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This is a Palisade (or Ten-Cells) puzzle. The rules are:

  • Thicken some of the squares' sides so the thick borders outline cells of ten squares apiece.
  • Any square with a number in it indicates how many of its sides are thickened. Note that if the square is along a side of the entire diagram, then that side counts as one of the thickened sides.
  • Thickened sides can be used only as parts of cell outlines: no thickened side can have both of its sides in the same cell.

You can work it online on Simon Tatham's site if you so choose. (If you press "Solve game" there, you'll be informed "Sorry, I can't solve this puzzle". Nonetheless, it is solvable logically.)

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  • $\begingroup$ I couldn't think of a better title and welcome suggestions. (The current one is a line from the song "Palisades Park".) $\endgroup$
    – msh210
    Commented Apr 18, 2021 at 17:30
  • $\begingroup$ FYI, this genre would probably be more commonly recognized as "Ten Cells" (as a parallel to the more well-known "Five Cells" and "Four Cells"). $\endgroup$
    – Deusovi ♦
    Commented Apr 18, 2021 at 18:09

1 Answer 1

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Some initial deductions around the edges already give some regions:

enter image description here

We can break in some more with internal clues:

A 1 that's next to two cells of the same region must be part of that region. Similarly, a 3 next to two cells of the same region must not be part of that region.
Using that logic and avoiding making groups of size more than 10 gives:
enter image description here

Some more clever deductions can lead to the next step:

enter image description here
I've marked off two areas in blue and yellow (and also drawn a temporary diagonal border line). The yellow area has 22 cells; combined with the region of 8 next to it, that makes 30, so the big 8 region must stop there.

Similarly, in the blue area, there are only 13 or 14 cells (depending on whether the 2 is up or down). Either way, at least 6 cells need to stick out, going down the left column. These six cannot be part of the nearby 0's region.

Those six cells are forced to continue this far (because if they used the 3s near the left side, they would stop short). So this drags that region down to the 1, and that 1 completes the region.

enter image description here
And now we can continue with deductions, since both colored regions have been satisfied.

That gives a break-in to the rest of the puzzle:

Continuing with deductions from that point, the top and left sides can be mostly resolved... enter image description here
Some more easy deductions finish off the top half:
enter image description here

Avoiding the 3s near the bottom cutting off a region too soon gives further progress:

enter image description here
And finally, the unassigned 3 going left would block off the bottom region.

So the solution to the puzzle is:

enter image description here

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