[BITList] Fwd: [INDIA-BRITISH-RAJ] Mathematical genius DR Kaprekar and Deolali Number

[John Feltham]

Begin forwarded message:

From: "Arvind Kolhatkar" <akolhatkar at rogers.com>
Date: 8 June 2009 11:36:05 PM
To: <india-british-raj at rootsweb.com>
Subject: [INDIA-BRITISH-RAJ] Mathematical genius DR Kaprekar and  
Deolali Number
Reply-To: india-british-raj at rootsweb.com

Dear Listers,

Like S. Ramanujan, I also know of another self-taught mathematical  
genius, the late D.R.Kaprekar (1905-1986), who was a humble school  
teacher in Devlali, near Nasik.  One of his discoveries in the Number  
Theory has been named after the town of Devlali.  For more information  
about him and the Deolali number, please see http://en.wikipedia.org/wiki/D._R._Kaprekar 
  and http://en.wikipedia.org/wiki/Self_number.  Many members of these  
Lists have Deolali connections.  They will be happy to know one more  
piece of info connected with that town.  (The word and phrase  
'Doolally' and 'Doolally Tap' have already been noticed in this List  
in March 2008.)

As a sample of his work I may mention that the so-called Kaprekar  
Constant, which is the number 6174.  Start with any four digits, all  
different from each other.  Form the largest number and the smallest  
number out of those four digits and subtract the smaller from the  
larger.  Do the same with the four digits of the answer.  Keep  
repeating this.  No matter how you start, the answer in seven or less  
steps, will be 6174.

For example, start with digits 3,5.9,4.

9543 - 3459 = 6084
8640 - 0468 = 8172
8721 - 1278 = 7443
7443 - 3447 = 3996
9963 - 3699 = 6264
6642 - 2466 = 4176
7641 - 1467 = 6174

(The Constant answer 6174 reached in 7 iterations).

Or, start with digits 0,2,3,4

4320 - 0234 = 4088
8840 - 0488 = 8352
8532 - 2358 = 6174

(The Constant answer 6174 reached in 3 iterations).

Arvind Kolhatkar, Toronto, June 08, 2009.

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ooroo

Bad typists of the word, untie.