Without loss of generality, we assume that the starting field is the bottom left, and the target field is the top right.

The transition to the right-adjacent field is symbolized by $r$, and the transition to the above-adjacent field by $o$. Such moves are called "elementary moves". Any allowed sequence of moves, for example,

$$
3 r \ldots 2 o \ldots r \ldots 4 o \ldots r \ldots o \ldots 2 r
$$

can be broken down into a sequence of 14 elementary moves: rrrooroooororr.

Thus, we have a permutation of 14 elements rrrrrrrooooooo, where 7 elements are identical. The number of permutations in this case is

$$
P(14)=\frac{14!}{7!\cdot 7!}=3432
$$

The tower can reach its goal in 3432 different ways.
## Task 10/68

In chess, rooks can make moves of any length (as long as no square is occupied) in horizontal and vertical directions.

In how many ways can a rook be moved from one corner square to the diagonally opposite corner square, if no backward moves are allowed?