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.
Solution
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