An art gallery’s walkways are shown as lines. Each black dot is a junction. A guard placed at a junction watches every walkway incident on it. Find the minimum number of guards needed to watch all walkways.
The five walkways form a cycle on five vertices. Each guard covers at most two of its five edges, so two guards cover at most four edges and cannot suffice. Three do suffice:place one at the roof apex and one at each lower corner. Every edge then has a guarded endpoint. The minimum is **3, B**.
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