In a square layout of size $5\;\text{m} \times 5\;\text{m}, 25$ equal sized square platforms of different heights are built. The heights (in metres) of individual platforms are as shown below:
$$\begin{array}{ccccc} 6 & 1 & 2 & 4 & 3 \\ 9 & 5 & 3 & 2 & 8 \\ 7 & 8 & 4 & 6 & 5 \\ 3 & 9 & 5 & 1 & 2 \\ 1 & 7 & 6 & 3 & 9 \end{array}$$
Individuals (all of same height) are seated on these platforms. We say an individual $\text{A}$ can reach an individual $\text{B}$ if all the three following conditions are met:
- $\text{A}$ and $\text{B}$ are in the same row or column
- $\text{A}$ is at a lower height than $\text{B}$
- If there is/are any individuals(s) between $\text{A}$ and $\text{B}$, such Individual(s) must be at a height tower than that of $\text{A}$.
Thus in the table given above, consider the Individual seated at height $8$ on $3$rd row and $2$nd column. He can be reached by four individuals. He can be reached by the individual on his left at height $7$, by the two individuals on his right at heights of $4$ and $6$ and by the individual above at height $5$.
Rows in the layout are numbered from top to bottom and columns are numbered from left to right.
How many individuals in this layout can be reached by just one individual?
- $3$
- $5$
- $7$
- $8$