46. 200 students lined up in a rectangle with 10 people in each transverse row and 20 people in each longitudinal row. In each longitudinal row, the tallest student was chosen, and from them, the shortest one was selected. Similarly, in each transverse row, the shortest student was chosen, and from them, the tallest one was selected. Which of the two selected students is taller?
46. Let's introduce the following notations: $A$ - the shortest of all the tallest students, $B$ - the tallest of all the shortest students. There are 3 and only 3 cases. 1) $A$ and $B$ stood in the same transverse row. In this case, $B$ is the shortest in this row. Therefore, $B$ is shorter than $A$. 2) $A$ and $B$ stood in the same longitudinal row. In this case, $A$ is the tallest in this row. Therefore, $B$ is shorter than $A$. 3) $A$ and $B$ stood in different longitudinal and transverse rows. Suppose $A$ stands, for example, in the 3rd longitudinal row, and $B$ in the 8th transverse row. Let's compare the height of each of the students $A$ and $B$ with the height of student $C$, who stands at the intersection of the 3rd longitudinal and 8th transverse rows. $C$ is shorter than $A$, since $C$ and $A$ stood in the same longitudinal row and $A$ was the tallest in this row. But $C$ is taller than $B$, since they stood in the same transverse row and $B$ was the shortest in this row. Therefore, in this case as well, $B$ is shorter than $A$.