Who is TallerLogic puzzles require you to think. You will have to be logical in your reasoning.
Fifty contestants for the Miss America pageant were arranged in ten rows and five columns on the Boardwalk in Atlantic City. One viewer of this display noticed that of the tallest women in each column that Miss Maryland was the shortest of the five. Another viewer noticed that of the shortest women in each row that Miss Nevada was the tallest of the ten. There are no ties, all fifty women have different heights. Who is taller, Miss Maryland or Miss Nevada?
AnswerMiss Maryland is taller.
There are three possible scenarios:
1) If Miss Maryland and Miss Nevada are in the same column then Miss Maryland would be taller, because she is the tallest in that column.
2)If Miss Maryland and Miss Nevada are in the same row then Miss Maryland would be taller, because Miss Nevada is the shortest in that row.
3)If Miss Maryland and Miss Nevada share neither a row nor column then there must be some other contestant who is both in Miss Maryland's column and Miss Nevada's row. Call this woman Miss Texas.
To illustrate her position consider the following diagram.
In this diagram the m stands for Miss Maryland, the n for Miss Nevada, and the t for Miss Texas.
Miss Maryland must be taller than miss Texas, because miss Maryland is the tallest in her column. Miss Texas must be taller than Miss Nevada, because Miss Nevada is the shortest in her row. Thus if M>T>N then M>N, or Miss Maryland is taller than Miss Nevada.
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