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• 15:55, 14 May 2024 Gispzjz talk contribs created page 组合数学 (Spring 2024)/Problem Set 3 (Created page with "== Problem 1 == Solve the following two existence problems: * You are given <math>n</math> integers <math>a_1,a_2,\dots,a_n</math>, such that for each <math> 1\leq i\leq n</math> it holds that <math>i-n\leq a_i\leq i-1</math>. Show that there exists a '''nonempty''' subsequence (not necessarily consecutive) of these integers, whose sum is equal to <math> 0 </math>. (Hint: Consider <math> b_i=a_i-i </math>) * You are given two '''multisets''' <math> A </math> and <ma...")