I have a doubt in the given example for the question. I’m pasting the question text below:

(copied from the pdf available at: https://www.iarcs.org.in/inoi/2012/zio2012/zio2012-qpaper.pdf)

You are given a grid of cells. Each cell has a positive integer written on it. You can

move from a cell *x* to a cell *y* if x and y are in the same row or same column, and the

number in *y* is strictly smaller than the number in *x*. You want to color some cells

red so that:

- Every cell can be reached by starting at a red cell and following a sequence of zero or more moves as defined above.
- The number of red cells is as small as possible.

You should report the following information:

- The number of red cells.
- The smallest number appearing amongst all red cells.

If there are multiple valid solutions, give any one solution

For example, suppose the grid is as follows:

*2 2 3
2 1 2
3 2 2*

It is sufficient to color the two cells labelled 3, and one cannot do better than this.

In this case, the number of red cells is 2 and the smallest number appearing amongst

all red cells is 3.

(followed by three grids, for which the student has to provide the answer)

What I’m understanding is that a cell *(x,y)* is reachable ONLY if at least one of its adjacent cells contain a number STRICTLY GREATER than the number in cell *(x,y)*, or it is adjacent to a red cell. So, in the example given, if we color the cells containing ‘3’, at *(1,3)* and *(3,1)*, all cells will be reachable except the cells containing ‘2’ at *(1,1)* and *(3,3)*. These two cells, i.e. *(1,1)* and *(3,3)* don’t have any adjacent cell which is colored or has a number strictly greater than itself.

I would also color the cells at *(1,1)* and *(3,3)*. Hence my answer for the example is:

- No. of colored cells : 4
- Least number among the colored cells : 2

My interpretation renders the example incorrect. And so I believe I’m missing out some important fact in the question. Don’t give me the logic to solve the question; just tell me how the given example in question is correct.

Thank You!