It's Getting Hot in Here!
(Published on 17. January 2024, 19:34 by BenTen)
Rules:
- Place the digits 1-9 once each in every row, column, and 3x3 box.
- Draw a path that starts and ends at a blue spot. The path moves orthogonally from cell to cell. It cannot branch or use the same cell twice.
- The path must cross through the green circles, but must not enter shaded cells.
- Parts of the path have been given (shown as blue lines).
- Thermo-Region Sum Line: The sum of the digits along the path in each 3x3 box strictly increases by one in each new box it enters, from one end of the path to the other. (For clarity, if the path visits the same 3x3 box more than once, then the sum value on each visit will be different).
f-puzzles link
CTC app link
Solution code: Row 5.
Comments
on 19. January 2024, 14:59 by MartinR
The break-in was a nice a-ha moment when the implications of the rules were seen.
on 19. January 2024, 09:31 by Allagem
What an utterly unique and fascinating break-in! At first, I struggled to find any meaningful deduction because it seemed like there were so many possibilities to consider and I wondered how you could ever prove the solution was unique. I nearly gave up but then finally noticed a tiny assertion I could prove about the way the path worked. Alone it wasn't enough, but then I found another tiny assertion, and then another, and another, and eventually I had just barely enough evidence to start sketching out some logic and slowly but surely each step became clear. The beginning of the puzzle is considerably harder than the end, but the logic is airtight and remarkably beautiful. Phenomenal puzzle BenTen!
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Thank you for your lovely comments Allagem. I'm glad you persevered at the start and saw the puzzle to the end.
on 18. January 2024, 23:55 by matzrh
I agree, great puzzle. Figuring out the path had just the right level of difficulty for me. Challenging, but feasible.
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That's great! Thank you for the positive feedback. :)
on 18. January 2024, 14:36 by FischmitFahrrad
Great puzzle! Loved that every single sum of the line contributes to the solve until the very end.
I found the initial pathfinding quite difficult, but that part had some stunning logic nonetheless. Afterwards flowed very nicely!
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Thank you FischmitFahrrad. I'm glad you got over that hurdle at the start and very glad you enjoyed it.
on 18. January 2024, 01:01 by BenTen
Minor edits made.
