In the diagram, a $4 \times 4$ grid is to be filled so that each of the digits 1, 2, 3, and 4 appears in each row and each column. The $4 \times 4$ grid is divided into four smaller $2 \times 2$ squares. Each of these $2 \times 2$ squares is also to contain each of the digits 1, 2, 3 and 4 . What digit replaces $P$ ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) The digit cannot be determined

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-062.jpg?height=317&width=311&top_left_y=1153&top_left_x=1357)
The first row is missing a 4 and a 2. Since there is already a 2 in the second column (in the second row), the first row, second column must contain a 4 and the first row, fourth column must contain a 2. To complete the upper left $2 \times 2$ square, the second row, first column must contain a 3. The second row is now missing both a 4 and a 1 . But the fourth column already contains a 4 (in the fourth row), therefore the second row, fourth column must contain a 1. To complete the fourth column, we place a 3 in the third row. Now the $P$ cannot be a 3 , since there is already a 3 in the third row. Also, the $P$ cannot be a 4 or a 2 , since the second column already contains these numbers. By process of elimination, the digit 1 must replace the $P$.

ANSWER: (A)

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