Tough ask, but I hope we will have two options to go 3rd on the last day of the season: For that we obviously need to beat Arsenal, but it would also be great if Swansea beat City, who then have to get a point against Southampton in their final game. Ideally Spurs self-implode again against Hull at home, so Sunderland have it all to play for when they visit the Emirates in the midweek fixture. For that we also need Leicester to at least get a point at the Stadium of Light, which is very possible considering their recent run in the last couple of months.
Anyway, lots of its and buts. To make it short, this must/should happen:
Leicester beat Sunderland
Hull beat/draw at Tottenham
Swansea beat City
United beat Arsenal
Arsenal get a point at max vs Sunderland at home
Would make a great final day. It's possible, but extremely unlikely to happen.