The three-letter path
Trace DIG from 1 at row 2, column 5; 2 at row 1, column 5; 3 at row 1, column 4. The letters read D → I → G in that order. This route starts on the board’s fifth-column edge, reaches the top edge on its second cell, and then continues to its final letter.
Move up once and then left once. That produces one turn and two straight segments across a span of two rows and two columns. All three cells are edge cells, and the middle cell is the route’s single corner visit. Both the starting and ending cells have two open orthogonal neighbors in the raw board layout. Since D and I each occur twice on the board, following the ordered moves is more reliable than matching those letters in isolation. Once these three cells are assigned, 15 open cells remain for the other paths.