An interesting problem

[AD_]

Students are arranged in n columns and m lines. From each column we choose the tallest student and out of these we choose the shortest one, who we call A. From each line (in the initial arrangement) we choose the shortest student and out of these we choose the tallest one, who we call B. What is the height relationship of A and B?

 

[Deleted member 4993]

Students are arranged in n columns and m lines. From each column we choose the tallest student and out of these we choose the shortest one, who we call A. From each line (in the initial arrangement) we choose the shortest student and out of these we choose the tallest one, who we call B. What is the height relationship of A and B?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[AD_]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

At first i tried some random examples to build up my intuition about this problem. I noticed that in all of them it was A>=B. So then i tried to prove that it is impossible to have A<B but i couldn't do it.

 

[JeffM]

I suspect (but am not certain) that trying weak induction twice will work

Let n = 1, m = 1. Then A = B so A >= B.