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        riddles >> medium >> MEDIUM: PAPER CUTTING
        
(Message started by: srowen on Jul 28^th, 2002, 6:07pm)

Title: MEDIUM: PAPER CUTTING
Post by srowen on Jul 28^th, 2002, 6:07pm

Somebody please post an answer to this! It is driving me and my friends nuts. Since it is listed as "medium" I hope someone has the answer.

Title: Re: MEDIUM: PAPER CUTTING
Post by kkw on Jul 28^th, 2002, 8:29pm

For the five by five square, label the vertices a1 through a6
for the top row, b1 through b6, c1 thru c6, etc up to
f1 through f6

The cut is made of the following 7 segments:

e1-e3, e3-d2, d2-d4, d4-c3, c3-c5, c5-b4, b4-b6

Title: Re: MEDIUM: PAPER CUTTING
Post by Kurt on Aug 8^th, 2002, 2:49am

I thought it should be possible to cut of a stroke (a5 to f5) and then making a cut in this stroke from b6 towards b5, but without cutting of the little triangle, so leaving it as only one piece.
Since paper is used, the little triangle can rotate around point b5 for 180 degrees. This resulted shape can be flipped and then fits exactly to complete the 6x4 rectangle.

Title: Re: MEDIUM: PAPER CUTTING
Post by Psychotic Venom on Aug 8^th, 2002, 8:33am

Kurt:

The whole idea of this is that you make one continuous cut. This would actually require cutting twice. Which means more than 2 pieces.

The first solution is exactly what was intended. It just requires realizing that you must create two identical pieces and shift them while accomodating for the cut out corners.

Title: Re: MEDIUM: PAPER CUTTING
Post by jeremiahsmith on Aug 24^th, 2002, 12:12am

Picture here:
http://www.wam.umd.edu/~xdt/squaredivision.bmp

The black lines are the original square. The blue lines are the cut. (And the truncated corners.) The red lines are there to show unit lengths. And the dots are just to show how the pieces move in relation to each other.

Title: Re: MEDIUM: PAPER CUTTING
Post by Çaylak on Sep 15^th, 2004, 4:39am

I must admit the beauty of the zig zag cut solution. But I interpreted "one continous cut" as a single straight cut, so came up with this solution, hope you like it:
using the same notation, fold the bottom left corner of the 5x5 paper by d1 - f3 axis.
start cutting from e6 until e2. at this point, a 4x1 row will be detached from the 5x5 square.
unfold the bottom left corner. continue the straight cut from e2 to e1. now the small triangle will also be detached.
the three pieces can be arreanged to form a 6x4 rectangle.