Design and Evaluate a Solver for a 36-Card Sum-Fifteen Game

Design a solver and evaluation plan for a card-removal game. The deck contains 36 cards whose values are between 1 and 9. Each move selects three available table cards summing to 15. After a move, up to three cards are added from the remaining deck when available. Winning means consuming all 36 cards in 12 valid groups. ### Part 1 — Clarify the Game State Explain the state representation and resolve the ambiguous visibility and dealing rules. The reported table size is uncertain between 15 and 16 cards; treat it as a configurable rule. The deck is described as visible, but that must be reconciled with only table cards being selectable and later cards being drawn randomly. #### What This Part Should Cover Separate knowledge of deck contents or draw order from legal availability. Preserve card multiplicities and distinguish deck exhaustion from clearing every card. ### Part 2 — Choose a Solving Strategy Explain legal-move generation and compare a fast heuristic with search that considers future states. State what information the solver may use and whether its result is a guarantee or an empirical success rate. #### What This Part Should Cover Valid triples, duplicate values, state transitions, dead ends, search cost, and the effect of known versus hidden future draws. ### Part 3 — Evaluate on Many Games Describe how you would assess correctness, win rate, and runtime on more than 1000 games without confusing sample noise or a changed workload with an algorithmic improvement. #### What This Part Should Cover Fixed game generation and seeds, identical comparisons, valid-move checks, reporting of failures, and an explicit resource budget. ### Constraints Do not assume four copies of each value merely because 36 cards use values 1 through 9. The actual multiplicities, draw distribution, initial table size, and full-deck visibility semantics must be specified. This stochastic strategy task has no single deterministic console output under the unresolved rules. ### Clarifying Questions - Does full visibility include future draw order, only remaining values, or something else? - Is each refill a uniform sample without replacement, and what happens when fewer than three cards remain? - Can the game ever add cards when no legal move exists? - Is a deck guaranteed to be solvable, or are losing instances part of evaluation? ```hint Track a necessary total-value invariant Twelve groups summing to 15 consume a total card value of 180. That condition alone does not prove that a legal sequence of table moves exists. ``` ### What a Strong Answer Covers - An honest treatment of the uncertain rules and legal information available to the solver. - A coherent search or heuristic strategy with correct multiset transitions. - Reproducible multi-game evaluation that separates correctness, success probability, and resource cost. ### Follow-up Questions - How would a value-count state reduce duplicate move exploration? - How would you compare two heuristics when many tested decks are unwinnable under either strategy?