this basically is not a puzzle,but a tribute to an unknown indian
mathematician.
Kaprekar's Constant:
This number activity has more general possibilities, but to introduce
it we focus on its four-digit case (because, Kaprekar introduced this
concept with this case). First, write down a four-figure number (not
all digits the same), say 3529. Now, rearrange the digits to form the
largest number that you can (ie., 9532) and the smallest such number
(2359). Subtract these two numbers (large minus small), and get a new
number, 7173. Repeat the process: 7731- 1377 = 6354. Repeat again: 6543
- 3456 = 3087. And again: 8730- 0378 = 8352. And again: 8532 - 2358 =
6174. Now, observe: 7641 -1467 = 6174 ... again, and again! For the
amateur mathematician who discovered it, D. R. Kaprekar (Shri
Dattathreya Ramachandra Kaprekar (1905-86?), a mathematician from
India), this number, 6174, is now known as Kaprekar's constant.
Four-figure numbers "lead to" 6174. Why? Show that 3256 leads to 6174
in two steps, 9017 leads to 6174 in seven steps. Would there be a
Kaprekar constant for three-figure numbers? ...for five-figure numbers?
Observe that for repeating-digits the Kaprekar's process trivially
terminates on the number zero.
thanx for reading
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