Read the information given below and answer the question that follows.
In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built. The heights (in metres) of individual platforms are as shown below:
| 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 |
Individuals (all of same height) are seated on these platforms. We say an individual A can reach an individual B if all the three following conditions are met:
(i) A and B are in the same row or column
(ii) A is at a lower height than B
(iii) If there is/are any individual(s) between A and B, such individual(s) must be at a height lower than that of A.
Thus in the table given above, consider the individual seated at height 8 on 3rd row and 2nd 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?
Correct Answer :
7
Solution :
The correct option is C.
Let us find the number of individuals who can reach each position in the grid. An individual A can reach B if:
1. They are in the same row or column.
2. Height of A < Height of B.
3. Any individuals between A and B must have a height strictly lower than A. This means, as we move from the adjacent neighbor of B outwards in any of the four directions (left, right, up, down), the heights must be strictly increasing and remain lower than the height of B.
Let us examine each position (Row, Column) and identify the individuals who can reach them:
- (1, 3) at height 2: Can be reached only by (1, 2) at height 1. (Total = 1)
- (3, 1) at height 7: Can be reached only by (4, 1) at height 3. (Note: (5, 1) is 1, but 3 > 1, so the intermediate element is not lower than 1). (Total = 1)
- (3, 3) at height 4: Can be reached only by (2, 3) at height 3. (Total = 1)
- (3, 5) at height 5: Can be reached only by (3, 3) at height 4. (Total = 1)
- (4, 1) at height 3: Can be reached only by (5, 1) at height 1. (Total = 1)
- (4, 5) at height 2: Can be reached only by (4, 4) at height 1. (Total = 1)
- (5, 4) at height 3: Can be reached only by (4, 4) at height 1. (Total = 1)
Thus, there are exactly 7 individuals in the layout who can be reached by just one individual.
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