A Gold Desert
You're lost in a vast desert with nothing but 1 gold bar and a surprisingly sharp knife. Luckily, you come across a local woman who knows how to get out of it. She says that the escape will be a seven-day journey and that she's willing to go with you for seven days showing the way, but she demands your gold bar in return.
You don't trust her fully and thus decide to give her of the gold bar at the end of each day.
What is the minimum number of cuts you need to make in order to execute your plan?
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1 solution
The answer is 2 cuts.
At the end of the first day you cut 1 seventh of the gold bar and give it to the woman.
At the end of the second day you cut a piece that equals 2 sevenths and give it to her in exchange for the seventh you gave to her the last day.
At the end of the third day you give her the seventh she returned to you the last day.
At the end of the fourth day you give her the piece that equals four sevenths that you're left with in exchange for the two pieces she has.
At the end of the fifth day you five her the piece of 1 seventh.
At the end of the sixth day you give her the 2 sevenths in exchange for the 1 seventh.
At the end of the seventh day you give her the 1 seventh, and thus your journey ends.
Drink lots of water.