Problem of the Week 1020

A Pandigital Puzzle

Let p(n) be the probability that a random n-digit integer has all 10 digits occurring (where for simplicity we do include leading 0s; that is, we consider 0000012345 as being a 10-digit number). So p(9) is 0 and p(10) = 10!/10¹⁰.

What is the smallest n for which p(n) > 1/2?

Suggested by Danny Lichtblau, Wolfram Research, Inc.

© Copyright 2004 Stan Wagon. Reproduced with permission.