LLMs aren’t reasoning about the puzzle. They’re predicting the most likely text to print out, based on the input and the model/training data.
If the solution is logical but unlikely (i.e. unseen in the training set and not mapped to an existing puzzle), then the probability of the puzzle answer appearing is very low.
If the solution is logical but unlikely (i.e. unseen in the training set and not mapped to an existing puzzle), then the probability of the puzzle answer appearing is very low.