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Find a 4x4 grid containing 16 unique positive integers with minimum sum, such that adjacent numbers have different parity.

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    $\begingroup$ Can't you just have a checkerboard grid with 0s and 1s? $\endgroup$ Jul 19, 2023 at 22:04
  • $\begingroup$ @newQOpenWid thanks forgot about that condition $\endgroup$ Jul 19, 2023 at 22:06
  • $\begingroup$ Oh, and are integers non-negative, or can they be negative numbers? $\endgroup$ Jul 19, 2023 at 22:11
  • $\begingroup$ thanks, minimal sum implied positive integers but I forgot about that too :( $\endgroup$ Jul 19, 2023 at 22:14

1 Answer 1

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Firstly, we note that the parity of the numbers must be in this arrangement, ignoring rotations and reflections (0 for even and 1 for odd):

1|0|1|0
0|1|0|1
1|0|1|0
0|1|0|1

It is now rather easy to generalize this, to unique positive integers:

1 |2 |3 |4
8 |7 |6 |5
9 |10|11|12
16|15|14|13

which has a total sum of 136.

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  • $\begingroup$ Yes, sounds about right. $\endgroup$ Jul 19, 2023 at 22:20

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