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ASU 151 All Soviet Union MO 1971 (a-d)(b-c)<0 for some numbers in ring

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July 3, 2019
combinatoricsalgebra

Problem Statement

Some numbers are written along the ring. If inequality (a−d)(b−c)<0(a-d)(b-c) < 0 is held for the four arbitrary numbers in sequence a,b,c,da,b,c,d, you have to change the numbers bb and cc places. Prove that you will have to do this operation finite number of times.
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