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1971 IMO Problems/Problem 2

Revision as of 13:59, 17 February 2018 by Durianaops (talk | contribs) (Created page with "==Problem== Consider a convex polyhedron <math>P_1</math> with nine vertices <math>A_1, A_2, \cdots, A_9;</math> let <math>P_i</math> be the polyhedron obtained from <math>P_1...")
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Problem

Consider a convex polyhedron $P_1$ with nine vertices $A_1, A_2, \cdots, A_9;$ let $P_i$ be the polyhedron obtained from $P_1$ by a translation that moves vertex $A_1$ to $A_i(i=2,3,\cdots, 9).$ Prove that at least two of the polyhedra $P_1, P_2,\cdots, P_9$ have an interior point in common.

Solution

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See Also

1971 IMO (Problems) • Resources
Preceded by
Problem 1 		1 • 2 • 3 • 4 • 5 • 6 Followed by
Problem 3
All IMO Problems and Solutions
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