Evaluating large language models (LLMs) on their linguistic reasoning capabilities is an important task to understand the gaps in their skills that may surface during large-scale adoption. In this work, we investigate the abilities of such models to perform abstract multilingual reasoning through the lens of linguistic puzzles on extremely low-resource languages. As these translation tasks involve inductive and deductive reasoning from reference instances, we examine whether diverse auxiliary demonstrations can be automatically induced from seed exemplars, through analogical prompting. We employ a two-stage procedure, first generating analogical exemplars with a language model, and then applying them in-context along with provided target language exemplars. Our results on the modeLing dataset show that analogical prompting is effective in eliciting models’ knowledge of language grammar similarities, boosting the performance of GPT-4o by as much as 8.1% and Llama-3.1-405B-Instruct by 5.9% over chain-of-thought approaches. Furthermore, we demonstrate that our method generalizes to other tasks present in Linguistics Olympiad competitions, achieving state-of-the-art results across nearly all problem types and difficulty levels in the LINGOLY dataset.