this story only makes sense because the town was in a state where all the debts cancelled out the $100 bill appearing didn't do anything but help them realize

this story only makes sense because the town was in a state where all the debts cancelled out the $100 bill appearing didn't do anything but help them realize that if they sat down at a whiteboard and drew it out they could have figured it out. if they didn't cancel out, the $100 bill would stop before it got back to the inn keeper and he'd be in trouble