Add Knights and Knaves logic problem analysis document

[VigneshHexo]

Summary

This PR adds a comprehensive educational document analyzing the Knights and Knaves logic puzzle, contrasting logical deduction with code simulation approaches. The document serves as a reference for understanding how RLMs (Reasoning Language Models) might circumvent reasoning benchmarks through computational shortcuts.

Key Changes

• New document: knights-and-knaves-rlm-simulation.md containing:
  • Complete problem statement with three inhabitants and their claims
  • Python code example showing how to brute-force solve the puzzle (the "cheating" approach)
  • Step-by-step logical deduction solution with contradiction analysis
  • Detailed comparison table between logical reasoning and code simulation
  • Discussion of implications for RLM evaluation and benchmarking

Notable Details

• The document demonstrates a concrete example of how RLMs could bypass reasoning benchmarks by writing enumeration code instead of performing logical deduction
• Includes both the computational solution (8 possible combinations checked) and the elegant logical proof
• Provides pedagogical value by showing why code simulation defeats the purpose of reasoning benchmarks
• Concludes with practical recommendations for benchmark design to prevent this circumvention

Purpose

This document is intended to inform discussions about RLM evaluation methodology and the importance of preventing computational shortcuts when testing logical reasoning capabilities.