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every viewer in i-th row gets to know just j viewers in j-th row in cinema

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 2014 p4

February 11, 2020
combinatorics

Problem Statement

234234 viewers came to the cinema. Determine for whichn≥4 n \ge 4 the viewers could be can be arranged in nn rows so that every viewer in ii-th row gets to know just jj viewers in jj-th row for any i,j∈{1,2,...,n},i≠ji, j \in \{1, 2,... , n\}, i\ne j. (The relationship of acquaintance is mutual.)
(Tomáš Jurík)
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