Chocolates that satisfy the equality for an arbitrary even number k.

It is easy to generalize the chocolate that satisfies Inequality $y\leq \lfloor {z/2} \rfloor$ , and we study the chocolate that satisfies the inequality $y\leq \lfloor {z/k} \rfloor$ , where $k$ is a natural number.
We generalize Definition 2.4 and define this chocolate game that satisfies the inequality $y\leq \lfloor {z/k} \rfloor$ mathematically.

 

Definition 3.1   There is a black $1 \times 1$ block, and on both side of it we have columns of blocks. The first, the second, the fourth,...,n-th column on the right side of the black block and $(-1)$ th, $(-2)$ th,...,$(-m)$ -th column on the left side of the black block.
The i-th column is $1 \times (1 + \lfloor \frac{n}{k} \rfloor)$ block for $n =1, 2, 3,...,n,...$ and the i-th column is $1 \times 1$ block for $i =-1, -2, -3,-4,-5,-m,...$ .
Gray blocks are sweet chocolate that can be eaten, and the black block is the bitter chocolate that cannot be eaten.
We define coordinates for this chocolate as in Definition 2.4, and it is easy to see that coordinates $\{x,y,z\}$ satisfy the inequality $y\leq \left\lfloor \frac{z}{k} \right\rfloor$ .

Example 3.1   Here we have chocolates that satisfy the inequality $y\leq \left\lfloor \frac{z}{k} \right\rfloor$ for $k = 1,4,6,8$ .

$y \leq z$

Figure 3.1  



$y\leq \left\lfloor \frac{z}{4} \right\rfloor$

Figure 3.2  

$y\leq \lfloor \frac{z}{6} \rfloor$

Figure 3.3  

$y\leq \lfloor \frac{z}{8} \rfloor$

Figure 3.4