My friend asked me this question earlier today.

"Arrange n^2 apples in a square. From each row find the largest one and let A be the smallest of these. From each column find the smallest one and let B be the largest of these. Which one is bigger, A or B? Give reason."

The obvious thought which crossed my mind was to replace apples with unique numbers between 1-9 in a 3×3 matrix. Also, the question itself suggested the algorithm within itself to go about and find evaluate A & B.

Case I: My immediate matrix looked like this >>

1   3   6

2   5   9

4   7   8

By following the above mentioned steps, the least value found across the maximum from each rows was 6 while the max value found across the minimum from each column was 6 again!

Case II: But when I use the matrix such as >>

1   3   9
7   8   6
5   4   2

By following the above mentioned steps, the least value found across the maximum from each rows was 5 while the max value found across the minimum from each column was 3!

Immediately I realized that, the variation is purely because of the way we distribute numbers.

In case I, I used sorted sequence of numbers while in case II, I uniformly distributed the numbers at random. Result became fairly obvious!