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You can divide the long diagonal of a square into different fractions by folding.
This problem is about the fractions of the long diagonal of a square which you can construct in this way.
To start with, we shall only consider points on the side of the square which can easily be found by folding. That is, $\frac{1}{2}$s or $\frac{1}{4}$s or $\frac{1}{8}$s and so on.
