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2016 CNMO Grade 10 P8

Source: 2016 China Northern MO, Grade 10, Problem 8

February 25, 2020
combinatorics

Problem Statement

Set A={1,2,⋯ ,n}A=\{1,2,\cdots,n\}. If there exists nonempty sets B,CB,C, such that B∩C=∅,B∪C=AB\cap C=\varnothing,B\cup C=A. Sum of Squares of all elements in BB is MM, Sum of Squares of all elements in CC is NN, M−N=2016M-N=2016. Find the minimum value of nn.
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