IIT JEE 1982 Maths - 'Adapted' - Subjective to Multi-Correct Q9

Algebra Level pending

\(mn\) squares of equal size are arranged to form a rectangle of dimension \(m\) by \(n\), where \(m, n \in\mathbb N\). Two squares will be called "neighbours" if they have exactly one common side. Distinct numbers are written in each square such that the number in any square is the arithmetic mean of the numbers written in neighbouring squares. Then the numbers can be

  • (A) \(1, 2, 3, \ldots , mn\)
  • (B) \(-\frac{mn}2, -\frac{mn}2+1, \ldots, -2, -1, 0, 1, 2, \ldots, \frac{mn}2-1, \frac{mn}2\)
  • (C) \(-1, 2, -3, 4, \ldots, (-1)^{mn}mn\)
  • (D) Such an arrangement is not possible.

Enter your answer as a 4 digit string of 1s and 9s - 1 for correct option, 9 for wrong. Eg. 1199 indicates A and B are correct, C and D are incorrect. None, one or all may also be correct.

In case you are preparing for IIT JEE, you may want to try IIT JEE 1982 Mathematics Archives.

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