Billiards handicaps transitivity: A gives B 6 in 50 and A gives C 13 in 65. In a game of 55, how many points can B give C?

Introduction / Context:
We use proportional scoring in equal time. From A:B and A:C ratios we infer B:C and then scale to a 55-point game.

Given Data / Assumptions:

• A gives B 6 in 50 ⇒ (A:B) = 50:44 = 25:22
• A gives C 13 in 65 ⇒ (A:C) = 65:52 = 5:4
• Game size in query = 55 points

Concept / Approach:
Compute B:C = (A:C)/(A:B). Then, when B scores 55, compute C’s score and find the points B can give C.

Step-by-Step Solution:

Verification / Alternative check:
Scaling either ratio to a common A-score yields the same B:C relation of 11:10.

Why Other Options Are Wrong:
They contradict the deduced B:C = 11:10.

Common Pitfalls:
Subtracting handicaps instead of converting them into proportional scoring rates.

Final Answer:
5