BMO 1966 Problem 10 One hundred people of different heights are arranged in a 10 x 10 array. X, the shortest of the 10 people who are the tallest in their row, is a different height from Y, the tallest of the 10 people who are the shortest in their column. Is X taller or shorter than Y? Solution
: taller. If X and Y are in the same row or column, then the result is immediate (by definition, X is taller than others in the row, and Y is shorter than others in the column). So suppose they are not. Take Z in the same row as X and the same column as Y. Then Z is shorter than X and taller than Y. 2nd BMO 1966 © John Scholes jscholes@kalva.demon.co.uk 30 Aug 2000