Kaprekar chains that end at 6174 are emitted as :kaprekar facts.
total emitted : 9990
omitted 0000 basin : 10
maximum steps to 6174 : 7
Selected facts, shown with four-digit padding for readability:
0001 :kaprekar (0999 8991 8082 8532 6174)
3524 :kaprekar (3087 8352 6174)
6174 :kaprekar (6174)
9831 :kaprekar (8442 5994 5355 1998 8082 8532 6174)
9998 :kaprekar (0999 8991 8082 8532 6174)
Each start is read as four digits, so 1 is treated as 0001.
The digits are sorted once, then the optimized identity computes the
same result as descending-number minus ascending-number.
The search is bounded to seven steps, matching the N3 source: any
four-digit start that reaches 6174 does so within that bound.
Step-count distribution for emitted starts:
0 step(s) : 1 start(s)
1 step(s) : 383 start(s)
2 step(s) : 576 start(s)
3 step(s) : 2400 start(s)
4 step(s) : 1272 start(s)
5 step(s) : 1518 start(s)
6 step(s) : 1656 start(s)
7 step(s) : 2184 start(s)
Examples omitted because they fall to 0000:
0000 -> (0000)
1111 -> (0000)
2222 -> (0000)
9999 -> (0000)