MathDB
not hard

Source: Yugoslav 2000

July 14, 2005
combinatorics unsolvedcombinatorics

Problem Statement

Among the points corresponding to number 1,2,...,2n1,2,...,2n on the real line, nn are colored in blue and nn in red. Let a1,a2,...,ana_1,a_2,...,a_n be the blue points and b1,b2,...,bnb_1,b_2,...,b_n be the red points. Prove that the sum ∣a1−b1∣+...+∣an−bn∣\mid a_1-b_1\mid+...+\mid a_n-b_n\mid does not depend on coloring , and compute its value. :roll:
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