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Problem of the Week
Problem E
Bug on the Outside

A ladybug walks on the surface of the \(2\) by \(3\) by \(12\) rectangular prism shown. The ladybug wishes to travel from \(P\) to \(Q\).

The bottom face of the prism has width 3 and length 12. Its height is 2. P is a vertex of the bottom face. Q is the vertex of the top face that is farthest from P (diagonally opposite corner of the prism).

What is the length of the shortest path from \(P\) to \(Q\) that the ladybug could take?