Question 2
Consider a $100\times100$ table, and identify its cell in row $a$ and column $b$, $1\le a,b\le100$, with $(a,b)$. Let $51\le k\le99$ be an integer. A $k$-knight moves one cell vertically or horizontally and $k$ cells in the other direction: from $(a,b)$ to $(c,d)$ with $(|a-c|,|b-d|)$ equal to $(1,k)$ or $(k,1)$. It starts at $(1,1)$ and makes several moves. A sequence of moves is a sequence $(x_0,y_0)=(1,1),(x_1,y_1),\ldots,(x_n,y_n)$ such that all cells lie in the table and each successive pair is a legal move. Each visited cell is called reachable. For each $k$, find $L(k)$, the number of reachable cells.