Shirley, a college student, has run short of cash and is unable to pay the rent on her apartment. Although she knows she will receive a final check from her former employer in 23 days, the apartment owner refuses to wait. Having recently received, from her grandparents, a valuable gold chain with 23 links, she proposes to pay for each day with one link. After she receives her check and pays cash, the apartment owner will return the links. Because of the history of mistrust, he wants payment every day, and Shirley does not want to pay any links in advance. She also wants to preserve the integrity of the chain to the degree that is possible. How many links must be cut while still paying the owner one link for each day