CUTTING THE CAKE
How do you cut a rectangular cake into two equal pieces when someone has already removed a rectangular piece of any size or orientation from it? You are allowed just one straight cut.
Hint: The center will hold.
This question definitely has a right answer. The key insight is
knowing or realizing that any line passing through the center point
of a rectangle bisects the rectangle. Before you remove the rectangular
piece from the cake, there are infinitely many lines that bisect
the cake. After you remove the rectangular piece, there is only
one—the line that passes through both the center of the cake and
the center of the removed rectangular piece. This line necessarily
divides the removed piece in half, and hence the same amount of
cake was removed from each half of the remaining portion.
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