We can find the number of games played. We are looking for the number of ways to form unique pairs out of 5 people.
Order does not matter.
nCr=(n−r)!r!n!
5C2=(5−2)!2!5!
5C2=3!2!5!
=3⋅2⋅25⋅4⋅3⋅2
=10
Norah must have won:
10−2−1−1−3=3
We can figure out the total number of games through inspection.
Starting at Collier, Collier must have played 4 games to play with everyone else.
Evangeline will play 4 games with everyone else, but 1 will be a duplicate with Collier, so we have 4+3 games.
Gabe plays 4 games, but 2 have already been mentioned, so the total games is 4+3+2.
Continuing the pattern...
Games played=4+3+2+1=10
Each game had a winner, so there are 10 games won.
2+1+1+?+3=10
?=3