POPCORN — seven cells across the upper part of the board
Trace POPCORN through these positions: 1 at row 3, column 2; 2 at row 3, column 3; 3 at row 2, column 3; 4 at row 1, column 3; 5 at row 1, column 4; 6 at row 1, column 5; 7 at row 2, column 5. Reading those cells in order gives P → O → P → C → O → R → N.
From the opening P, move right, go up twice, turn right for two cells, and finish by moving down. The route has three turns and four straight segments while spanning three rows and four columns. It visits three edge cells without entering a corner. The first cell has three open orthogonal neighbors, while the final N has two. Assigning this path uses seven cells and leaves 21 open cells for the other three answers.