P = A
The figure is comprised of 29 unit squares and has a perimeter of 29. That means its area and perimeter are numerically equal.
However, not every number can work like this as the same numerical value for the area and perimeter of a collection of non-overlapping unit squares.
Find the sum of all such numbers that don't work.
The answer is 137.
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1 solution
A small number of squares will not work as the perimeter is too large.
16 is the smallest possible as a 4x4 array. You can then increase by 2's by adding pairs to one side as shown.
19 is the smallest odd number possible as in the right-hand picture. Again, you can increase it by 2's.
This leaves 1 through 15 and 17 as impossible. They sum to 137.