MathDB

7

Part of 2001 Korea Junior Math Olympiad

Problems(1)

2001 KJMO P7 (arrangement difference sum = n^2)

Source: 2001 KJMO P7

6/29/2024
Finite set {a1,a2,...,an,b1,b2,...,bn}={1,2,…,2n}\{a_1, a_2, ..., a_n, b_1, b_2, ..., b_n\}=\{1, 2, …, 2n\} is given. If a1<a2<...<ana_1<a_2<...<a_n and b1>b2>...>bnb_1>b_2>...>b_n, show that ∑i=1n∣ai−bi∣=n2\sum_{i=1}^n |a_i-b_i|=n^2
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