What is the Size of the Smallest Latin Square for Which a Weakly Completable Critical Set of Cells Exists?

It has been shown by Sittampalam and Keedwell that weak critical sets exist for certain latin squares of order six and that previously claimed examples (for certain latin squares of order \(12\)) are incorrect. This led to the question raised in the title of this paper. Our purpose is to show that five is the smallest order for which weakly completable critical sets exist. In the process of proving this result, we show that, for each of the two types of latin square of order four, all minimal critical sets are of the same type.