2019 Math Kangaroo Levels 9-10 Problem #25

2019 Math Kangaroo Levels 9-10 Problem #25 25. A graph consists of 16 vertices and some edges that connect them, as in the picture. An ant is now at the vertex labelled 𝑨. At each move, it can walk from one vertex to any neighboring vertex by traveling along a connecting edge. At which of the vertices labelled 𝑷, 𝑸, 𝑹, 𝑺, 𝑻 can the ant be after 2019 moves? (A) only 𝑃, 𝑅 or 𝑆, not 𝑄 and 𝑇 (B) only 𝑃, 𝑅, 𝑆 or 𝑇, not 𝑄 (C) only 𝑄 (D) only 𝑇 (E) all of these are possible