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An entry in Fortnightly Topic Challenge #52: Polyominoes.

This puzzle is a hybrid between Pentominous and Star Battle. Your job is to divide the grid below into pentominoes according to the rules of Pentominous, and then place stars in the grid according to the (slightly modified) rules of Star Battle. Specific to this puzzle:

  • You must partition the grid into pentominoes such that:
    • All cells are covered and no pentominoes overlap.
    • No two pentominoes of the same shape (including rotations and reflections) are orthogonally adjacent.
    • Each given letter in the grid must lie in a pentomino of the corresponding shape.
  • You must also place stars in the grid such that:
    • Each row and column contains two stars.
    • Each pentomino contains ONE star.
    • The star in each pentomino must be in a cell that is orthogonally adjacent to at least two other cells of the pentomino. So for example, the star in an X must go in the center.
    • No two stars can be adjacent, neither orthogonally nor diagonally.
    • Several star (★) locations are given in the puzzle. Stars may go in squares marked with pentomino letters.

I hope you enjoy!

Puzzle Grid

SOLVER HELPS

Link to Penpa version

The pieces (adapted from Wikipedia):

Pieces

TEXT VERSION

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| |★| | | | | | | |I|
---------------------
| | | | | | |Z| | | |
---------------------
|P| | | | | | |V|P| |
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| | |★| | | |Y| | | |
---------------------
| | | | |N|N| |★| | |
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| | | | |P|P| | | | |
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| | | |W| | | | | | |
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| |X|U| | | | | | | |
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| | | |L| | | | | |N|
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|L| | | | | |★| | | |
---------------------

Pieces:

FF
 FF  IIIII  L     NN
 F          LLLL   NNN
 
PP   TTT          V
PP    T    U U    V
P     T    UUU    VVV

WW     X         ZZ
 WW   XXX   Y     Z
  W    X   YYYY   ZZ
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  • 1
    $\begingroup$ Maybe it would be better to use circles instead of stars for the star battle? Grid squares have a really strong association with "exactly one thing lives in here", and the stars and letters are so similar, that it feels like they are clashing with each other. On the other hand, a circled (or otherwise highlighted) letter in a grid square is perfectly fine. $\endgroup$
    – Bass
    Mar 29 at 20:23
  • $\begingroup$ I added a sample solved grid with that idea to the answer below. Seems to work pretty well. $\endgroup$
    – Bass
    Mar 29 at 20:52
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Here's the finished grid:

enter image description here

You can see some of the original letter clues got covered by the stars. I'm not sure how I feel about that; on one hand, it's just a puzzle rule that allows for a unique solution. On the other hand, it feels like having two words intersect in a crossword puzzle even though they have different letters at the intersection square. Well, it's not very important in any case, or in so many fewer words: Meh.

Here are some of the solution steps:

Start with the givens:

The X and the V are placed right at the start. There are only two options for the X, one of which cuts off the corner. The V cannot reach row 1, because that would make the I vertical, and leave an unreachable empty square in the top row. The V cannot reach row 5 either: the star would mean the V would have to connect to the edge, and after placing the P and I, there would be unreachable squares on row 2. So the V must span rows 2 to 4, and there's only one way to do that without forcing the P on top of the I.
enter image description here

We have more progress on the top:

The Y cannot be vertical, the nearby star would prevent us from adding a star to the Y. Placing the Y on its back, the Z also gets placed, and we get some stars in their (sometimes approximate) places. The yellow piece starting at the X's nook cannot reach the nearby star, so we have to give it one. (The top four rows already have their two stars.) enter image description here

The star positions now force the N piece into place, and after some minor trial and error, we find the P in the top left corner cannot use the star in the top row, so there's only one way to fill the top left corner. The W is also forced.

enter image description here

Since we know the central P piece must have a star in column 6, we can place all the stars except the final two

enter image description here

And finally, we need to make some deductions about the grey piece at the bottom. It cannot be an L (because it's next to another) or an N (the other N in the corner would chop off an area of the wrong size), or a V (too many stars), so the other options are I and Y.

Trying the Y option, there are several ways to place the N in the corner, but all of them immediately lead to illegally placed stars or or isolated areas of the wrong size.

So the grey piece along the bottom can only be an I, which places the N in the corner. The rest follows easily, as long as we avoid adjacent Ps and Vs.

enter image description here


EDIT: This is a nice puzzle type combination, and I hope to see more, so here's an idea for sidestepping the minor inconvenience of having to cover up some of the clues:

enter image description here

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  • $\begingroup$ Ninja'd! At least my solution matches XD $\endgroup$
    – samm82
    Mar 29 at 19:48
  • $\begingroup$ Nice! I had done this earlier on my phone but didn't want to spend the effort to write up a solution on it. As for the overlap, I don't really mind it, if it makes the puzzle construction easier (I'm sure there's a way to divide up the grid so that none of the stars overlap with any of the letters, but it's probably not that easy) $\endgroup$
    – HTM
    Mar 29 at 19:52
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    $\begingroup$ @samm82, sometimes I get to be the FGITW, but since I took about 2 hours for proving (for myself) and then confirming with OP that there cannot be a solution without overlapping stars and clues, and then used at least an hour after the solve to do the complete writeup before posting, maybe LSGITW might be a more appropriate title here :-) $\endgroup$
    – Bass
    Mar 29 at 20:05
  • $\begingroup$ That is, of course, the correct answer! Great job, I hope you enjoyed. Apologies regarding the star/letter overlap, I absolutely see your point, but referencing the comment of @HTM this puzzle was surprisingly difficult to construct (for me at least). I had a lot of false starts before getting this to work at all. $\endgroup$ Mar 29 at 20:19
  • $\begingroup$ Thanks for the suggestions about puzzle marking to make a cleaner solution. Not sure another one of these is on my calendar any time soon (it was a bear), but I'll keep in mind if I revisit. $\endgroup$ Mar 30 at 17:51

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