This is a classic puzzle that can be solved with a bit of logical reasoning. Since you’re only allowed to make two breaks in the gold bar, you need to find a way to use the three resulting pieces to create combinations equal to the payments for each of the seven days.
On Day 1, you give your worker one piece (Piece A). Thus, you make your first break at 1/7 of the gold bar. Now, you have two remaining pieces: Piece B representing 2/7 and Piece C representing 4/7.
On Day 2, take back the piece you gave them initially (Piece A), and instead give them Piece B (which is 2/7 of the gold bar). In this way, the worker has received an additional 1/7 of the gold bar, equalling the daily payment.
On Day 3, give them back the first piece (Piece A) without taking back Piece B. Now they have 3/7 of the gold bar.
On Day 4, take back Piece A and Piece B to give them Piece C, which is 4/7 of the gold bar.
On Day 5, you give them back Piece A again without taking back Piece C. Now they have 5/7 of the gold bar.
On Day 6, take back Piece A and give them back Piece B. Now they have 2/7 + 4/7 = 6/7 of the full gold bar.
On Day 7, give them back Piece A. At this point, they have received equal the full gold bar’s worth for the full seven days.
To summarize:
- Day 1: Give away Piece A (1/7)
- Day 2: Take back Piece A, give away Piece B (2/7)
- Day 3: Give away Piece A without taking back Piece B (1/7 + 2/7 = 3/7)
- Day 4: Take back Piece A and Piece B, give away Piece C (4/7)
- Day 5: Give away Piece A without taking back Piece C (1/7 + 4/7 = 5/7)
- Day 6: Take back Piece A, give away Piece B (2/7 + 4/7 = 6/7)
- Day 7: Give away Piece A (7/7, so they now have the full gold bar)