Balance of Power
(Published on 26. June 2022, 14:40 by Raumplaner)
The next puzzle with JeremyDover and the final puzzle from the Entropic Power Lines Pack. This puzzle uses a similar ruleset as our puzzle Balance = Entropy
If you are new to entropic lines we recommend to start with an easier puzzle of this series or watch this video by BremSter first.
Rules
Normal sudoku rules apply.
Entropic lines (orange): Any set of three sequential cells along an entropic line must contain a low digit (1,2,3), a middle digit (4,5,6), and a high digit (7,8,9). An entropic line of length 2 may not contain two digits from the same low, middle or high rank. Digits may repeat on a line, if allowed by other rules. All lines in the puzzle are entropic; coloration is used solely to distinguish between entropic lines that intersect.
Kropki rules apply: Cells separated by a white dot must contain consecutive digits. Cells separated by a black dot must have digits in a 2:1 ratio. Not all possible dots are given.
Balance rules: Each bullseye is the fulcrum of a balance, whose balance arm is a straight line passing through it. The digits in the large circles are the weights hanging from the balance; in this puzzle, you must use the digits 2-9, each exactly once, as weights. Balance calculations are made using total torque: a weight three cells away from a fulcrum contributes thrice the torque of the same weight hanging one cell from the fulcrum. The lines are massless and do not affect the torque calculation. All balances in this puzzle have equal torque on each side.
Example for torque calculation
SudokuPad
This is puzzle #12 from the series with JeremyDover on entropic lines.
previous puzzle (#11)
next puzzle (#13)
Solution code: Row 2 (from left) and column 5 (from top - 18 digits in total):
Comments
on 30. September 2022, 22:15 by KyleBaran
A very wonderful puzzle!
Had to restart a few times because of a misunderstanding between weight and torque but got it sorted out. If you solve it properly, probably 3.5/5 for difficultly. Good solve path.
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Many thanks. (Raumplaner)
on 12. September 2022, 15:48 by Raumplaner
Added link to the next puzzle in the series.
on 14. July 2022, 17:54 by DerMaddi
Danke für die Puzzle! Entropie Linien haben sehr viel Spaß gemacht und das mit den Gewichten ist auch ein sehr interessantes Konzept.
Hab irgendwie die falschen tuple für die unteren Gewichte ausgeschlossen und hing dann ewig lange fest bis ich die Gewichte brute forced habe, weil ich dachte das kann doch nicht sein! Wenn man das macht, wird das Puzzle vom Schwierigkeitsgrad aber eher eine 2-3/5.
on 28. June 2022, 23:22 by Raumplaner
Example for torque calculations added.
on 28. June 2022, 11:27 by Bankey
A clarification please : for calculating the distance of a weight from the fulcrum, only the horizontal distance till the cell it hangs from is to be counted, or also the vertical "drop" from the hang point?
For example, would the weight in r4c1 be taken as 3 away (or 4, if we add the 1 from r3c1 to r4c1). If it is 3, that would mean that the distance would be the same if the weight in r4c1 were instead in r5c1?
Thanks !
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Hey Bankey. Only the horizontal distance from the fulcrum is relevant for the torque calculation. You can find some examples in the linked puzzle "Balance = Entropy" - Raumplaner
- Thanks, Raumplaner.
on 26. June 2022, 22:02 by bansalsaab
What an idea. Thank you so much for brilliant construction. My solution wasnt elegant but able to solve it.
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Many thanks. There is an elegant solution to be found:) - Raumplaner
