MathDB

6

Part of 1983 Federal Competition For Advanced Students, P2

Problems(1)

cube

Source: Austria 1983

7/7/2009
Planes π1 \pi _1 and π2 \pi _2 in Euclidean space R3 \mathbb{R} ^3 partition S\equal{}\mathbb{R} ^3 \setminus (\pi _1 \cup \pi _2) into several components. Show that for any cube in R3 \mathbb{R} ^3, at least one of the components of S S meets at least three faces of the cube.
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