Large Language Models (LLMs) have demonstrated impressive performance on many Natural Language Processing (NLP) tasks. However, their ability to solve more creative, lateral thinking puzzles remains relatively unexplored. In this work, we develop methods to enhance the lateral thinking and puzzle-solving capabilities of LLMs. We curate a dataset of word-type and sentence-type brain teasers requiring creative problem-solving abilities beyond commonsense reasoning. We first evaluate the zero-shot performance of models like GPT-3.5 and GPT-4 on this dataset. To improve their puzzle-solving skills, we employ prompting techniques like providing reasoning clues and chaining multiple examples to demonstrate the desired thinking process. We also fine-tune the state-of-the-art Mixtral 7x8b LLM on ourdataset. Our methods enable the models to achieve strong results, securing 2nd and 3rd places in the brain teaser task. Our work highlights the potential of LLMs in acquiring complex reasoning abilities with the appropriate training. The efficacy of our approaches opens up new research avenues into advancing lateral thinking and creative problem-solving with AI systems.