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@neuronet I enjoy these sorts of math/logic puzzles too (and have actually had this conversation in this forum before so I am going to borrow from my own posts). Here is why it has to be the way it is:
We know 6 games are against the division and 4 against the NFC, so let's throw those out. We also rotate through the other 3 AFC divisions every 3 years. For example, in 2017 we play the AFCW (home against KC and SD, on the road against Oak and Den). We will play the AFCW again in 2020, reversing the home team of 2017 (so in 2020 we are home against Oak and Dev, on the road against KC and SD).
So the trick is how do you schedule the 2 "positional" games every year? (By "positional game" I mean the game where the Patriots play 1 team from another AFC division who finished in the same position the previous year).
Here are the position games for the AFC East for 6 years. The challenge is to construct them in such a way that you do not have 2 consecutive home or 2 consecutive away games with one division.
2014: North, South
2015: North, West
2016: South, West
2017: North, South
2018: North, West
2019: South, West
So let's say we set it like this:
2014: North Home, South Away
2015: West Home, North Away
2016: South Home, West Away
2017: North Home, South Away
2018: West Home, North Away
2019: South Home, West Away
Here are the positional games for the AFC North:
2014: East, West
2015: East, South
2016: West, South
2017: East, West
2018: East, South
2019: West, South
Here's the impossible part: Construct those in such a way so that you do not have 2 consecutive home or 2 consecutive away games against one division AND it stays compatible with the schedule we already set up for the AFC East AND (needless to say) you have maintain the integrity of every team have 8 home games and 8 road games.
Thanks a lot. Literally the first post at patsfans I needed to print out and study and diagram to understand.