The Worker and the Gold Bar | Solution
The answer: 2
The key here is recognizing that you can get 1/7 of the bar back as change if you pay her a 2/7-size chunk on day 2. You’ll have to make two cuts, so the bar is in three pieces: 1/7, 2/7, and 4/7:
• On day 1, you pay her with the 1/7-size piece of the bar.
• On day 2, you pay her with the 2/7-size piece. She will give you back the 1/7-size piece from day 1 as change.
• On day 3, you pay her that 1/7-size piece.
And here’s the real beautiful, elegant part:
• On day 4, you pay her the larger part of the bar—given that 3/7 is already removed from it, so it’s now a 4/7-size piece. She now has the 2/7-size piece you gave her on day 2, as well as the 1/7-size piece you gave her yesterday. She will give these to you as change, so you now have those back.
The rest just falls in place:
• On day 5, you pay her the 1/7-size piece.
• On day 6, you pay her the 2/7-size piece and she gives you the 1/7-size piece as change.
• On day 7, you give her the 1/7-size piece and you’re all done.
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