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Maximize score in 15-sum card game | Meta Coding Question

Quick Overview

This question evaluates algorithmic problem-solving in combinatorial search, state-space optimization, and memoization by asking for the maximum achievable score in a constrained card-removal game; it falls under the Coding & Algorithms domain, specifically combinatorics, search, and dynamic programming.

Maximize score in 15-sum card game

Company: Meta

Role: Software Engineer

Category: Coding & Algorithms

Difficulty: medium

Interview Round: Onsite

## Problem A deck has **36 cards**: 4 suits × ranks 1 through 9 (so there are exactly four `1`s, four `2`s, …, four `9`s). Suits do not affect scoring; only ranks matter. A game proceeds as follows: 1. The deck is shuffled into a fixed order. The first **16 cards** are dealt face-up onto the table (the “board”). The remaining cards stay in the draw pile. 2. While possible, you may repeatedly: - Choose **three cards currently on the board** whose ranks sum to **15**. - Remove those three cards and gain **15 points**. - Draw cards from the draw pile to restore the board back to **16 cards** (draw exactly 3 if available; otherwise draw as many as remain). 3. The game ends when either: - The draw pile is empty and no further 15-sum triple exists on the board, or - No 15-sum triple exists on the board (even if cards remain in the pile, you cannot draw unless you remove a triple). The theoretical maximum score is `180` (12 triples × 15 points) because there are 36 cards. ### Task Given the full shuffled deck order, compute the **maximum total score** achievable by choosing triples optimally. ### Input - A list `deck` of length 36. Each element is an integer rank in `[1..9]`. - The multiset of ranks in `deck` satisfies: each rank 1..9 appears exactly 4 times. ### Output - An integer: the maximum score achievable. ### Examples (illustrative) - If the initial 16-card board contains no triple summing to 15, output is `0`. - If an optimal play can remove 12 triples, output is `180`. ### Follow-ups (if time) 1. Implement a baseline greedy strategy (e.g., pick any available 15-sum triple). 2. Write a test that runs the game for 100 random shuffles and reports how often the strategy achieves 180. ### Constraints - Deck size is fixed (36), but the branching factor can be high; design an approach that avoids exponential blow-ups where possible (e.g., memoization).

Quick Answer: This question evaluates algorithmic problem-solving in combinatorial search, state-space optimization, and memoization by asking for the maximum achievable score in a constrained card-removal game; it falls under the Coding & Algorithms domain, specifically combinatorics, search, and dynamic programming.

A deck has card values. Deal 16 cards, then repeatedly remove triples summing to 15 or draw the next card. Return the maximum number of triples removable.

Constraints

Inputs are provided as Python literals compatible with the function signature.
Return a deterministic value exactly matching the requested output.

Examples

Input: ([1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9],)

Expected Output: 12

Explanation: Sorted valid deck.

Input: ([1, 5, 9, 2, 4, 9, 3, 5, 7, 6, 7, 2, 8, 1, 6, 3, 4, 8, 9, 5, 1, 7, 2, 6, 3, 8, 4, 9, 5, 1, 7, 2, 6, 3, 8, 4],)

Expected Output: 12

Explanation: Shuffled valid deck.

Hints

Start with a direct data structure representation.
Handle edge cases before the main loop.

Quick Overview