When calculating paths for an ant moving in a grid, how should the pathways be divided?

The correct answer is about dividing the pathways by unique pathways to each intermediate point. This approach is essential in combinatorial problems like the ant moving on a grid, as it allows for a systematic counting of all possible routes the ant can take to reach its destination.

When the pathways are divided based on unique pathways to each intermediate point, it becomes easier to apply combinatorial principles, such as counting pathways using the binomial coefficient. Each intermediate point represents a decision point where the ant can choose to move either right or up (in a grid scenario). By considering the unique pathways to each of these points, you effectively account for the various combinations of moves that lead to the final destination.

This method also helps avoid duplication of counting, ensuring that each pathway is only counted once. Such precision is crucial in combinatorial calculations, where the order of movements and the specific route taken matter for determining the total number of distinct paths.

In contrast, other options focus on narrower criteria (like only horizontal moves, total moves in one direction, or symmetrical distances), which do not encompass the complexity of all potential pathways the ant could take to reach the target square in the grid. This holistic view is vital for an accurate calculation of the total unique paths available.