A problem from the Soviet Mathematical Olympiad:
Two hundred 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?
|
SelectClick for Answer |
B is taller:
- If A and B stand in the same row, then B is taller, since we know that B is the tallest student in his row.
- If A and B stand in the same column, then again B is taller, since we know that A is the shortest student in his column.
- If A and B share neither a row nor a column, then let C be the student who’s in the same column as A and the same row as B. Then C is shorter than B (who is the tallest in his row) and taller than A (who is the shortest in his column), so B > C > A.
In every case, then, B is taller than A.
|
