The gold of the traveler
It should cut the first time so that the first piece should have 1/7 (one seventh) of the total bar.
Then it should cut for the second and last time, each part having respectively 2/7 (two sevenths) and 4/7 (four sevenths) of the total bar.
Then the payment must be made as follows:
1st daily: pays with 1/7 of the bar.
2nd daily: pay with 2/7 bar and get 1/7 bar back.
3rd daily: pays again with 1/7 of the bar.
4th daily: pays with 4/7 of the bar and gets back 3/7 of the bar (being two pieces: 1/7 and 2/7 of the bar).
5th daily: pays with 1/7 bar again.
6th daily: pay with 2/7 bar and get 1/7 bar back.
7th daily: pays with 1/7 of the bar.
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