Shortest path across a grid to collect every key, where locked doors open only once you hold the matching key.

The reason this gets asked instead of plain grid BFS is that it quietly tests whether a candidate understands what a graph node is. Most people carry an intuition that a node is a position, so they mark cells visited and the search dies the first time it needs to walk back through a corridor holding a new key. Candidates who say 'the state is where I am plus what I hold' before writing anything are done in ten minutes; candidates who write the standard template first usually cannot see why it fails, because it fails silently by returning -1 rather than by crashing.