Find a 4x4 grid containing 16 unique positive integers with minimum sum, such that adjacent numbers have different parity.
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1$\begingroup$ Can't you just have a checkerboard grid with 0s and 1s? $\endgroup$– new Q Open WidJul 19 at 22:04
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$\begingroup$ @newQOpenWid thanks forgot about that condition $\endgroup$– web adventurerJul 19 at 22:06
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$\begingroup$ Oh, and are integers non-negative, or can they be negative numbers? $\endgroup$– new Q Open WidJul 19 at 22:11
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$\begingroup$ thanks, minimal sum implied positive integers but I forgot about that too :( $\endgroup$– web adventurerJul 19 at 22:14
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1 Answer
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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.
