GATE 2024 BM – Question 9
In the 4 × 4 array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule.
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
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Correct answer: (C) 2
Explanation
Let the empty column from the top be $a, b, c, d$ (1 for a cross). The top 2 in column 3 has one known cross (below-left), so $a + b = 1$. The 3 below it has two known crosses, so $a + b + c = 1$, which gives $c = 0$. The 4 has three known crosses, so $b + c + d = 1$, which gives $b + d = 1$. The total is $a + b + c + d = 1 + 0 + d$ with $d = 1 - b$. It is largest at $b = 0$: $a = 1, d = 1$, a total of 2.
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