Question 71
A square $ABCD$ is divided into $n^2$ equal small elementary squares, by drawing parallel lines to its sides. A spider starts from $A$ moving only to the right and up and tries to approach point $C$. Every movement of the spider consists of $k$ steps right and $m$ steps up or of $m$ steps right and $k$ steps up (which can be done in any way she wants).
The spider makes $l$ “movements” and in the sequel moves only to the right or up without any restriction. If $n = m \cdot l$, find the number of all possible routes the spider can follow to approach point $C$, where $n, m, k, l$ are positive integers and $k \lt m$.
The spider makes $l$ “movements” and in the sequel moves only to the right or up without any restriction. If $n = m \cdot l$, find the number of all possible routes the spider can follow to approach point $C$, where $n, m, k, l$ are positive integers and $k \lt m$.