### Arsenal Collection: Half Time

from nrich.maths.org/8821

When Arsenal played Aston Villa in the 2010/11 Premier League, the final score was $4 - 2$.

What could the half time score have been?
Can you find all the possible half time scores?
How will you make sure you don't miss any out?

Later in the season Arsenal played Tottenham Hotspur.  The final score was a draw, $3 - 3$.

Can you find all the possible half time scores for this match?