Sandwich Fillomino #1 - Vicious Circle
(Published on 19. March 2021, 10:00 by Mark Sweep)
Here is a Fillomino variant that I have not really seen before (which does not mean it has not been done before though). I found it particularly hard to force much at the start of the solve, so the break-in can be quite hard. Because of this, I put it up at 5 stars as a warning, but it may well be 4 stars. Feel free to leave a hidden comment for a hint, as it will get a better flow after the break-in. Enjoy!
Rules
Fill the grid with regions containing numbers indicating their size. No regions of the same size may touch orthogonally. Clues outside the grid indicate the sum of numbers between the unique segments of highest numbers and lowest numbers in the row or column. Question marks are a non-zero integer.
Example
A dash (-) means there is no valid sandwich clue in that row/column. Note how in row 5, there is no valid clue, because even though the highest numbers in the row (the 8s) are from the same region, it is unclear which one would have to be chosen for the sandwich because they are separated. This is not a problem in for instance column 1, where all 8s in the column are connected within the column and thus form a single, unique segment of largest digits.
The puzzle
Solve on Penpa
Solution code: Digits in row 5 (left to right) and column 5 (top to bottom).
Comments
on 18. December 2022, 16:37 by peacherwu2
Absolute genius! Thank you so much!
on 10. November 2022, 19:18 by polar
I'm not a big fan of sandwich normally, but I thoroughly enjoyed this twist on it. Brilliant puzzle - thanks!
on 13. December 2021, 00:50 by harrison
Very Very cool puzzle. Needs and deserves more solves!!
on 22. November 2021, 20:08 by Statistica
WOW. Finally I found the right opening... Very clever til the end!
on 17. November 2021, 12:11 by Mark Sweep
Changed title from 'Vicious Circle (Sandwich Fillomino)' to 'Sandwich Fillomino #1 - Vicious Circle'
on 28. July 2021, 17:55 by Mark Sweep
Updated tags
on 25. March 2021, 17:57 by Mark Sweep
Thanks Wessel :)
on 21. March 2021, 20:42 by Wessel Strijkstra
One awesome puzzle :D
on 19. March 2021, 23:54 by Mark Sweep
Thanks for your nice comments MagnusJosefsson and Jesper! Your excellent Fillomino variants actually inspired me to try one with sandwich @Jesper, so thank you for that!
on 19. March 2021, 16:30 by Jesper
Very nice! It is no secret that I like Fillomino variants, and I really appreciate when other authors with new interesting ideas help to push and expand this category of puzzles.
on 19. March 2021, 14:54 by MagnusJosefsson
Awesome puzzle! Very interesting and exciting. While the break-in was perhaps the hardest part, I found it persistently challenging and enjoyable all the way through.
