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This is another Statue View puzzle. It's easily the hardest of the three I've made, so I recommend trying the other two as practice first.

Rules of Statue View:

  • Shade some cells of the grid to form the given set of pieces. Pieces may be rotated or reflected.
  • Pieces cannot be adjacent (though they can touch at a corner).
  • All unshaded cells must be (orthogonally) connected.
  • Any cells with numbers in them must be unshaded. These numbers give the total lengths of the runs of shaded cells starting immediately adjacent to the clue, and extending outwards from the clue.

grid with only 4 clues: 2, 3, 5, and 7

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    $\begingroup$ These are amazing, how do you come up with these? $\endgroup$
    – greenturtle3141
    May 25, 2019 at 19:24
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    $\begingroup$ @greenturtle3141 Place clues to force an interesting deduction to be made, mark down all possible things you can figure out from there, and repeat until unique! The tough part is finding interesting deductions and figuring out how to force them with clues... $\endgroup$
    – Deusovi ♦
    May 26, 2019 at 0:52
  • $\begingroup$ Are these your own puzzles? Because if so, I really suggest publishing it. Like, as an official puzzle! These are bloody superb, I can tell you that much. If I was in a position to hire you, I would. Excellent job, Deusovi! Well done! :) $\endgroup$
    – Mr Pie
    Jul 5, 2019 at 0:17
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    $\begingroup$ @MrPie Yes, these are all my own! I'm not sure what you mean by an "official" puzzle, but sharing them here seems like publication to me. I'm glad you're enjoying the puzzles, though! $\endgroup$
    – Deusovi ♦
    Jul 5, 2019 at 2:59
  • $\begingroup$ @Deusovi by "official" I mean in a magazine or on Simon Tatham's puzzles, or something. Yeah, it's a bad word because I too consider sharing them here as publication :P $\endgroup$
    – Mr Pie
    Jul 8, 2019 at 9:32

1 Answer 1

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The solution:

enter image description here

First of all,

Since there are no stretches of 4 or 6 in any of the pieces, the 7 can only be 2+5 or 1+3+3. Also, we can see that no stretch of 3 fits the 3 squares north of the 7 without filling either the 2 or the 3 square.

Also, the only other choices for 3+3 around the 7 are west and south, and there is no way to fit a piece to complete the southward part without touching the westward part.
enter image description here
By contradiction, we can deduce that the 7 square has to be made up of 2+5.

From there,

There are only two pieces with a stretch of 5, so let's try all their positions. A northward three-piece would make it impossible to complete the 3 with any of the remaining pieces.
enter image description here

Same story with a northward seven-piece in either direction.
enter image description here
enter image description here

So the stretch of five needs to be westward. Note that we cannot fit the two-piece into any of the stretches of 2 required, so the stretch of 2 has to be filled in by a seven-piece. That leaves only the three-piece for the stretch of 5.
enter image description here

If we put the three-piece facing south, there is only one way to complete the 7, but this puts a stretch of 5 next to the 3-square.

enter image description here
Thus we conclude that the three-piece must face north. There is exactly one way to complete the 7 now, and we've completed the 2 in the process as well.
enter image description here

Then,

We know the 3 cannot be 2+1, because there is no way to complete the 3 if we use the stretch of two in either direction.
enter image description here

So the 3 has to be a stretch of 3 to the north. We have two pieces that fit that stretch of three. Let's try the two-piece first.

If we touch the five with a stretch of 3, we can't complete it with the remaining pieces which has no stretch of 2.
enter image description here

Putting the two-piece the other way, we would need a stretch of 5 to finish the 5-square.
enter image description here
So we have to use the five-piece for the 3, and there are two ways to do it. Let's try the wrong way first – this would require a stretch of 4 to complete the 5-square.
enter image description here

Only one position we haven't tried:
enter image description here

From there, the remaining piece only fits one way to complete the 5:

enter image description here

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    $\begingroup$ yeah, i think this is correct! i wish i didn't take 20 minutes to figure out how the puzzle worked though (ugh for my noticing skills) +1 $\endgroup$
    – Alto
    May 25, 2019 at 21:31
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    $\begingroup$ That's correct, nice job! There's some slightly easier logic towards the end, though: once you have the first two pieces placed, you can also notice that the piece touching the 3 clue must also touch the 5 clue (with at least two cells), and then place that shape (apart from maybe the upper left corner, since you don't know yet if it's the two-piece or the five-piece). $\endgroup$
    – Deusovi ♦
    May 26, 2019 at 0:41
  • $\begingroup$ How did you create all those images? Is there some specialized software for that, or ist is just paint/gimp/photoshop and a lot of manual work? $\endgroup$
    – Guntram Blohm
    May 26, 2019 at 11:12
  • $\begingroup$ @GuntramBlohm Just the paint bucket tool in Paint :) $\endgroup$
    – Jafe
    May 26, 2019 at 11:59

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