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CustomCC0-1.0#cp-tp3-0072100

Endless Game: Minimum Score to Lose

Thinking Mode

Summary

  • •Phase 3 / game-theory
  • •Reasoning-first competitive programming drill

Problem Description

You are playing a single-player game: on each move, you can subtract any power of 2 (up to the current value) from your current score. Given a starting score x, what is the minimum number of moves to reduce the score to zero such that on every move, the result is not divisible by 3? If impossible, output -1. How to read this problem in plain language: - This is a Phase 3 reasoning drill focused on game-theory. - Typical lenses to test first: game-theory, bitmask, number-theory. - Constraints reminder: 1 ≤ x≤1e18 Mini examples for mental simulation: 1) Boundary example: Describe why this case is tricky. Explain expected behavior and why naive logic may fail. 2) Adversarial example: Adversarial case where naive greedy/local decision looks correct but fails globally. Lite-mode writing target: - Write 1~2 observations that shrink the search space. - Name one final algorithm and state target complexity explicitly. - Validate with at least 2 edge cases and one hand simulation.

Constraints

  • •
    1 ≤ x≤1e18

Analysis

Key Insight

Use this hint to refine your reasoning. This step should reduce search space or formalize correctness. State why this insight changes your algorithm choice.

game-theorybitmasknumber-theory
game-theorybitmasknumber-theory