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 Sevenths Sliced Square (Posted on 2011-02-24)
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)

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 n = 5 (spoiler) | Comment 2 of 7 |
One way to do it with 5 lines:

a) Draw three parallel lines parallel to the top edge of the square, at distances from the top of 1/7, 2/7 and 3/7 of a side.
b) The remaining rectangle at the bottom constitutes 4/7 of the square.   Divide it into fourths using two diagonals.

 Posted by Steve Herman on 2011-02-25 01:03:41

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