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f :P -> P, ABCD convex , f(A),f(B),f(C),f (D) vertices of concave

Source: Mathcenter Contest / Oly - Thai Forum 2010 (R1) p4 https://artofproblemsolving.com/community/c3196914_mathcenter_contes

November 15, 2022
geometryfunctionalconvex

Problem Statement

Let PP be a plane. Prove that there is no function f:Pā†’Pf :P\rightarrow P where, for any convex quadrilateral ABCDABCD, the points f(A)f(A), f(B)f(B), f(C)f(C), f(D)f (D) are the vertices of a concave quadrilateral.
(tatari/nightmare)
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