Optimal Three-Question Solution to Boolos' Hardest Logic Puzzle — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-14
DOI
https://doi.org/10.5281/zenodo.22741951
Primary Topic
Computability, Logic, AI Algorithms
Type
preprint
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preprint

Optimal Three-Question Solution to Boolos' Hardest Logic Puzzle — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
preprint

Optimal Three-Question Solution to Boolos' Hardest Logic Puzzle — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Boolos' "Hardest Logic Puzzle Ever" is solvable in exactly three admissible questions, with a rigorous axiomatic proof framework; the puzzle's structure encodes a ternary decision tree requiring information-theoretic optimality. | MATH: The puzzle reduces to identifying three gods (True, False, Random) with binary answers (yes/no) but a liar/truthteller ambiguity. Information-theoretic lower bound: 3 gods × 2 states (identity) = 6 possibilities, requiring ⌈log₂(6)⌉ = 3 bits. However, the liar/truthteller inversion and Random's unpredictability force a **ternary logic** — each question yields 3 outcomes (yes, no, or Random's chaotic response), so the decision tree has 3³ = 27 leaves, sufficient for 6 identities. The key theorem (arXiv:1804.05677v3) proves exactly 3 admissible questions are necessary and sufficient, with admissibility defined by Boolos' constraints (gods always answer, but Random's answers are unconstrained). The solution exploits **self-referential question enc Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
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Computability, Logic, AI Algorithms
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Optimal Three-Question Solution to Boolos' Hardest Logic Puzzle — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS