Who's Taller: Allen or Betty?
Allen and Betty are two students in a class of 40 math students. Each of the 40 students are a different height. They stand in a rectangular formation with 8 columns and 5 rows.
For each column, the name of the tallest student is written down. Among these 8 names, Allen is the shortest .
For each row, the name of the shortest student is written down. Among these 5 names, Betty is the tallest .
Who is taller: Allen or Betty?
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1 solution
Suppose there is a student (Curtis) who stands the same column as Allen and the same row as Betty.
Because Betty is shortest in her row, we know that Betty is shorter than Curtis.
Similarly, because Allen is the tallest in his column, we know that Allen is taller than Curtis.
Therefore we can conclude A l l e n ≥ B e t t y .