Discussion
How many players are playing only one game ?
Answer: C
61 players play only one game.
Those in exactly two games are the pairwise figures minus the 3 who play all three:
\[ \begin{aligned} \text{two} &= (8-3) + (10-3) + (7-3) = 16 \\ \text{union} &= 102 - (8 + 10 + 7) + 3 = 80 \\ \text{one} &= 80 - 16 - 3 = 61 \end{aligned} \]
The union equals the 80 players, so everyone plays at least one game. 102 is the plain sum 35 + 42 + 25 without removing overlaps, 80 is everyone, and 63 does not match any count that can be formed from the figures given, such as one game (61) or two games (16).
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