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**