Pointing Pairs Fillomino
(Published on 16. April 2021, 10:00 by Mark Sweep)
Here is another Fillomino variant, based on a ruleset used in Pointing Digits, which is one of the first puzzles I posted on this portal. This puzzle is quite a tough one and might be harder than 4/5, so I promise I will try to make the next few Fillomino ideas I have somewhat easier. Enjoy!
Rules
Standard Fillomino rules: Fill the grid with regions. A region of size N is filled entirely with the digit N. No regions of the same size may touch orthogonally.
In addition, the arrows indicate ‘pointing pairs’. A cell with an arrow that contains the digit N points at the digit N at a distance of N in the arrow’s direction. There is also a negative constraint: if a pair of two digits N exists that are N cells away from each other, at least one of them should have an arrow pointing at the other.
Note: this distance is only counted in a straight or diagonal line, and thus not in a taxicab or anti-knight kind of way.
Solve on Penpa
Solution code: Row 6, column 6 (both digits for two-digit numbers)
Comments
on 28. July 2021, 17:56 by Mark Sweep
Updated tags
on 5. May 2021, 21:38 by SudokuExplorer
Absolutely wonderful puzzle!!! Very interesting fillomino variant making good use of the positive and negative constraints. The end-game was very fun to work out and there were many aha moments throughout the solve. Thanks so much for making this gorgeous puzzle! :-)
--- Thank you very much! It is nice to hear you had so much fun with it.
on 19. April 2021, 10:26 by Aspartagcus
Fantastic puzzle, really kept you on your toes. Testing the puzzle before it was released, I thought it was broken three times until I noticed my errors. Very interesting ruleset, and very well executed. I enjoyed it a lot, thank you!
--- Thank you for your kind words, and for the test ofcourse!
on 18. April 2021, 19:43 by Statistica
Nice idea, great puzzle. Thanks!
--- Thank you for solving it!
on 17. April 2021, 20:28 by marcmees
very nice.
--- Thank you!
on 17. April 2021, 10:59 by MartinR
Enjoyable solve, tricky ending, but that made the "a-ha" moment very satisfying:)
--- Thank you, I'm glad to hear the ending was rewarding as well.
on 16. April 2021, 19:54 by MagnusJosefsson
Great puzzle! The ending was quite tricky, but satisfying once you find the right logic.
Curiously, I have also been playing around with a Fillomino concept with 8-way arrows and negative restrictions (but with completely different logic). I'm not sure yet if that concept will play well enough that I will post a puzzle, but I must say the ruleset you used here works really well.
--- Thank you! Apparently we have been thinking about very similar Fillomino variants recently. I'm curious about yours now, hopefully it will make it to this portal.
on 16. April 2021, 14:55 by Jesper
Very nice! Great use of the negative restriction. I think the difficulty level is quite alright (not extreme), though it is easy to make mistakes in this kind of puzzle, if you are not careful. I particularly liked the endgame.
--- Thanks Jesper! Good to hear that it was not as difficult as I thought it would be.
