Path one: four cells and two turns
Trace PUMP through these cells: 1 at row 4, column 7; 2 at row 5, column 7; 3 at row 5, column 6; 4 at row 6, column 6.
Read the letters as P, U, M, P. Move down, turn left, and turn down again. The route spans three rows and two columns, with two direction changes across three straight segments. It visits two edge cells and no corners. Its opening has two open orthogonal neighbors, while its finish has four. Completing this trace assigns four cells and leaves 39.