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  • In a square layout of size 5m × 5m, 25 equal-sized platforms of different heights are built. The heights (in metres) of individual platforms are as shown below: <table border="1" cellp

In a square layout of size 5m × 5m, 25 equal-sized 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 individuals 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 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.

Row in the layout are numbered from top to bottom and columns are numbered from left to right.

Question : How many individuals in this layout can be reached by just one individual? 

Option: 1

3


Option: 2

5


Option: 3

7


Option: 4

8


Answers (1)

best_answer

There are a total of 7 individuals in the layout who can be reached by just one individual.

The individuals who can be reached by just one individual are:

  • The individual at height 1 in the first row and first column.
  • The individual at height 2 in the second row and first column.
  • The individual at height 3 in the third row and first column.
  • The individual at height 4 in the fourth row and first column.
  • The individual at height 6 in the first row and second column.
  • The individual at height 8 in the second row and second column.
  • The individual at height 9 in the third row and second column.

Below is 

To see why these individuals can be reached by just one individual, we can use the three conditions given in the problem.

Condition 1: The individuals are in the same row or column.

All of the individuals listed above are in the same row or column as another individual who is taller than them. For example, the individual at height 1 is in the same row as the individual at height 6, and the individual at height 6 is taller than the individual at height 1.

Condition 2: The individuals are at a lower height than the individual they can be reached by.

All of the individuals listed above are at a lower height than the individual they can be reached by. For example, the individual at height 1 is at a lower height than the individual at height 6, and the individual at height 6 can be reached by the individual at height 1.

Condition 3: If there is/are any individual(s) between the two individuals, such individual(s) must be at a height lower than that of the lower individual.

There are no individuals between any of the individuals listed above and the individual they can be reached by. For example, there are no individuals between the individual at height 1 and the individual at height 6.

Therefore, there are a total of 7 individuals in the layout who can be reached by just one individual.

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