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Union of squares (Posted on 2014-07-09) Difficulty: 3 of 5
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    
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Solution re: Partial solution - another part | Comment 4 of 10 |
(In reply to Partial solution by tomarken)

Right after posting I realized that an odd number can't be possible.  Consider a single unit square.  Its perimeter is 4.  If we append another square, we are adding 4 sides to the total perimeter, minus 2x however many sides it's touching.  This will always be the case, so the perimeter of the resulting shape will always be even, and thus the area must also be even.  So we can never make a shape satisfying the conditions of the puzzle with an odd number of unit squares.

  Posted by tomarken on 2014-07-09 12:15:47

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