MathDB

4

Part of 2019 Flanders Math Olympiad

Problems(1)

Knights of the Round Table , 34 chairs

Source: Flanders Math Olympiad 2019 p4

12/24/2022
The Knights of the Round Table are gathering. Around the table are 3434 chairs, numbered from 1 to 3434. When everyone has sat down, it turns out that between every two knights there is a maximum of rr places, which can be either empty or occupied by another knight. (a) For each r≤15r \le 15, determine the maximum number of knights present. (b) Determine for each r≤15r \le 15 how many sets of occupied seats there are that match meet the given and where the maximum number of knights is present.
combinatorics