The Divisibility DAG
In the above DAG for the divisibility relation on \(\{1, \ldots, 12\}\), there is an upward path from \(a\) to \(b\) iff \(a\) divides \(b\). If \(24\) was added as a vertex, what is the minimum number of edges that must be added to the DAG to represent divisibility on \(\{1, \ldots, 12, 24\}\)?
Edges from 8 and 12 to 24 are all that are needed.