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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?

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Solution Solution | Comment 3 of 10 |
16 + 2N.

The only rectangles are 4x4 and 6x3, though there can be other shapes too.
But one can add a 2x1 rectangle to the side of an existing structure and add 2 units of area and 2 units of perimeter.  This is also true for adding a 2xN rectangle to the structure.  Example, start with a 4x4 square and add 2x? rectangles to its right side:

****             ****               ****
****    --->   *****    --->   *********
****             *****             *********
****             ****               ****

Edited on July 9, 2014, 12:30 pm
  Posted by Larry on 2014-07-09 12:13:48

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