The graph is small. Similar graphs (e.g. this algorithm for 2 or 5 digit, or 3-4 digit numbers for base 9 or 11) have multiple cycles: https://en.wikipedia.org/

The graph is small. Similar graphs (e.g. this algorithm for 2 or 5 digit, or 3-4 digit numbers for base 9 or 11) have multiple cycles: https://en.wikipedia.org/wiki/Kaprekar's_routine#Kaprekar's_constants_and_cycles_of_the_Kaprekar_mapping_for_specific_base_b https://en.wikipedia.org/wiki/Kaprekar's_routine#Kaprekar's_...