Large language models show promising performance on reasoning tasks, yet evaluation methods for low-resource languages remain limited, particularly for complex STEM problem-solving. We introduce Trojsten Benchmark, a Slovak-language dataset of 1,108 high-school competition problems with reference solutions across mathematics, physics, and programming, and a rubric-based LLM grading framework. Using GPT-4 to generate rubrics and grade solutions, we observe 1.05 average absolute deviation from human graders (5-point scale), while benchmarking GPT-3.5-Turbo, GPT-4, GPT-4o, and open-weight models (Llama 3, Phi-3). We quantify multistep reasoning performance by difficulty, show consistent underperformance on harder items, and demonstrate language sensitivity: accuracy drops on English translations of Slovak statements, evidencing challenges beyond translation. Trojsten Benchmark complements English-centric math datasets (e.g., MATH, GSM8K) by targeting open-response, rubric-gradable reasoning under low-resource linguistic framing. We release code and data to enable reproducible evaluation and human-aligned auto-grading for STEM in under-served languages.