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Answer to puzzle 77: Minimal straight cut

The length of the shortest straight cut which divides the board into two parts of equal area is root ((root 2) - 1).

The location of the cut is shown below, to scale.  Of course, by symmetry, there is an equivalent cut of equal length from BC to AC.

Isosceles right triangle with sides AB=1, BC=1, AC=square root of 2. If AX = AY = fourth root of one half, then the minimal straight cut, XY, has length square root of ((root 2) - 1)