First path: TIE
Trace TIE from 1 at row 1, column 4; 2 at row 1, column 5; 3 at row 2, column 5. The letters read T → I → E in that order. This assigns the three cells required by the first answer and leaves 16 of the board’s 19 open cells for the remaining paths.
The motion goes right once and down once, producing one turn and two straight segments. It spans two rows and two columns. All three cells count as edge visits, and one is a corner visit. The starting and ending cells each have two open orthogonal neighbors on the raw board, so the exact letter order is the clearest confirmation.