Card suits and counts puzzle: 13 cards (7 black, 6 red) with suit ratios – find the number of clubs

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:

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