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Here are two $5 \times 5$ Latin-Square Adjacent puzzles. For each cell, put a digit between $1$ and $5$ such that:

  • Each row and column contains one occurrence of each digit $1$ to $5$.
  • If two cells are adjacent and their digits are numerically adjacent (i.e. one higher or one lower), then there will be a (black) border between them.
  • All borders are given, thus two cells that are adjacent and not having a border between them means their digits are not numerically adjacent.
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Solved grid:

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Solving path for right grid:

Next to a border we always have one odd and one even number. This leads to even numbers in the last two cells of the last row and odd numbers for all other cells without a border.
In the second row, the number $2$ can only go in the third or fifth cell which deduces the fourth cell as $5$ and the second cell in the first row follows as $5$ as well.
Now the first row can only be filled by $2,5,3,1,4$ and the second row follows with $1,4,2,5,3$. The rest of the grid can then be filled accordingly.

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    $\begingroup$ Great explanation, very well done and good job! :D $\endgroup$ – athin Jan 7 at 21:59

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