Could Man City and Liverpool stop Man United or Arsenal qualifying for the Champions League?

It's a puzzle doing the rounds, with the real possibility increasing by the game.

Manchester City face Real Madrid in the semi-finals of the Champions League, whilst Liverpool have been drawn with Villarreal in the final four of the Europa League. But what if one or both of the Premier League sides overcome their Spanish foes and go on to win their respective European trophies? With UEFA promising qualification into next season's Champions League for the victors of both of this year's competitions, how will it affect the fourth placed team in the Premier League? Let us do our best to provide the answers. First some basic facts:

• The winners of the Champions League will go into the group stages of next season's Champions League;
• The winners of the Europa League will go into the play-off stage (at least) of next season's Champions League;
• If the winners of the Champions League have already qualified for next season's group stages via their league position, the winners of the Europa League will go straight into the group stages too.

But let us imagine a scenario in which Man City finish fifth or below in the Premier League, and along with Liverpool fail to break into the top four Champions League qualifying positions. Will the fourth place team's Champions League qualification for next season be affected by City and/or Liverpool winning a European trophy this season? The short answer is: Yes, very possibly. The key thing to note here is that UEFA only allow a maximum of five clubs in the Champions League per country. So here are a few scenarios explained: Man City finish outside the top four and win the Champions League: Positions 1, 2, 3 and Man City qualify for the Champions League group stages; the fourth placed side go into the Champions League play-off stage. Man City finish outside the top four and Liverpool win the Europa League: Positions 1, 2 and 3 qualify for the Champions League group stages; the fourth placed side and Liverpool go into the Champions League play-off stage. Man City finish third and Liverpool win the Europa League: Positions 1, 2 and 3 (City) and Liverpool qualify for the Champions League group stage; the fourth placed side go into the Champions League play-off stage. Man City finish fourth and Liverpool win the Europa League: Positions 1, 2 and 3 qualify for the Champions League group stage; the fourth placed side (City) and Liverpool go into the Champions League play-off stage. Man City finish outside the top four but win the Champions League, as well as Liverpool winning the Europa League: Positions 1, 2, 3 and Man City qualify for the Champions League group stage; Liverpool go into the Champions League play-off stage. The fourth-placed side enter the Europa League. So as you can see, a nightmare scenario for the likes of Arsenal or Man United is that they finish ahead of City in fourth, but both City and Liverpool win their respective European trophies, thus robbing them of a Champions League place.