The notion of ''don't care'', that encapsulates the unimportance of which of several scenarios will occur, is a fundamental notion in computer science. It is the core of non-determinism; it is essential in various computational models; it is central in distributed and concurrent algorithms; and it also is relevant in sequential, deterministic algorithms. It is a valuable tool in algorithmic problem solving. Yet, in the teaching of (deterministic) algorithms it is not made explicit, and left unexplored. Its implicit exposition yields limited student invocations and limited student comprehension upon its utilization. These phenomena are also due to its rather unintuitive ''black-box'' characteristic. In this paper, we illuminate and elaborate on this notion with six algorithmic illustrations, and describe our experience with novice difficulties with respect to this notion.