...William Abel tells us that when each TUCO puzzle was produced, two distinct cuts were made; see below. First the puzzle was cut into horizontal strips; then vertical strips. (Or vice-versa.)
...So if a person counts the number of pieces along one edge, there will be the same number of pieces along the opposite edge.
And if one counts the pieces along one edge, and then turns the corner and counts the pieces along the adjacent edge, when those two counts are multiplied together, the result is the total number of pieces in the puzzle.