MathSticks: A Benchmark for Visual Symbolic Compositional Reasoning with Matchstick Puzzles

We introduce \textsc{MathSticks}, a benchmark for Visual Symbolic Compositional Reasoning (VSCR), which unifies visual perception, symbolic manipulation, and arithmetic consistency. Each task presents an incorrect matchstick equation that must be corrected by moving one or two sticks under strict conservation rules. The benchmark includes both text-guided and purely visual settings, systematically covering digit scale, move complexity, solution multiplicity, and operator variation, with a full dataset of 1.4M generated instances. For standardized evaluation, we release a balanced 400-item benchmark set. Evaluations of 14 vision–language models reveal substantial limitations: closed-source models succeed only on simple cases, open-source models fail in the visual regime, while humans exceed 90\% accuracy. These findings establish \textsc{MathSticks} as a rigorous testbed for advancing compositional reasoning across vision and symbols. Our code and dataset are publicly available at \url{https://github.com/Yuheng2000/MathSticks}.