MATH STINGER #90
by Dr. Joel C. Fowler
Associate Professor of Mathematics  

 

 

        The puzzle for this issue concerns permutations of the digits 1 through 9.  A permutation of these digits is nothing more than an arrangement of all 9.  For example, 964581327 and 123549876 are both permutations of 1 through 9.  Note that in each permutation all of the digits must appear and none are repeated.  There are a total of 9! = (9)(8)(7)...(3)(2)(1) = 362,880 different permutations of 1 through 9.  Suppose that each of these 362,880 permutations are treated as numbers and listed in order from smallest to largest.  The puzzle is to determine which permutation would be 100,000th in that list.