Double negative
(Published on 26. January 2025, 12:28 by filuta)
Enjoy!
Rules:
grid 1:
-(sudoku) Place digits 1 to 9 each once in every row, column and 3x3 box.
-(split peas) The sum of the digits on a line strictly between two circles must be equal to a concatenation of the digits in that line's circles in some order. (r2c8 is counted only once even though there is a crossing)
grid 2:
-(cave) Shade some cells in the grid such that all unshaded cells are orthogonally connected, and all orthogonally connected groups of shaded cells touch the edge of the grid.
-(circles) The digit in grid 1 in the same respective position as each circle is a valid cave clue - i.e. it represents the number of unshaded cells seen in all four directions from the cell containing the clue, including itself. Shaded cells obstruct vision and circles are always unshaded.
All circles are given (and so is one shaded cell).
grid 3:
-(fillomino) Divide the grid into polyominoes so that polyominoes of the same size don't share an edge. Each cell contains a number equal to its polyomino's size.
-(interaction) In addition, the cells containing the same digit in grid 1 and grid 3 are exactly the shaded cells in grid 2.
solve online in penpa+ (answer check on digits in grids 1 and 3 and shading in grid 2)
Solution code: row 8 in all three grids in order - for grids 1 and 3 just write digits, for grid 2 write U for unshaded cells and S for shaded cells
Comments
on 28. February 2025, 11:19 by 3good5you
At the start, I felt that it was insane that this was solvable. At the end, I was additionally amazed that it didn't break. Incredible construction!
on 2. February 2025, 01:38 by Agent
Great combination of rules and a very smooth solve!
on 29. January 2025, 09:02 by Christounet
Excellent! The first part had me writing some weird equations to figure out the split pea logic (but that may be because I have never solved any split pea puzzle before). Not so satanic after all, but an extremely enjoyable combination and solve path. Thanks :)
on 27. January 2025, 17:38 by wullemuus
Three for the prize of one and worthwhile every second!
Again the solution checker didn't work (this problem also existed in "The Professor"). I'm working with Safari, but it's not a general problem with Penpa ... .
on 27. January 2025, 15:08 by Jesper
Fantastic, really enjoyed this ruleset combination.
on 26. January 2025, 18:45 by SamuPiano
What a fantastic gift this was! I was so amazed at several moments of this solve that I laughed out loud :)
Thank you so much for this puzzle! It was truly extraordinary!
on 26. January 2025, 14:06 by goodcity
Great puzzle with nice interactions between the grids, glad to see some new ideas !
on 26. January 2025, 12:46 by Andrewsarchus
Amazing puzzle! The interactions between the grids led to some very interesting logic. Brilliant setting!
on 26. January 2025, 12:32 by Piatato
Absolutely wonderful puzzle, so rich in charming and fun logic! Nothing too monstrous, just a long and beautiful journey :-D
