Structural Analysis of Competition Problem Sets and Benchmark Datasets — E8 Intelligence Research

Q: What does this research mean for the field?

The analyzed corpus consists of competition-problem showcases and the MATH benchmark dataset rather than a single unified mathematical discovery, with its deepest structural content found in the 2011 IMO windmill problem and the combinatorial and geometric breadth of the MATH dataset. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22244945

September 2, 2026Open Access

Structural Analysis of Competition Problem Sets and Benchmark Datasets — E8 Intelligence Research

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Key Points

To analyze the underlying mathematical structures, invariants, and combinatorial properties embedded within competition problem showcases and the MATH benchmark dataset.
Evaluated structural invariants within competition problems, focusing on the 2011 International Mathematical Olympiad (IMO) windmill problem and the 100 Prisoners riddle.
Characterized the scope and distribution of the MATH benchmark dataset across 12,500 problems spanning seven core mathematical domains.
Demonstrated that the windmill problem exhibits finite distinct configurations that cycle periodically, governed by invariant pivot transitions across 180-degree rotations.
Determined that the optimal strategy for the 100 Prisoners problem relies on permutation cycle structures, yielding an exact success rate of ~31.18% for n=100 (asymptotically 1 - ln 2 ≈ 0.30685).

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Implication

Mathematical analysis reveals invariant geometric and permutation cycles across competition problem sets and benchmark datasets, indicating distinct structural foundations in combinatorial reasoning.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9a860d5d9e33f25c63190a https://doi.org/10.5281/zenodo.22244945

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Structural Analysis of Competition Problem Sets and Benchmark Datasets — E8 Intelligence Research

Key Points

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Cite This Study

Structural Analysis of Competition Problem Sets and Benchmark Datasets — E8 Intelligence Research

Key Points

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Implication

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Cite This Study

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