Answer 1: the four-letter route
Trace AJAR from row 1, column 4 by moving right once, then turning downward and continuing for two cells. The letters appear A → J → A → R. This four-cell route spans three rows and two columns, with one turn and two straight segments. All four visits touch an outer edge, and row 1, column 5 supplies the route’s single corner visit.
Use this ordered check: 1 at row 1, column 4; 2 at row 1, column 5; 3 at row 2, column 5; 4 at row 3, column 5. The sequence contains one right move followed by two down moves, with no upward or leftward step. Its first and last cells each have three open orthogonal neighbors on the unfilled board. Assigning these four cells leaves 18 of the 22 open cells for the remaining words.