Durga Constant: 495
Posted: 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.
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.