In a game, A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?

Suppose, P points make the game.
Clearly, when A scores P points, B scores (P - 20) points and C scores (P - 32) points.
Now, when B scores P points, C scores (P - 15) points.
When B scores (P - 20) points,
C scores [( P - 15 ) / P * P (P - 20)] points
∴ (P - 15)( P - 20) / P = P - 20 or, P = 100
Hence, 100 points make the game.