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Dear PSE users and moderators,
I’m new here in PSE, but I really need your help. There was this person who gave me a black envelope consisting 10+1 pages of puzzles, and also a scribble saying: “Find our favorites and you will be accepted to join our ‘pyramid cult’. Feel free to ask for help from your beloved friends on PSE. They will surely guide you into all the truth.” I’m also a newbie on grid puzzles, so, could you please give me any hint to solve these? It’s getting harder and harder later on..
- athin

Jump to the first page: #1 Numberlink | Previous page: #7 Fillomino | Next page: #9 Shikaku


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Rules:

  1. The areas divided by bold lines are called "Rooms". Fill in all empty cells with numbers under the following rules.
  2. Each Room contains consecutive numbers starting from 1.
  3. If a number is duplicated in 3-directions (parallel with one of the board sides), the space between the duplicated numbers must be equal to or larger than the value of the number.

Special thanks to chaotic_iak for testing this puzzle series!

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First, some trivial deductions:

enter image description here

Next, note that

in any region of size n shaped like a line, the cells just before and after that line cannot contain the number n. For example, the cells marked "t" and "l" on the left border, above and below the size-5 region, cannot contain the number 5.

We can use this logic to place a 2 three cells left of the center 1: the 2 below it rules out three of the cells in the region, and the diamond above that region rules out a fourth. (Then a few more cells follow from that.)
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For ease of visualization, I'll mark the cells that must be non-2s.

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Now look at the two yellow cells in the size-4 region just right of the central triangle. They must be 3 and 4; in fact, the top one must be 4 and the bottom one must be 3, because the region just above the center must have a 3 in its northeasternmost three cells. So the region just southwest of the center can be resolved, and the 6 and 7 can be placed in the bottom region.

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Next, look at occurrences of the number 3:

>

The two light blue 3s mark locations where a 3 must be in one of two cells.
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Because of these, the cell just under the single-cell region at the top must be a 2, and this lets us place several more 2s around the grid:

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At this point, it's probably more helpful to switch to looking at places 3s can't go:

And sure enough, a bunch of 3s can be placed. (And a few of the ambiguous 2s can be resolved as well.)

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Next, look at the 4s:

specifically, the only 4 we've placed so far. It forces the 4 in the region just above and left of it, and then that forces a 4 in the 5-cell region on the left edge.

Then, the third cell in column 6 can have a 5 placed,which then constrains the placement in the 6-cell region just above center; either way, the lower unoccupied cell in the left edge 5-cell region is not a 5, and we can complete that region.

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And then the majority of the puzzle falls pretty easily:

We can resolve the top middle region: the 5 can only go in one place, and then the 3, 4, and 1.
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Then we can resolve the region just above the center (in the order 5-3-2-1-6), and then the very top region (4-5-7-6):
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The lower left region can also be resolved (1-5-8).

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In the bottom middle region,

the two cells just above the empty cells in the bottom region must contain 1 and 3 (since all other cells are not allowed to have them). This lets us place 4, 5, and 6, which lets us finish the region to the left, which lets us finish the entire bottom and left sections of the grid.

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And finally:

In the middle right region, the fourth and fifth cells down must contain 2 and 5 in some order (since no other cells can have them). Then 4 can only fit into the bottom, and then everything else can be resolved fairly easily.
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Taking the letters of cells that contain 1s gives the answer: STEALTH.

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  • $\begingroup$ Great answer, as always! :) $\endgroup$ – athin Aug 6 at 2:50

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