Consider all nine-digit numbers consisting of one each of the digits 1 through 9.
What is the sum of these numbers?
HINTS:
(i)Consider all possible 9 digit numbers satisfying conditions of the problem.
(ii)Arrange these numbers , WLOG, in ascending order of magnitude.
(iii)Determine , the number of times any given digit i , where 1< i < 9, is the first digit in the said arrangement and for that matter, the digit i is the pth digit (1<=p<=9) in the arrangement.
(iv) Work out the required sum in terms of hints (i)-(iii).
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Edited on April 14, 2006, 10:42 am
Edited on April 14, 2006, 12:12 pm
Some Hints For Solving The Problem
