QUIZ 2. 4 Plane Dividers
Suppose you have an infinitely large plane. If you draw \(3\) lines here, then the maximum amount of area you can create is \(7\), as drawn below.
Caption
The white lines are \(3\) lines you draw on the plane, and black areas are separated parts of the plane. There is no way to separate more than \(7\) areas with \(3\) lines.
Now you have an infinitely large \(3\)-dimensional cube. How many areas you can separate with \(4\) infinitely large planes? Maximize it, and explain why.
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