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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)

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Solution What numbers are possible? Comment 4 of 4 |

The last question asks: What numbers are possible by this method?

One can divide a square into smaller portions based on n^2 + m^2 (n > 0 and n>=m>0)
"n" is the number of segments that each side is divided into and   (-n/m) and (m/n) are the slopes of the lines going through the square.

These are some of the possible combinations, with the total squares that could be made:

n   m   tot
1   1    2
2   1    5
2   2    8
3   1    10
3   2    13
3   3    18
4   1    17
4   2    20
4   3    25
4   4    32
5   1    26
5   2    29
5   3    34
5   4    41
5   5    50
.
.
7   3    58
.
.
100 5 10025
.
.

Edited on May 16, 2006, 12:35 pm
  Posted by Leming on 2006-05-16 12:34:33

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