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Rules of Gaps:

  1. Fill some cells with stars, so that each row and column contains exactly two stars.
  2. The stars cannot touch each other, not even diagonally.
  3. Numbers outside the grid indicate the number of empty cells between the stars in the respective row or column.

enter image description here

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  • $\begingroup$ Looks like a variation of Star Battle, try adding to the title: Star Battle: Gaps $\endgroup$
    – Anonymus 25
    Apr 25, 2021 at 10:24
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    $\begingroup$ Penpa link for interested solvers: git.io/JO7Cq $\endgroup$
    – Jeremy Dover
    Apr 25, 2021 at 13:20
  • $\begingroup$ @Anonymus25-ReinstateMonica actually, I believe that Gaps grid puzzle is a stand-alone genre yet indeed share some similarity with Star Battle. (I recall Gaps grid puzzle is already existed for years... cmiiw) $\endgroup$
    – athin
    Apr 25, 2021 at 17:31

1 Answer 1

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The completed grid:

enter image description here

Step-by-step solution:

As a first step, note that for all the columns and rows with a gap of size at least 6, we know that some of the middle cells need to be empty:
enter image description here

This yields a number of other cells which also need to be empty, since they cannot form a gap of the required size:
enter image description here

Now comes the first deduction which is a bit trickier:

Consider the two rows with the 2 and the 5. In the case that the 5-row does not have a star in the first or last column of the grid, then it will block off cells in the 2-row above it in a specific pattern: the first few (0, 1, 2 or 3) cells are not blocked off, then 3 cells are blocked off, then 3 cells are not blocked off again, and finally a few (0, 1, 2 or 3) cells are not blocked off again. For example, if the 5-row has stars at positions 3 and 9, then the pattern of blocked off cells looks as follows (focus on the row with the 2): enter image description here

Note that in such a situation, it is impossible to complete the 2 row in a valid manner. The only way of avoiding a situation like this, is by filling the 5 row as follows:
enter image description here

This leaves only one way of completing the 2 row. By furthermore marking some cells which cannot contain stars anymore, we get the following situation:
enter image description here

Next, we look at

the consecutive columns with the 1 and 6. These two columns can only be filled in a single manner: The 6-colums will have a star somewhere in the top four cells, which makes it impossible for the stars of the 1-column to go in the top four cells. This 1-column should therefore have a star in row 10, which in turn only leaves one possibility for the 6-column:
enter image description here

Now the 9-row can be completed in only one way, which in turn forces the position of one of the stars in the 4-column:
enter image description here

Now we are almost done!

The remaining 6-column (column 7) may not block off both possibilities for completing the 3-column next to it. This eliminates one of the possibilities of this column:
enter image description here

This leaves only one way of filling the 1-row, which leaves one possibility for completing the 4-column:
enter image description here

Now row 2 and column 11 can be completed, which quickly resolves the rest of the puzzle:
enter image description here

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  • $\begingroup$ On-point explanations! Very well done! :D $\endgroup$
    – athin
    Apr 25, 2021 at 17:31
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    $\begingroup$ Heh, that first major deduction step looks like someone with glasses awkwardly looking to their left $\endgroup$
    – HTM
    Apr 25, 2021 at 18:19

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