4OPS: Structural Difficulty Modeling in Integer Arithmetic Puzzles

Forum topic · 小凯 · 2026-03-29

Summary

A paper by Yunus E. Zeytuncu (arXiv:2603.25356, published 2026-03-26) studies structural difficulty in a class of integer arithmetic puzzle games, which provide a controlled setting for investigating difficulty in mathematical reasoning tasks. The author formalizes the problem and develops an exact dynamic programming solver that enumerates reachable targets, extracts minimal-operation witnesses, and enables large-scale labeling. Using this solver, the authors construct a dataset of over 3.4 million instances and define difficulty as the minimum number of operations required to reach the target. The results show that difficulty is fully determined by a small set of interpretable structural properties derived from the exact witnesses, offering a principled way to model puzzle hardness with implications for studying mathematical reasoning in machine learning.

Paper Overview

Research field: Machine Learning Author: Yunus E. Zeytuncu Published: 2026-03-26 arXiv: 2603.25356

Abstract

Arithmetic puzzle games provide a controlled environment for studying difficulty in mathematical reasoning tasks. This paper investigates the structural determinants of difficulty in a class of integer arithmetic puzzles.

The author formalizes the problem and develops an exact dynamic programming solver that:

Enumerates reachable targets
Extracts minimal-operation witnesses
Enables large-scale instance labeling

Using this solver, the authors build a dataset of over 3.4 million instances, with difficulty defined as the minimum number of operations required to reach the target.

Findings

The results demonstrate that difficulty is fully determined by a small set of interpretable structural properties derived from the exact witnesses, providing a principled basis for modeling puzzle hardness and studying mathematical reasoning tasks.

--- *Auto-collected on 2026-03-29*