[FAO] 6174....Interesting Mathematical Property

Interesting! This is the famous Kaprekar Constant for 4-digit numbers. A similar constant exists for 3-digit numbers viz. 495. Also try the Collatz algorithm or Collatz sequence. 1. Take any positive integer (no limit on the digits). 2. If it is even, halve it. If it is odd, then triple it and add 1. 3. Repeat 2. The Collatz Conjecture states that this algorithm always converges to 1. e.g. consider 23 23*3 + 1 = 70 70/2 = 35 35*3 + 1 = 106 106/2 = 53 53*3 + 1 = 160 160/2 = 80 80/2 = 40 40/2 = 20 20/2 = 10 10/2 = 5 5*3 + 1 = 16 16/2 = 8 8/2 = 4 4/2 = 2 2/2 = 1. What's even more interesting is that the Collatz Conjecture is still unproved :) I read following interesting information on this number. 1. Consider a 4 digit number. Let us take 2781. 2. Arrange the digits in ascending and descending order and subtract smaller from larger. 8721-1278 = 7443 3. Repeat this operation. 7443-3447 = 3996 9963-3699 = 6264 6642-2466 = 4176 7641-1467 = 6174 7641-1467 = 6174... 4. This seems to be applicable to all 4 digit numbers where at least one digit is different from others. This property was found by one Shri Kaprekar, staying at Igatpuri.   Need More Interesting Stuff??? Click here  Click here to Join forangelsonly Group |  Join Us thru Email     |    Join Us thru Web     |  Visit Our Group Visit Our Website

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