All without debt
What happened in this situation was that the traveler's $ 100 bill only circulated, with each character (hotel manager, butcher, breeder and veterinarian) paying off one debt but no longer lending to another.
For example, the hotel manager paid off his debt to the butcher, but stopped being the vet's creditor, who owed him the same $ 100.
The traveler, who was the only one who had no debt (at least according to the statement), only received back the amount he had left.
Back to the statement