Denote the three games as X, Y, Z.
Consider 8 regions as follows in terms of the number of players:
A Players of X only
B Players of Y only
C Players of Z only
D Players of X and Y
E Players of X and Z
F Players of Y and Z
G Players of all three games
H Observers only (to be found)
From the given facts:
G=17
A+B+C+D+E+F+G+H=50
A+D+E+G played X
B+D+F+G played Y
C+E+F+G played Z
50-37=13 were observers or played only one game: A+B+C+H=13
24.25/0.25=97 games played: (A+D+E+G)+(B+D+F+G)+(C+E+F+G)=97,
A+B+C+2(D+E+F)+3G=97,
13-H+2(D+E+F)+51=97,
2(D+E+F)-H=33, D+E+F=(H+33)/2
A+B+C+D+E+F+G+H=50=13-H+(H+33)/2+17+H,
(H+33)/2=20,
H+33=40, H=7.
So 7 students watched and didn't play.