Deconstructed Fog
(Published on 11. September 2024, 19:24 by DiMono)
Fog covers the grid. As correct digits are placed, the surrounding cells will be revealed. No guessing is necessary.
Numbers outside the grid are X-Sum clues, and give the sum of the first X cells that are seen in the row or column from the clue, where X is the first digit contained in a box in the row or column. i.e. an X-Sum clue of 8 could be satisfied by [void] 3 5.
Thermometers must strictly increase from round bulb to tip, including void cells. Arrows must sum to the digit in the attached circle, including void cells.
Void cells on thermometers and arrows must also contain numbers, which must be valid X-Sum clues in all directions where the adjacent cell is in a box. i.e. [box] [void 15] [void] [box] would be an X-Sum of 15 going left but not right. X-Sums may not extend beyond the end of the grid. i.e. if there are 4 cells available for an X-Sum, the first digit may not be > 4.
Void cells are always counted as 0 for X-Sums, even if they contain a number (i.e. 5 8 2 [void 10] 3 would be an X-Sum of 18).
Example:
Note that since X-Sums may not extend beyond the edge of the grid, if R3C5 in the example were an X-Sum clue, the 4 below it would be invalid because it would extend two cells beyond the end of the grid.
Solve Example on SudokuPad
Solve Full Puzzle on SudokuPad
Solution code: Row 9, using - for cells with no digits (i.e. 1234-567-89)
Comments
on 13. September 2024, 20:15 by dpsy
Really lovable ! Unique ruleset that takes some time to become familiar with and understand all the implications, that's what makes it fun for me !
on 13. September 2024, 14:26 by HumanBirdsong
Wow, this was extremely difficult for me, with quite an unfamiliar ruleset! But it really began to flow after a little while and became extremely rewarding with each deduction. It took me 133 minutes in total, which is probably my longest solve yet!
@HumanBirdsong: Thank you for sticking with it! I'm glad you enjoyed it.
on 12. September 2024, 14:55 by DiMono
Added clarity for X-Sums extending beyond edge of grid rule.
on 12. September 2024, 14:13 by TripleABattery
Very fun puzzle, though I felt it was easy to overlook certain possibilities (which is a me problem and not necessarily a detriment to the puzzle itsself)
@TripleABattery: It's definitely a tricky one. Thank you for sticking it out!
on 12. September 2024, 06:29 by Deino42
I just want to get a clarification on the rules, but “X-Sums cannot extend beyond the grid” mean that if there’s a void cell on an arrow 3 cells to the left of the end of the grid with a normal cell to the right of it, that normal cell cannot be like a 5, since it would extend beyond the grid, right? Or does it mean “Once it reaches the end of the grid, the sum ends there”?
@Deino42: In the example puzzle, imagine R3C5 is an X-Sum clue. The 4 below it would require two additional cells beyond the edge of the grid, and would therefore be invalid. I have added this to the rules for clarity. Thank you for pointing it out!
on 11. September 2024, 19:37 by vitaminz
It's been a long time since I solved this but I remember it being quite lovely :)
