Question

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

Answer 1

The solution to the problem involves minimizing the number of cuts necessary in a gold chain so that one link can be paid each day, requiring a systematic mathematical approach.

Step-by-step explanation:

The question asks how many links Shirley must cut from her gold chain to pay the apartment owner one link each day for 23 days. This is a problem based on mathematical reasoning and strategy, often involving sequences and arithmetic operations. Shirley needs to minimize the number of cuts so that she can pay each day without giving any links in advance.

The optimal solution involves cutting the chain at certain intervals that allow the links to be combined in different ways to count for each day up to 23. She should cut the first link to give the apartment owner immediately. Then, for the subsequent days, she can give and take back some links to make up the exact amount for each day. Without providing the exact mathematical solution, one must employ a systematic approach to work out the minimum number of cuts required.

Answer 2

Shirley must cut 22 links from the gold chain to pay the apartment owner one link for each day for 23 days while preserving the integrity of the chain.

Step-by-step explanation:

To pay the apartment owner one link for each day, Shirley must cut 22 links from the valuable gold chain. Since she will receive her final check in 23 days, she needs to make a payment each day for 23 days. However, she doesn't want to pay any links in advance. So, she can pay with one link each day for 22 days, and on the 23rd day, she can pay with her cash. After that, the apartment owner will return the links to Shirley. By cutting 22 links while still paying the owner one link for each day, Shirley can preserve the integrity of the chain to the best possible degree.