Is there more simple, mathematical way to solve this problem other than actually play the game with some smart heuristics (what I did in my solution)?

yes, there is :)
I used no array, just 4 variables n,t and legendary pair i,j ;)

I used greedy approach. Prefer jumping to movement. Do not allow blockades. In case of tie keep empty space closer to border.

I used simple brute-force =)