I have made a function to plot a graph of stairs with heigth '$h$' & length '$l$' ( Desmos link) where I assume that $l$ & $h$ and $x$ are positive, real and not equal to zero(i.e the stairs lie in the 4th Quadrant).
Now if I take any point $\alpha$ on the $nth$ stair. The $y$ co-ordinate will be $n*h$ and the $x$ co-ordinate will be $(nl-m)$ where m is the distance from the edge of the $nth$ stair.
Now using the equations :- $$\begin{align} y &= -h\left\lfloor\frac xl+1\right\rfloor \\ -nh &= -h\left\lfloor\frac{nl-m}l + 1\right\rfloor \\ n &= \left(\left\lfloor n -\frac ml\right\rfloor + 1\right) \\ \end{align} $$ As we know $n$ will be natural}: $$\begin{align} n &= n -\left\lfloor\frac ml\right\rfloor + 1 \\ -1 &= -{\left\lfloor\frac ml\right\rfloor} \\ \left\lfloor\frac ml\right\rfloor &= 1 \end{align}$$
Therefore, $m\ge l.$ But I have taken '$m$' such that it can be less than or equal to m. Therefore $m$ will be equal to $l$. This means that every point lies on the edge. I want to know the flaw in my thinking.
Image of graph:-
The original question I was trying to solve was if throw a ball with $u$ horizontal velocity from the top of the stairs each of height of $h$ and length $l$ then on which step it will strike and how much distance from the edge?
$\lfloor n -\frac ml\rfloor + 1\ne n -\left\lfloor\frac ml\right\rfloor + 1$
$\lfloor n -\frac ml\rfloor + 1= n -\left\lceil\frac ml\right\rceil + 1$
so
$\lceil \frac ml\rceil = 1 $
And $\frac ml \le 1$