Pandemonium
(Published on 23. July 2025, 13:45 by Andrewsarchus)
Rules:
Doppelganger Chaos Construction:
- Divide the main 9x9 grid into 9 orthogonally connected regions of 9 cells each.
- Place the digits 0-9 in the grid without repeats in any row, column, or region.
- Every row, column, and region must contain a 0, and must therefore omit one of the digits from 1-9.
- Each digit from 1-9 is missing from exactly one row, one column, and one region.
- For each 0, the digit missing in its row, column, and region must be three distinct digits.
Auxiliary Grids:
- Three auxiliary grids are provided for recording the missing digits.
- The 9x1 strip below the main grid records the digit missing in the corresponding column of the main grid.
- The 1x9 strip to the right of the main grid records the digit missing from the corresponding row of the main grid.
- The 2x9 strip to the far right records each region's region number in the left column and its missing digit in the right column.
- Regions in the 2x9 strip appear in the order they are encountered when scanning the main grid in reading order.
Region Numbers / ID Cells:
- A region's region number is contained in an ID cell whose location and digit is encoded by one of the zeros in the grid.
- For each 0, let X, Y, Z be the digits missing in its row, column, and region respectively.
- Then the cell in Row X Column Y, contains the digit Z and is the ID cell for region Z.
Region Border Arrows:
- Small black arrows indicate the number of region borders seen in the indicated direction (not including the outside grid border).
- If a cell, with digit N contains multiple arrows, each arrow sees N borders in its direction individually. (N is not the sum).
- All possible arrows in the main grid with at least one cell in the indicated direction are given.
Coordinate Arrows:
- Gray arrows connecting the centers of two cells, are coordinate arrows which identify the locations of the 0s in the main grid.
- with the row indicated by the arrow tail, and the column indicated by the arrow tip.
- Each gray arrow corresponds to a distinct location.
- The tip and tail of each arrow in the main grid are in the same region.
Next-Region Pointers:
- Each region from 1-8 contains a pointer to the next region (not necesarily the first cell in that region).
- In region N, the digit in a cell behind a large triangular arrow tip indicates the distance to a cell in region N+1.
- Region 9 contains no pointer.
Clones:
- The letters A,B,C,D in the auxiliary grids identify cloned horizontal dominos.
- Dominos with the same letter in the upper left corner of their left cell, contain the same two digits in the same order.
Example 7x7 puzzle
In the example puzzle, regions 1-5 have next-region pointers.
Regions 6 and 7 have no pointers.
example puzzle blank grid: try example puzzle in sudokupad
example puzzle solved grid:
example puzzle showing only next-region pointers and ID-cells
Play Online:
sudokupad: Pandemonium
penpa:Pandemonium
Solution code: column 6 top to bottom with x inserted for region borders
example: 123x45x789
Comments
today, 09:20 by wullemuus
Phew!
Congrats to this really creative and brilliant use of two of my favourite rulesets: Doppelgänger and CC. The combination with the arrows and esp. the IC cells led to unexpected and really intricate deductions. Without your solution guide I wouldn't have fully understood the implications of this, (esp. that every zero codes for one region number) so I solved the example puzzles twice to get familiar with it. What a beautiful logic inside! Hopefully you use these combination of rulesets again!
yesterday, 18:54 by kingoffries
1200+ minutes... Without a doubt the most time I have ever spent on any puzzle. Lost and Found finale... Derezzed... Stationary Loop Deconstruction (1-9)... I may have spent more time on this puzzle than the previous 2 or 3 hardest puzzles combined.
I was on the right track too. I had it almost cracked, but made one miscalculation and broke the whole thing. I reworked this puzzle from the beginning three times only to arrive at the same spot. But once I found it... Good heavens! What a brilliant puzzle! I found myself almost as in love as with one of my own. Almost as frustrated as trying to get a brilliant concept to finally work. Andrewsarchus, you have done it again! Thanks for the pointer on CTC. For anyone who loves an intense and treacherous 5 star masterpiece, push through this one to the end.
on 25. July 2025, 23:20 by PierreTombal
That was quite brutal. 600 minutes in I had exactly 6 digits identified. Hadn't actually spent all that time on the puzzle and as I had trouble interpreting the rules done the example in between too, but that only gave me a hand full of very tiny additional hints for the main puzzle. After about 1000 minutes on the clock (quite likely a real 6 hours by then) I thought I had the break in I needed, and then the rules stated that I had to copy a region ID to a column remainder and it instantly broke another region which was meant to miss another digit. I wasn't far off though. I had misplaced just one region border line, but except for the conflict I'm fairly clueless how I was supposed to logically determine that I was meant to go that way.
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Thanks for the persistence.
If you're curious about the intended solution path, the hidden comment at the bottom of the page contains a link to my solution guide (PDF file).
on 24. July 2025, 21:06 by Playmaker6174
Anyway, I may admit that this is perhaps the most well telegraphed doppelganger puzzle I've solved so far despite my usual struggle of scanning with it. Even though it took me just over 5 hours of solving, not a single part ever really felt brutal or unfair for me at all, but I had to really concentrate well on certain parts throughout the solve, especially the negative constraint and the region numbers.
If anything, the coordinate arrows were definitely the most vital part of the solve and they really help controlling my thought process between different parts during the solve.
on 24. July 2025, 21:04 by Playmaker6174
Super proud of myself to be among the earliest solvers to conquer this entire wonderful pandemonic creation x)
I highly recommend giving that nice 7x7 example puzzle a try first to wrap your mind around the entire concept and how to get used of the scanning methods.
on 24. July 2025, 02:43 by bodemeister
Very nice construction! Lots of fun stuff packed into here. Took me a little while to fully grasp how important the negative constraints are, but there's always enough information available to proceed to the next step. And always good to see more awesome doppelganger puzzles hitting the puzzle pages! Thanks for the puzzle!
on 23. July 2025, 16:50 by earthpuzzles
Fantastic construction! The rules are perfectly intertwined: close enough to work smoothly together, yet distinct enough in their contributions.
Highly recommend the example puzzle too — I solved it after the full size one, yet the smaller size provided some helpful situations that clarified the approach!
