Logical path through Oubliette Sudoku

[CannyK9]

***Spoilers*** This is a logical path through my Oubliette Sudoku. Please follow the link if you'd like to try yourself.

Post 1 of 2, due to image limit.


1. Initial pencil marks:
7s are at the top of zone 7. 5s are at the bottom of zone 3:



2. Is the central zone raised or flat? Flat.
If the central zone was raised, the 5s would conflict with zones 3 and 9 looking from the South, forcing zone 6 to be raised. Likewise, the 7s would conflict with zones 1 and 7 looking from the North, forcing zone 4 to be raised. The only way to avoid a row of three raised zones is to 'block' a conflict with either zone 2 or 8 (but not both, or we'll get a row of 3), or to make the central zone flat.

If the central zone is raised, there are 2 possibilities:
- Zone 2 is also raised, 8 is flat:
    From the previous 'blocking' logic, zone 9 is now flat, zones 6 and 7 are raised. In this configuration, there are no 7s on the South side:
    

    
- Zone 8 is also raised, 2 is flat:
    From the previous logic, zone 1 is now flat, zones 3 and 4 are raised.
    From North, zones 3, 4 and 5 are visible. There isn't a combination of values in the cages in zones 2, 3, 5 and 8 that don't break either the cages, or the North 6s. Example:
    

    
Therefore: Zone 5 is flat (I admit that getting so involved straight away is harsh. If I was going to make this puzzle significantly easier, I think giving away that the centre is flat is a good first step. I've also just noticed that I've put givens inside cages for no good reason, a beginner mistake!).

3. Is zone 2 raised or flat? Raised.
If you make zone 2 flat. It can cascade in a few different ways, since there's now nowhere for a North 3 in the top 6 zones:



- If a 3 goes in zone 8, we can't flatten zone 9, becauses it will mean flattening zone 6 to keep a South 5 and now the 3 conflicts with the tiny cage in zone 4. So instead we end up with this broken configuration:



- If the 3 goes in zone 7 then zones 1 and 4 must be flat and we're left with this, which forces a 3 into the West side twice (if the 3 and 7 in zone 7 are swapped then the 7s are present twice):



- Finally, if a 3 goes in zone 9 then zones 3 and 6 must be flat and we're left with this, where the 7s conflict:



4. Is zone 3 raised or flat? Flat.
If you make zone 3 raised, there's a knock-on effect with the 7s that leads to this arrangeement, which breaks the South 5s.



5. Is Zone 5's cage 1-8 or 3-6? 3-6.
If it's 1-8, zone 2's cage cannot have a one, and since zone 3 must have either a 2 or 4 this is the only arrangement, which breaks zone 8's cage:

[CannyK9]

6. Is r1c5 a 2 or a 4? 2.
Here's the grid with the pencil marks from putting 3 and 6 in zone 5:



If I make r1c5 a 4, it forces 239 into the top of zone 3, and now the North 3 must be in either zone 7 or zone 9. Therefore, either zone 6 must be flat or zones 1 and 4 must be flat:



If zone 6 is flat then the North 6s conflict.
If zones 1 and 4 are flat then the grid ends up like this, where there are presumably many problems but at the very least the East 2s and 5s are conflicting:



7. If we fill everything in now, we end up with this:



Because of the North 6s and 3s, both zones 1 and 6 must be raised.

8. Which of the bottom zones are flat? Only zone 8.
Here's what it looks after filling in the cages in zones 1 and 6. The only use of the extra constaint is that the 5 must be away from the edge of zone 6:



That pushes a 3 to the middle column of zone 2, and to the right of zone 8. Now if zone 9 was flat, zone 8 would conflict on East 3s and must also be flat, and the South 5s break:



If zone 7 was flat, the South 7s conflict unless zone 4 is also flat. Now the cage in zone 1 fixes the cage in zone 8, suggesting zone 8 is flat too. This results in a configuration that falls apart pretty quickly:



Therefore only zone 8 is flat on the bottom row. This means that zone 4 must be flat, because neither zones 1 nor 7 are flat.

And this is final configuration of the grid. All of the hard work is done so I'll leave it here~

[glum_hippo]

Thanks for sharing this. I hope to see more such posts in our forum.