CZ-SK-MO 2018 Problem 1

In a group of people, there are some mutually friendly pairs. For positive integer $k\ge3$ we say the group is $k$ -great, if every (unordered) $k$ -tuple of people from the group can be seated around a round table it the way that all pairs of neighbors are mutually friendly. (Since this was the 67th year of CZE/SVK MO,) show that if the group is 6-great, then it is 7-great as well.Bonus (not included in the competition): Determine all positive integers $k\ge3$ for which, if the group is $k$ -great, then it is $(k+1)$ -great as well.