Card suits and counts puzzle: 13 cards (7 black, 6 red) with suit ratios – find the number of clubs
-
A4
-
B5
-
C6
-
D7
Answer
Correct Answer: 6
Explanation
Introduction / Context:This is a suit-distribution puzzle on a 13-card hand. You are given totals by color and proportional relations among suits. Translate the relationships into equations and solve for the unknown suit count (clubs).
Given Data / Assumptions:
- Total cards = 13; blacks = 7; reds = 6.
- Let spades = s (black), clubs = c (black), diamonds = d (red), hearts = h (red).
- Twice as many diamonds as spades: d = 2s.
- Twice as many hearts as diamonds: h = 2d = 4s.
Concept / Approach:Use color totals and the ratio constraints to determine s, then compute c from the total. Keep black vs. red counts consistent with the given 7 and 6.
Step-by-Step Solution:
Total = s + c + d + h = s + c + 2s + 4s = 7s + c = 13.Red total = d + h = 2s + 4s = 6s = 6 ⇒ s = 1.Then 7s + c = 13 ⇒ 7*1 + c = 13 ⇒ c = 6.Thus clubs = 6.Verification / Alternative check:Check color totals: black = s + c = 1 + 6 = 7; red = d + h = 2 + 4 = 6; total = 13. All conditions satisfied.
Why Other Options Are Wrong:
- 4, 5, 7: These break either the color totals or the 2x and 4x suit-ratio constraints.
Common Pitfalls:Forgetting reds sum to 6, or mixing up which suits are black (spades, clubs) and which are red (diamonds, hearts).
Final Answer:6