MathDB

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Part of 2020 South East Mathematical Olympiad

Problems(2)

2019 CSMO Grade 11 Problem 1

Source: 2019 CSMO Grade 11 Problem 1

8/10/2020
Let a1,a2,…,a17a_1,a_2,\dots, a_{17} be a permutation of 1,2,…,171,2,\dots, 17 such that (a1−a2)(a2−a3)…(a17−a1)=2n(a_1-a_2)(a_2-a_3)\dots(a_{17}-a_1)=2^n . Find the maximum possible value of positive integer nn .
maximum valuecombinatorics
China South East Mathematical Olympiad 2020 Grade10 Q1

Source: China Zhuji

8/5/2020
Let f(x)=a(3a+2c)x2−2b(2a+c)x+b2+(c+a)2f(x)=a(3a+2c)x^2-2b(2a+c)x+b^2+(c+a)^2 (a,b,c∈R,a(3a+2c)≠0).(a,b,c\in R, a(3a+2c)\neq 0). If f(x)≤1f(x)\leq 1for any real xx, find the maximum of ∣ab∣.|ab|.
inequalitiesChinaalgebra