Durga Constant: 495

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Avik Roy
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Joined: Tue Dec 07, 2010 2:07 am

Durga Constant: 495

Unread post by Avik Roy » Tue Jan 04, 2011 11:40 pm

The number $495$ is called the Durga Constant. Consider any three digit numbers where at least one of the digits is different. Take its highest value permutation and deduct it from the lowest value permutation. Repeat the same procedure for the three digit number you receive as result in earlier stage. Continuing this will lead you to the ultimate result of $495$.

For example, consider the number $484$
Highest value permutation: $844$ and lowest value permuation: $448$
$844-448 = 396$
Next comes: $963-369 = 594$
and then comes: $954 - 459 = 495$

The question is: (a) Prove this property of the number $495$, and (b) Extend this property for $n$ digit numbers, if possible.
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

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nayel
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Joined: Tue Dec 07, 2010 7:38 pm
Location: Dhaka, Bangladesh or Cambridge, UK

Re: Durga Constant: 495

Unread post by nayel » Wed Jan 05, 2011 9:53 pm

Here is my solution for the 4-digit case, which can be easily worked out for three digits. But there is no single constant when the number of digits is more than four.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein

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