Knights of the Round Table , 34 chairs
Source: Flanders Math Olympiad 2019 p4
December 24, 2022
combinatorics
Problem Statement
The Knights of the Round Table are gathering. Around the table are chairs, numbered from 1 to . When everyone has sat down, it turns out that between every two knights there is a maximum of places, which can be either empty or occupied by another knight.
(a) For each , determine the maximum number of knights present.
(b) Determine for each how many sets of occupied seats there are that match meet the given and where the maximum number of knights is present.