Revenge of the Fillometers
(Published on 2. August 2023, 11:10 by zzw)
You may want to try my earlier puzzle Invisible Fillometer as an easier introduction to the same ideas used here.
Normal fillomino rules apply: divide the grid into orthogonally-connected regions such that regions of the same size don't share an edge. Each cell within a region contains a number equal to its size.
Thermometers: there are a number of invisible thermometers that travel along paths of orthogonally-adjacent cells without branching or crossing. Along each thermometer, numbers in cells are strictly increasing. Each region can be visited by at most one thermometer, and in at most one cell. The solution must use the fewest number of these thermometers such that all other rules can be satisfied.
Cells with a small square are visited by a thermometer. The other cells in the thermometers, the number of thermometers, and the directions in which they increase must all be deduced by the solver.
NOTE: to clarify the "fewest number of thermometers" rule, and to perhaps make the solve less frustrating, there is no trick here where using too few thermometers will make the puzzle unsolvable at the very end. The correct, minimal number of thermometers can be determined just by looking at the lengths of paths needed to cover all the squares.
Solution code: Digits on the main diagonal (top left to bottom right) followed by the anti diagonal (bottom left to top right)
Comments
on 16. May 2024, 01:15 by Niverio
Very lovely puzzle! After you grasp what "minimal" means it flows amazingly well.
on 11. November 2023, 21:43 by Gliperal
Brutal puzzle. Not that hard to intuit the solution, but actually proving it is a nightmare. I can see where you're coming from with the rules, but I would still just change it to explicitly give the number of thermometers used and not really lose any of the solve path.
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I'm not sure how that information would help much beyond the "note" at the end of the rules. Like you said, finding a number that could work isn't too hard, it seems to me that the hard/annoying part is allocating squares to thermometers, and proving that there's only one way to do it.
Regardless, I see this puzzle as a failed experiment. I was really happy with it originally but I long ago gave up hope of it getting a good rating (if it ever even gets one at all).
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I suppose the point I am trying to make is not that it would make the logic any easier, but that it would make understanding the rules a lot less confusing. Since you don't see much of that phrasing on the portal, I suspect that alone turned some people away from trying the puzzle.
on 12. August 2023, 23:35 by filuta
I have to say I have a bit mixed feelings about this puzzle. I am among the people who (repeatedly) get genuinely confused by ambiguous rules. The clarifying note about in the end made me understand the setters intention, even though the rules can still be understood in different ways in my opinion. I understand though why the setter didn't want to formulate everything too precisely, since that would spoil the break in idea too much. Also unless I missed something simple, a truly formal proof of the distribution of the thermometers would require a bit too much of case checking.
All that being said, I really loved the idea and the implementation is absolutely flawless and a true joy to solve. Certainly worth trying.
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Thank you very much for your kind words! I was quite happy with this puzzle, yet it seemed to languish. One good review (even with significant caveats!) is really all I need :) And if there's any way you can see to clarify the rules, that would be greatly appreciated.
The break-in is definitely the hardest part, and does involve a lot of case checking if you want to be rigorous. I actually wrote two programs to prove this correct while setting, and one was just for the break-in, assigning squares to thermometers...
--zzw
on 7. August 2023, 18:40 by zzw
Clarify rules, add a link to easier version of puzzle
