# Statue View: 2, 3, 5, 7

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.

• These are amazing, how do you come up with these? May 25, 2019 at 19:24
• @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...
– Deusovi
May 26, 2019 at 0:52
• 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! :) Jul 5, 2019 at 0:17
• @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!
– Deusovi
Jul 5, 2019 at 2:59
• @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 Jul 8, 2019 at 9:32

The solution:

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.

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.

Same story with a northward seven-piece in either direction.

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.

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.

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.

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.

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.

Putting the two-piece the other way, we would need a stretch of 5 to finish the 5-square.

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.

Only one position we haven't tried:

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

• 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
– Alto
May 25, 2019 at 21:31
• 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).
– Deusovi
May 26, 2019 at 0:41
• 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? May 26, 2019 at 11:12
• @GuntramBlohm Just the paint bucket tool in Paint :)
– Jafe
May 26, 2019 at 11:59