CZ-SK-MO 2014 Problem 4

$234$ viewers came to the cinema. Determine for which $n \ge 4$ the viewers could be can be arranged in $n$ rows so that every viewer in $i$ -th row gets to know just $j$ viewers in $j$ -th row for any $i, j \in \{1, 2,... , n\}, i\ne j$ . (The relationship of acquaintance is mutual.)

(Tomáš Jurík)