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Some thoughts

*11+22+33+44+55+66+77+88+99=495

*111+222+333+444+555+666+777+888+999+1110+69=6174

*6174+495=6669

*Square root of (1467,1476,1647,1674....) Only hole numbers 42 and 69. 42*42=1764 69*69=4761

* 69+42=111

* 0000,1111,2222,3333,4444,5555,6666,7777,8888,9999. 6174 should have a property similar from the rest of them.

(1467,1476,1674,1647 ...etc)/5555 -average of above, 6174 is 1,111. If variations are in order, 1,111 is in the middle of the variations.

* All numbers in Kaprekar process are divisible by 9.