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 Union of squares (Posted on 2014-07-09)
For what number of non-overlapping unit squares can a figure be formed whose perimeter is numerically equal to the area?

 No Solution Yet Submitted by Jer Rating: 3.0000 (1 votes)

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 set of numbers | Comment 9 of 10 |

Adding one square offset by 1/2 unit adds 1 unit area and 3 units perimeter so it subtracts 2 units from the quantity (A-P).
Adding on a unit square like this to a 4x5 rectangle makes A=P=21; and doing so to a 3x8 rectangle makes A=P=25.
Also, adding any number of 2x1 rectangles so that the side of length 2 is fully touching the wall of any existing structure (with length 1 sides not touching) adds 2 to both A and P.
I haven't ruled out smaller odd structures, but so far the allowable number of non-overlapping unit squares is:

16, 18, and all integers even and odd greater than or equal to 20

 Posted by Larry on 2014-07-10 10:57:00

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