  Recent large language models (LLMs) have shown indications of mathematical
reasoning ability on challenging competition-level problems, especially with
self-generated verbalizations of intermediate reasoning steps (i.e.,
chain-of-thought prompting). However, current evaluations mainly focus on the
end-to-end final answer correctness, and it is unclear whether LLMs can make
use of helpful side information such as problem-specific hints. In this paper,
we propose a challenging benchmark dataset for enabling such analyses. The
Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math
competition problems, annotated with concepts, or general math facts, and
hints, or problem-specific tricks. These annotations allow us to explore the
effects of additional information, such as relevant hints, misleading concepts,
or related problems. This benchmark is difficult, with the best model only
scoring 58.1% in standard settings. With concepts and hints, performance
sometimes improves, indicating that some models can make use of such side
information. Furthermore, we annotate model-generated solutions for their
correctness. Using this corpus, we find that models often arrive at the correct
final answer through wrong reasoning steps. In addition, we test whether models
are able to verify these solutions, and find that most models struggle.
