Thermo variant #23: Incomplete Maximal Thermos
(Published on 23. December 2021, 14:00 by djorr)
I've made a few thermo variants. All are standard thermo sudokus + an extra rule. Check out the others using the following link:
Thermo Variant Series puzzles
If you enjoy "Maximal Thermos", I invite you to look at the others with the same (or similar) constraint:
14. Maximal Thermos
19. Maximal Thermos 2
21. All Maximal Thermos are Given
23. Incomplete Maximal Thermos
26. Maximal Thermos 3: Stubs
31. All Maximal Thermos are Given 2
35. Maximal Thermos 4ever
Rules: Normal sudoku rules apply. Along thermometers, digits must increase from the bulb end.
Variant: All of the thermos in the grid are maximal thermos but some have to be completed first!
The thermos that are already maximal thermos satisfy two properties:
(1) The digit in the bulb equals the length of the thermo
(2) The thermo cannot extend its tip by a king's move to a non-thermo (i.e., white) cell to create a larger thermo.
The thermos that need extended must therefore satisfy the following:
(1) The digit in the bulb is 1 larger than the thermo length currently provided.
(2) There exists at least one cell that is a king's move apart from the current thermo's tip such that the thermo can extend by one. And, once this thermo extends, it can no longer extend itself further to yet another digit that is a king's move apart from the extension.
It is up to the solver to determine which thermos are completed maximal thermos and which thermos are incomplete.
For example, a valid grid could look like this.
The colors indicate the extension of the thermo. The 6 in r4c8 could not be the extension of r3c9 because it would see the 8 above it in r3c8 and that would mean it could extend again. So we can take the 8 in r3c8 as the extension. In box 9, for similar reasons, we cannot take the 7 in r7c8 as the extension for r8c9. However, another valid extension for r8c9 is the 8 in r9c9. It is not necessary for the extensions to be unique. The thermo beginning in r9c7 is valid and complete, as long as there is no 9 in r7c5 or r8c5.
F-puzzles link: https://f-puzzles.com/?id=yhcnvaz3
CTC link: https://tinyurl.com/vwu2kwsx
Thermo Variant Series puzzles
If you enjoy "Maximal Thermos", I invite you to look at the others with the same (or similar) constraint:
14. Maximal Thermos
19. Maximal Thermos 2
21. All Maximal Thermos are Given
23. Incomplete Maximal Thermos
26. Maximal Thermos 3: Stubs
31. All Maximal Thermos are Given 2
35. Maximal Thermos 4ever
Rules: Normal sudoku rules apply. Along thermometers, digits must increase from the bulb end.
Variant: All of the thermos in the grid are maximal thermos but some have to be completed first!
The thermos that are already maximal thermos satisfy two properties:
(1) The digit in the bulb equals the length of the thermo
(2) The thermo cannot extend its tip by a king's move to a non-thermo (i.e., white) cell to create a larger thermo.
The thermos that need extended must therefore satisfy the following:
(1) The digit in the bulb is 1 larger than the thermo length currently provided.
(2) There exists at least one cell that is a king's move apart from the current thermo's tip such that the thermo can extend by one. And, once this thermo extends, it can no longer extend itself further to yet another digit that is a king's move apart from the extension.
It is up to the solver to determine which thermos are completed maximal thermos and which thermos are incomplete.
For example, a valid grid could look like this.
The colors indicate the extension of the thermo. The 6 in r4c8 could not be the extension of r3c9 because it would see the 8 above it in r3c8 and that would mean it could extend again. So we can take the 8 in r3c8 as the extension. In box 9, for similar reasons, we cannot take the 7 in r7c8 as the extension for r8c9. However, another valid extension for r8c9 is the 8 in r9c9. It is not necessary for the extensions to be unique. The thermo beginning in r9c7 is valid and complete, as long as there is no 9 in r7c5 or r8c5.
F-puzzles link: https://f-puzzles.com/?id=yhcnvaz3
CTC link: https://tinyurl.com/vwu2kwsx
Solution code: Row 3 Column 3 (18 digits, no spaces)
Last changed on on 13. February 2022, 17:23
Solved by tenaliraman, kublai, butch02, MagnusJosefsson, zuzanina, rimodech, Mikemerin, larinae, Vebby, sandmoppe
Comments
Last changed on 23. December 2021, 16:38
on 23. December 2021, 16:29 by kublai
Note to self: Non-thermo, Non-thermo, Non-thermo.
Great puzzle!
.
.
Hahaha yes indeed, non-thermo cells! Glad you enjoyed it :) this is definitely the toughest (or close to the toughest) puzzle in the maximal thermo series, for sure!
