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Square dissection (Posted on 2006-05-16) Difficulty: 3 of 5
Take a square and place two equally spaced points on each side (trisecting the sides.) Starting at one corner label the points and corners around the perimeter A, B, C, D, , L.
Connect with straight lines the pairs AI, BH, CG, DL, EK, and FJ. The resulting figure has four squares and pieces around the edge that can be rearranged to make 6 more (for a total of 10.)

How could you use a similar method to dissect a square into twenty-nine squares? How about 58? What numbers are possible by this method?

See The Solution Submitted by Jer    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Question re: Solution | Comment 2 of 4 |
(In reply to Solution by Leming)


"For 29 squares:

Divide each side into 5 segments. So the first side would have A,B,C,D,E and F. Then F,G,H,I,J and K make the second side. K,L,M,N,O and P for the third, and P,Q,R,S,T and A for the fourth.

Connect AN, BM and similar parallel lines. Connect FS, GR, and their parrellel lines.  Each point should have a parallel line drawn from it.  

Line AN will be sqrt(5^2 + 2^2) = sqrt(29) long. Each square will be sqrt(25/29) units long, creating 29 squares of area 25/29."

... are you saying for example, to make a line from O parallel to NA, so as to intersect a side midway between R and S? ... and from T parallel to SF to midway between C and D?

  Posted by Charlie on 2006-05-16 10:25:22
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