Problem 166 Solution

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.

   xxxxx
   xmxxx
   xxxxx
   xxxxx
   xxxxx
   xxxxx
   xtxxn
   xxxxx
   xxxxx
   xxxxx

   In this digram 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.

   Michael Shackleford, ASA - July 19, 2001