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That's a lotta numbers! (Posted on 2006-04-14) Difficulty: 2 of 5
Consider all nine-digit numbers consisting of one each of the digits 1 through 9.

What is the sum of these numbers?

See The Solution Submitted by Jer    
Rating: 3.2500 (4 votes)

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Hints/Tips Some Hints For Solving The Problem | Comment 1 of 10


(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). 

<o:p> </o:p>

Edited on April 14, 2006, 10:42 am

Edited on April 14, 2006, 12:12 pm
  Posted by K Sengupta on 2006-04-14 09:45:40

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