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Series of Reversed Differences

abc
- cba
-----
xyz

Beginning with a three-digit number, reverse the order of the digits and
subtract the smaller number from the larger. If the result is a three-digit
number, repeat until the result has less than three digits or
is a duplicate of a previous result.
- What is the longest series of subtractions before reaching a
two-digit number or a duplicate?
- If a cycle exists (a duplicate result is found), what is the longest
cycle?
- What is the most likely 2-digit result to end the series?
If we continue to reverse and subtract, what is the most common 1-digit
result?

Repeat the problem for 2-digit numbers and for 4-digit numbers.
Source: Original.

Solutions were received from
Al Zimmermann, Denis Borris, David Peck, Joseph DeVincentis,
Dane Brooke, Samantha Levin, David Arnold, Ross Millikan,
and Sudipta Das.
Samantha Levin's submission is a good summary, with some examples from
Ross Millikan and Joseph DeVincentis:
Very interesting puzzle! In the 2 (3) digit cases, everything degenerates to 9
(99) - there are no cycles. The longest series is 6 (5 not counting the final 1
or 2 digit number) in both cases (achieved by 16 different 2-digit numbers and
160 different 3-digit numbers).

[One example of each from Ross Millikan:
654->198->693->297->495->99.
35->18->63->27->45->9]

In the 4-digit case, there is one cycle of length 2: 2178, 6534. Some numbers
degenerate to this cycle; all other numbers degenerate to 999, with the longest
series being 13 (achieved by 173 different numbers).

[One example from Joseph DeVincentis:
This would
be satisfied by a number such as 3800, which follows the path 3717, 3456,
3087, 4716, 1458, 7083, 3276, 3447, 3996, 2997, 4995, 999.]

For higher numbers of digits, there are also cycles of length 2, which are
variations of the 2178, 6534 cycle:

21(any number of 9's)78, 65(same number of 9's)34 is a 2-cycle

21782178,65346534 is a 2-cycle (etc. for 3,4,.... repeats)

The only other cycle I found was a cycle of length 14 for 8-digit numbers,
generated by 11436678.

Mail to Ken