## Durga Constant: 495

For students of class 11-12 (age 16+)
Avik Roy
Posts: 156
Joined: Tue Dec 07, 2010 2:07 am

### Durga Constant: 495

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

nayel
Posts: 268
Joined: Tue Dec 07, 2010 7:38 pm
Location: Dhaka, Bangladesh or Cambridge, UK

### Re: Durga Constant: 495

"Everything should be made as simple as possible, but not simpler." - Albert Einstein