Solution: Let $n = 4$, so the deck has $3n = 12$ cards labeled from 1 to 12. We want the probability that the sum of 3 randomly drawn distinct cards is divisible by 3.

Fri, 17 Apr 2026 08:15:32 +0000

**How Probability Shapes Our Understanding of Chance—Even in Everyday Choices** Curious about patterns hidden in randomness? Recent discussions among math enthusiasts, educators, and digital learners reveal growing interest in probability puzzles—especially those involving fair divides and modular arithmetic. One such intriguing problem uses 12 distinct cards labeled 1 through 12. By selecting three randomly drawn cards, what’s the chance their sum is divisible by 3? This question blends everyday math with deeper insights into number theory, and it’s gaining traction across the U.S. as people explore logic behind seemingly random outcomes. The approach leverages modular arithmetic, a foundational tool in probability. When analyzing card numbers 1 to 12, each integer maps to a remainder when divided by 3: either 0, 1, or 2. With 12 cards evenly distributed—4 in each residue class—mathematical symmetry emerges. This structure offers a clean way to calculate the probability using combinatorial reasoning without explicit numbers. **Why This Problem Is Rising in Visibility**