Balance = Entropy
(Published on 12. February 2022, 23:59 by JeremyDover)
A puzzle with Raumplaner
(image credit to Riffclown...thanks!)
Rules
Normal sudoku rules apply.
Entropic lines: Any set of three sequential cells along an entropic line must contain a low digit (1-3), a middle digit (4-6), and a high digit (7-9). 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.
Balance rules: Each circle is the fulcrum of a balance, whose balance arm is a straight line passing through it. The digits in the squares are the weights hanging from the balance. If the line that passes through a fulcrum is horizontal, then the two sides are balanced; if not, the lower side is heavier. Balance calculations are made using total torque: a weight three cells away from a fulcrum (cells can be counted horizontally on a horizontal balance arm, diagonally on a diagonal balance arm) 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. An example balance calculation is available. Please note that there are two separate balances in this puzzle: the main one with fulcrum at R1C5, and a smaller balance with fulcrum in R5C8.
Solution code: Solution code: Row 5 followed by column 8 (18 digits, left to right, top to bottom, no spaces/commas).
Comments
on 24. October 2024, 18:53 by The Book Wyrm
Great puzzle! Flowed nicely, and the balances interacted well with the entropic lines.
on 22. July 2023, 01:49 by SpicyShark
Great puzzle! I was pleasantly surprised at how well this flowed given the difficulty rating. A steady pace of fun realizations and deductions.
on 10. June 2023, 07:37 by annaswan
This puzzle was incredible! I always enjoy entropic lines, and the interplay they had with the fulcra was ingenious. I had so much fun solving this. Despite the complexity and originality of the ruleset, it was also a very intuitive solve. I will admit that it took me a few minutes to grasp how the fulcra worked, but once I did it all flowed beautifully.
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JeremyDover: Thank you so much for your kind words!
on 1. March 2022, 21:49 by ough
I was having SO MUCH difficulty with this until I realized this was entropic LINES, not the original entropy constraint by Mad-Tyas. Elegant implementation of two logic puzzles that, once you get the hang of the rules, isn't too much harder than a fairly clever killer, but still, the implementation is the most impressive part.
on 21. February 2022, 22:03 by biscuitboy
I loved this puzzle! Very original idea. It was challenging at times but I still found it quite accessible despite the complex rules :)
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JeremyDover: Thank you for your kind words. Glad it seems to have been a pleasant challenge!
on 20. February 2022, 20:00 by mishaaku
Wonderful chain of logic. I enjoy that there are always myriad places from which to glean more information.
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JeremyDover: Thank you so much! Hope you enjoyed :-)
on 20. February 2022, 09:05 by DomL
I love puzzles like this that combine two variant rules and make it visually pleasing all in one package.
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JeremyDover: Thanks so much for the compliments!
on 20. February 2022, 03:12 by ArticulateAardvark
My first completed 4 star puzzle! Very fun!
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JeremyDover: Congratulations! Very glad you enjoyed.
on 19. February 2022, 07:36 by Phistomefel
I really enjoyed this puzzle. It had a lot of small 'Aha'-moments and the concept of the scales feels fresh and interesting. Thank you for setting it, JeremyDover and Raumplaner!
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JeremyDover: Thank you so much for the kind words!
on 18. February 2022, 18:38 by pianobarry87
Wow! This tested all parts of my brain. Lovely puzzle!
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JeremyDover: Thank you for the kind words!
on 18. February 2022, 11:18 by Mox
I should have looked at the example instead of messing up 2 times - lesson learnt! That was good fun, thank you.
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JeremyDover: Thank you for the kind words...glad you had fun!
on 18. February 2022, 07:04 by Qril
God, what a crazy solve. Resolving the big scale was an absolute pleasure, I had a stupid grin on my face the whole time. Excellent fun!
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JeremyDover: So glad you enjoyed...thanks for the kind words!
on 16. February 2022, 22:00 by Wonderment
It took me a few tries, but in the end it was very interesting and satisfying. Thank you.
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JeremyDover: Great! Hope you enjoyed.
on 14. February 2022, 22:39 by Krokant
The entropy constraint and the scales complement each other nicely. This is a lovely puzzle. :)
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JeremyDover: Thank you so much for your kind words!
on 13. February 2022, 18:55 by wilsig
What a brillant Puzzle! Congratulations!
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JeremyDover: Thanks very much for the kind words!
on 13. February 2022, 18:14 by Prince Joffrey
Wow!
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JeremyDover: Thanks for the shout out!
on 13. February 2022, 01:20 by zegres
Very neat and original idea! Really enjoyable!
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JeremyDover: Thank you so much for the kind words!
