallest among them is B.

Now who is taller A or B ?

Both are same as A and B are the same person.

EXPLANATION-
As it is mentioned that 500 men are arranged in an array of 10 rows and 50 columns according to their heights.
Let’s assume that position numbers represent their heights.
Hence,
the shortest among the 50, 100, 150, … 450, 500 is person with height 50 i.e. A. Similarly the tallest among 1, 2, 3, 4, 5, ….. 48, 48, 50 is person with height 50 i.e. B

Now, both A and B are the person with height 50.
Hence both are same.

• The key is to notice that the men are placed according to their heights. If it were any other way the answer could not be deduced

Now, assign natural numbers in increasing order to each of the men, indicative of their heights.
Last man in row 1 is assigned 50, last one in row2 -100 and so on till last one in row 10-500
The last person in each row is the tallest one, A is the shortest in this set (50,100,150… 500), therefore  A is 50
Also the shortest in the last column, ie the set of(50,100,150… 500), is 50.
Since all other elements in the set containing shortest of each column, will ultimately contain elements from the first row (men in higher rows are taller),50 is the tallest of this set. Therefore B is 50

a and b are same i.e it is one with two names a and b

Both A and B are of the same height.

Because,
when we arange the matrix in increasiong order we get 50 is the shortest among each row and 50 is the the tallest among shortest from each column.