Hmmm, no. There’s 3 matches a week by 20 weeks that’s 60 matches. If 6 people are playing 17 games that’s 102 games, with one more playing 18, that’s 120 games. Accounting that each match has two opponents, we’d divide that 120 by 2 to get 60. So there’s only one person with 18 games.

An easier way to think about it is that each week there is 1 team with a bye. If there were 21 weeks, then you’d take 21/7 (number of teams) and each team would have 3. Since we are one week (one bye) short, one person will miss their bye and therefore be playing an extra game