  The performance of Large Language Models (LLMs) in reasoning tasks depends
heavily on prompt design, with Chain-of-Thought (CoT) and self-consistency
being critical methods that enhance this ability. However, these methods do not
fully exploit the answers generated by the LLM to guide subsequent responses.
This paper proposes a new prompting method, named Progressive-Hint Prompting
(PHP), that enables automatic multiple interactions between users and LLMs by
using previously generated answers as hints to progressively guide toward the
correct answers. PHP is orthogonal to CoT and self-consistency, making it easy
to combine with state-of-the-art techniques to further improve performance. We
conducted extensive and comprehensive experiments on seven benchmarks. The
results show that PHP significantly improves accuracy while remaining highly
efficient. For instance, with text-davinci-003, we observed a 4.2% improvement
on GSM8K with greedy decoding compared to Complex CoT, and a 46.17% reduction
in sample paths with self-consistency. With GPT-4 and PHP, we achieve
state-of-the-art performances on SVAMP (89.1% -> 91.9%), GSM8K (92% -> 95.5%),
AQuA (76.4% -> 79.9%) and MATH (50.3% -> 53.9%).
