April 17, 2025: Gold Bar Puzzle
Question: You hire a worker for 7 days. You must pay him one-seventh of a gold bar at the end of each day. However, you only have one gold bar and can make only two cuts. How can you pay the worker exactly 1/7 of the bar each day?
Answer: Make two cuts to divide the bar into pieces of size 1/7, 2/7, and 4/7. This allows you to pay the worker daily using a exchange strategy:
- Day 1 (Goal --> pay 1/7): Give the 1/7 piece. (You: 2/7, 4/7 — Worker: 1/7)
- Day 2 (Goal --> pay 2/7): Give 2/7, take back 1/7. (You: 1/7, 4/7 — Worker: 2/7)
- Day 3 (Goal --> pay 3/7): Give 1/7 again. (You: 4/7 — Worker: 1/7 + 2/7 = 3/7)
- Day 4 (Goal --> pay 4/7): Give 4/7, take back 1/7 and 2/7. (You: 1/7, 2/7 — Worker: 4/7)
- Day 5 (Goal --> pay 5/7): Give 1/7. (You: 2/7 — Worker: 1/7 + 4/7 = 5/7)
- Day 6 (Goal --> pay 6/7): Give 2/7, take back 1/7. (You: 1/7 — Worker: 2/7 + 4/7 = 6/7)
- Day 7 (Goal --> pay 7/7: full bar): Give 1/7 again. (You: none — Worker: 1/7 + 2/7 + 4/7 = full bar)
This method ensures the worker receives exactly 1/7 of the gold bar each day, using only two cuts.