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gjm comments on Open Thread, Apr. 13 - Apr. 19, 2015 - Less Wrong
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In keeping with the "puzzle" theme:
You are given a rectangular piece of paper (such as the placemat at a fast-food restaurant). Without using any measuring tools (such as a ruler, a tape measure, some clever length-measuring app on your smartphone, etc.), divide the paper into five equal parts.
Could you confirm or correct some guesses about exactly what problem is intended?
Folding is allowed, yes.
Parts can have different shapes (if you want), but must have the same area.
You cannot use compasses, but you can use an unmarked straightedge if you want to make precise creases, or to avoid ripping the paper in an untidy fashion. You are not allowed to mark the straightedge, of course.
If the procedure were carried out with infinite precision, then it would indeed produce exact fifths.