AI Coding — Card Game (Three Cards Summing to 15)

Card game with 36 cards (4 suits × values 1-9). Starting table has 16 random cards; each round pick 3 cards summing to 15 for 15 points, then refill until no more pairs are possible. Perfect score is 12 pairs × 15 = 180. Four progressive sub-tasks: debug a draw method → naive scorer → simulate to measure quality → optimize with DP. Requirements Game mechanics (confirmed across multiple reports): Deck: 36 cards, 4 suits × values 1-9. Initial table: 16 cards randomly dealt. Round: pick any 3 distinct cards summing to 15 (e.g. three different 5s, or 9 + 3 + 2). Score 15 points per pair. After each round, refill the table until the deck is exhausted or no triple-sum-15 remains. Perfect game = 12 pairs cleared = 180 points. Sub-tasks: Q1 — Debug the draw-cards method. Unit test fails because the drawn triple isn't guaranteed to come from the cards currently on the table; the fix is often in the main flow (an if/else gate), not the unit test itself. Read the codebase carefully — interviewer hints at the failing assertion line but the bug is elsewhere. Q2 — Naive scoring strategy. Per round, draw any three cards summing to 15 (3Sum-style two-pointer or hash-set complement). Optimize per-round, not whole-game. Q3 — Measure strategy quality. Run a simulation harness over many shuffled games (commonly 100) and report perfect-game rate. Reported baseline: naive strategy ≈ 20-40% perfect games. AI typically scaffolds the simulator; you may need to tweak. Q4 — Optimize. Backtrack over all draw orderings or DP on remaining-cards state; keep the best whole-game score. Reported result after optimization: 60-90% perfect games. Interviewers may ask whether a strategy can guarantee 100% — the answer is no (counterexample: a starting table of only 4×9, 4×8, 4×7, 4×6 has no sum-15 triple). Examples One candidate reported: naive 3Sum greedy → 20/100 perfect games; DP-based optimization → 60/100. Another reports 40% → 90% with backtracking. Notes Confirmed as one of the four core AI-Coding prompts. The Q3 simulation step is the differentiator from Maze / Max-Unique — be ready to argue why simulation is a valid quality measure. One candidate's interviewer ate most of the time on Q1. Pace target: ~10 min Q1, ~10 min Q2, ~15 min Q3, ~20 min Q4. Be ready for the "is there a perfect strategy?" closing question — argue from a degenerate starting table. Preparation Practice the 3Sum LeetCode 15 / 3Sum Closest pattern until two-pointer ↔ hash-set switch is automatic. Drill backtracking over draw orderings for the Q4 optimization — define state (remaining cards), transition (pick one triple), base case (no valid triple). Pre-write a simulate-and-score harness in your head so Q3 is a 5-minute exercise: shuffle deck → loop rounds → count perfect games. Pre-script the "no guaranteed perfect strategy" closing argument.