It's impossible for all the teams in a division to have losing records in their divisional games--every time someone loses a game, someone else in the division wins it. But the home team could win every game, and everyone would be 3-3 in divisional play. But as far as I can tell there's no reason why the teams in this unhappy division couldn't lose all ten of their other games. Is this true--is it mathematically possible for a three win team to go to the playoffs?
Naturally, this question is motivated by the fact that there's serious talk of a six win team representing the NFC South.