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200 students are arranged in 10 rows of 20 children. The
shortest student in each column is identified, and the tallest of these
is marked A. The tallest student in each row is identified, and the
shortest of these is marked B. If A and B are different people, which is
taller?
This person will be taller in any case!
Why the height comparison?
B will be always taller in any case.
Case 1 : If A and B are standing in the same row the obviously B is taller than A as B is tallest among all in that row.
Case 2 : If A and B are standing in the same column then still B is taller than A as A is shortest among all in that column.
Case 3 : If A and B are standing in different row and column then there must be somebody C which has same column as A and same row as B. This C is shorter than B (as B is tallest in row) and he is taller than A (as A is shortest in that column). That is B > C and C > A.
Hence, in any case, B is always taller than A.