You have a gold chain with seven links. You need to hire an assistant at a fee of one gold link per day for seven days. Each day, the assistant needs to be paid for his or her services without overpayment or underpayment. What is the fewest number of cuts to the chain to facilitate this arrangement?
Solution: The major insight required for this puzzle is that the assistant is prepared to give change. It is not the case that you need to pay the assis-tant with one link at a time. The solution is to cut the third link. That cut will separate the chain to create three chains of four links, two links, plus the single cut link itself.
Day 1: Give the assistant the cut link.
Day 2: Take back the cut link; give the assistant the two-link chain.
Day 3: Give the assistant the cut link.
Day 4: Take back both the cut link and the two-link chain; give the assistant the four-link chain.
Day 5: Give the assistant the cut link.
Day 6: Take back the cut link, give the assistant the two-link chain.
Day 7: Give the assistant the cut link.
Answer: One cut, at the third link.