Question

Every row and every column of this 3 x 3 square must contain

each of the numbers 1, 2 and 3.
What is the value of N + M?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Answer 1

Answer: (C) 4

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Reason:

We have "1" in the upper left corner and "2" in the direct middle. This means "3" goes to the left of the "2" since each row and column cannot use repeats. Just below that "3" will go "2".

In summary so far, the first column has 1, 3, 2 in that order when moving from top to bottom. Refer to the values in green in the diagram below.

For identical reasoning, the first row has 1, 3, 2 in that order when moving from left to right. These are the values in light blue.

Once the first row is filled out, we can determine the middle entry of the bottom row, which is "1" marked in pink. This item helps us determine that M = 3 which in turn leads to N = 1.

Therefore, N+M = 1+3 = 4 is the final answer.

Side note: This square has symmetry along the northwest diagonal