Friday, 26 October 2012

Kaprekar constant 5 digits-rejoinder

With reference to my earlier post date 10 sep 2012,I have to indicate the following details-
There is no constant of 5 digits like 74943 and 82962 as mentioned by me.
However there appear 2 series in which these 2 numbers are included.
For instance,we can start with the digits 2,3,5,8 and 9
The difference between the highest number 98532 and the smallest number 23589 formed with these digits is
of course 74943.Using these new set of digits viz 3,4,4,7 and 9 we do not get back 74943 ,in which case only we can treat 74943 as a Kaprekar constant like 6174 you get with 4 digit numbers.
In fact you get 97443-34479=62964.
You repeat now and get 96642-24669=71973
Again repeat you get 97731-13779=83952.
Repeat again,only now you get back 74943.as the same digits 2,3,5,8 and 9 are now involved.
Thus 74943 forms part of the series 74943,62964,71973,83952,74943...repeated back.
Similarly the other number 82962 forms part of the series 82962,75953,63954,61974,82962 repeated back.
You can in fact say if you like that all the 8 numbers involved are Kaprekar constants,instead of only one number like 6174 involved with 4 digits. 

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