52nd Polish Mathematical Olympiad Problems 2001

52nd Polish Mathematical Olympiad Problems 2001A1.  Show that x1 + 2x2 + 3x3 + ... + nxn ≤ ½n(n-1) + x1 + x22 + x33 + ... + xnn for all non-negative reals xi. A2.  P is a point inside a regular tetrahedron with

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