GATE Chemical 2024 | GA | Question: 9

Question

In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross $(X)$ or a number, as per the given rule.
\begin{array}{|l|l|l|l|}
\hline 1 & 1 & 2 & \\
\hline 2 & X & 3 & \\
\hline 2 & X & 4 & \\
\hline 1 & 2 & X & \\
\hline
\end{array}

Rule: The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top, bottom, diagonals).

As per this rule, the maximum number of crosses possible in the empty column is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Try different combinations for all 4 positions in last column with X and 0

Now you will have 16 different possible combinations

here, 0 is being used because requirement says that maximum no of X in last column and for that we should consider value 0 otherwise we will not have max no of X.

Possible Combination with maximum no of X

COL 1	COL 2	COL 3	COL 4
1	1	2	X
2	X	3	0
2	X	4	0
1	2	X	X

 

 

Answer 2

You can put only 1 in immediate vicinity of 3, for that to be valid you can't put 3 X's as there will always be two near 3. Hence 2 maximum possible.

 

Answer 3

2 Cross possible. So option c is correct.