This paper investigates the utilization of Large Language Models (LLMs) for solving complex linguistic puzzles, a domain requiring advanced reasoning and adept translation capabilities akin to human cognitive processes. We explore specific prompting techniques designed to enhance ability of LLMs to reason and elucidate their decision-making pathways, with a focus on Input-Output Prompting (IO), Chain-of-Thought Prompting (CoT), and Solo Performance Prompting (SPP). Utilizing datasets from the Puzzling Machine Competition and various Linguistics Olympiads, we employ a comprehensive set of metrics to assess the performance of GPT-4 0603, a prominent LLM, across these prompting methods. Our findings illuminate the potential of LLMs in linguistic reasoning and complex translation tasks, highlighting their capabilities and identifying limitations in the context of linguistic puzzles. This research contributes significantly to the broader field of Natural Language Processing (NLP) by providing insights into the optimization of LLM applications for improved reasoning and translation accuracy, thereby enriching the ongoing dialogue in NLP advancements.