Imagine a piece of plywood with an array of evenly spaced nails forming small squares and consider that each square has side lengths of 1 unit. A simple closed shape is formed with a rubber band. If you knew the number of nails used in the perimeter and the perimeter itself, how could you predict how many squares can be counted inside this rubber band shape?

for example say the rubber band shape is outlining these nails:

* - * - * - * - *

| /

* * * *

| /

* - * - *

Perimeter = 8 + 2*sqrt(2)

Nails = 12

Squares: 6 squares (5 - 1x1 and 1 - 2x2) --- the result of 6, at a minimum, is what we are trying to predict.

Imagine a piece of plywood with an array of evenly spaced nails forming small squares and consider that each square has side lengths of 1 unit. A simple closed shape is formed with a rubber band. If you knew the number of nails used in the perimeter and the perimeter itself, how could you predict how many squares can be counted inside this rubber band shape?

for example say the rubber band shape is outlining these nails:

* - * - * - * - *

| /

* * * *

| /

* - * - *

Perimeter = 8 + 2*sqrt(2)

Nails = 12

Squares: 6 squares (5 - 1x1 and 1 - 2x2) --- the result of 6, at a minimum, is what we are trying to predict.

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