8. The Golden Chain Challenge
8. A landlady allows students to rent her apartment for 7 days under a specific condition: the student must pay rent daily using her 7-link golden chain. However, the student can only make two cuts in total, and they cannot cut multiple links in one go—each cut can only separate one chain at a time. Despite these restrictions, the student must pay exactly one chain link each day for the full 7-day stay. How can the student achieve this with just two cuts?
Added 1 January 2007 · Updated 2 July 2026
Hint: You can ask for change.
Solution:
Here’s how the student can pay the rent using the 7-link golden chain with only two cuts:
Step-by-step Process
- First cut: Separate a single link (1-link piece).
- Second cut: Separate a 2-link piece from the remaining chain.
Now, you have three pieces: 1-link piece, a 2-link piece and 4-link piece.
Paying the Rent Daily
- Day 1: Give the 1-link piece.
- Day 2: Take back the 1-link piece and give the 2-link piece.
- Day 3: Give the 1-link piece along with the 2-link piece, making 3 links in total.
- Day 4: Take back both the 1-link and 2-link pieces and give the 4-link piece.
- Day 5: Give the 1-link piece along with the 4-link piece, making 5 links in total.
- Day 6: Take back the 1-link piece and give the 2-link piece along with the 4-link piece, making 6 links in total.
- Day 7: Give the 1-link piece again, bringing the total to 7 links.
By following this strategy of giving and taking back the pieces, the student can meet the condition of paying exactly one chain link per day, using only two cuts.
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