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Sevenths Sliced Square (Posted on 2011-02-24) Difficulty: 3 of 5
Define a slice of a square to be a line segment with ends on

two different sides,
one corner and an opposing side, or
two opposite corners of the square.

Sequential slices may or may not cross previous ones, but a set of slices will subdivide the square into polygonal regions.

Find (or prove impossible) a way to slice a square into 7 pieces of equal area with n distinct slices for each n={3,4,5,6,7}

See The Solution Submitted by Jer    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: n = 4 (spoiler) | Comment 6 of 7 |
(In reply to n = 4 (spoiler) by Steve Herman)

A concrete construction of the n=4 case:

Start with square ABCD.  Add point E on AB so that AE=3/7; points F, G, and H on BC so that BF=1/2 and GH=HC=17/84; point I on CD so that ID=3/7; and points J and K so that KJ=JD=31/84.  Draw lines EF, GK, HJ, and EI to create the seven areas.

  Posted by Brian Smith on 2011-02-25 20:24:47
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