Billiards handicap translation: In a 120-point game, A can give B 20 points and C 30 points. In a 90-point game, how many points can B give C?

Introduction / Context:
Convert the given handicaps to speed ratios and then apply to the new total. This preserves relative strengths across game lengths.

Given Data / Assumptions:
A vs B: 120 vs 100 → 6:5. A vs C: 120 vs 90 → 4:3. Uniform rates.

Concept / Approach:
B : C = (A : C) / (A : B) = (4/3) / (6/5) = 10/9. B is faster than C in the ratio 10:9.

Step-by-Step Solution:

Verification / Alternative check:
Alternatively, at C = 90, B = 100, which implies a 10-point edge in C's frame; translating to B's 90-point frame yields 9 as above.

Why Other Options Are Wrong:
18/6/3 do not align with the 10:9 ratio at 90 total.

Common Pitfalls:
Using differences directly; always use ratios across different totals.

Final Answer:
9 points