Dynamic Quiver
(Published on 22. November 2023, 18:41 by Niverio)
Rules:
Sudoku: Place the digits 1-9 into each row, column and outlined box without repeats.
Arrow: Digits along an arrow sum to that arrow's circle. Digits can repeat on arrows if permitted by other rules.
Ambiguity: Arrows stemming from R4C5 are normal arrows. All other arrows in the grid have an additional line constraint assigned to them from the list below. Which arrow corresponds to which constraint must be deduced by the solver. The assignments are unique, so it is possible to map each constraint to a unique arrow. The circle of the arrow counts as part of the line for the constraints.
Hidden arrow: 7 of the 8 special arrows are given in the grid. The 8th arrow's corresponding constraint and it's location must be deduced by the solver. Following information is known about this hidden arrow:
- It is a 4 cell arrow (1 circle - 3 summed digits)
- It doesn't cross or overlap any existing arrow.
- All cells of the arrow are found in a single box, and the box number of the arrow doesn't appear on the arrow. (So if the arrow is in Box 6, the arrow doesn't have a 6 on it.)
List of constraints:
Entropic Line: 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).
German Whispers: Adjacent digits along a German Whisper line differ by at least 5.
Kreska Line: Adjacent digits along a Kreska line must either be consecutive, or have a ratio of 1:2. Digits along a Kreska line cannot repeat.
Lockout Line: Digits on a lockout line cannot be between or equal to the digits on the diamond endpoints. Digits on the endpoints must differ by at least 4.
Modular Line: Any set of three sequential cells along a modular line must include one digit from [1,4,7], one digit from [2,5,8] and one digit from [3,6,9].
Nabner: Values along a Nabner line form a set of non-consecutive, non-repeating values in any order (e.g. if a cell value of 3 appears on a Nabner line, then the values of 2 and 4 cannot appear).
Renban: A Renban line contains a set of consecutive, non-repeating digits in any order.
Ten Line: Each line consists of one or more contiguous groups of cells, each of which sums to 10. These groups of cells cannot overlap; every cell is part of one group. Digits may repeat on lines and even within sums.
Puzzle Links:
Solution code: Digits along the hidden arrow (top to bottom and left to right, including the circle), followed by Column 2, no commas or spaces.
Comments
on 1. December 2023, 01:55 by Playmaker6174
Great fun puzzle! Very satisfying to tie all of the clues together :)
on 24. November 2023, 13:25 by Niverio
@peacherwu2 @simoons @rameshsrivats The givens 2 and 4 were not present in the first version of the puzzle, without them, the rule was needed to break the symmetry of the grid. Although the extra givens lead to a logic which allows for the placement of the hidden arrow, I don't mind having divergent paths that lead to the same logic so left the rule as is. Hope this did not take any enjoyment out of the puzzle for all of you, and thanks a lot for the comments!
on 24. November 2023, 11:59 by peacherwu2
Just curious how is the rule about box number used.
on 24. November 2023, 03:07 by cam
A very intense adventure! It's extremely overwhelming at the start, but as you slowly chip away, the beautiful piece of art is revealed. It felt less like a challenging puzzle and more like a guided adventure. This is my favorite puzzle so far this month :)
on 23. November 2023, 13:15 by simoons
Very enjoyable puzzle, thanks!
I agree with rameshsrivats about the box number rule: I used a nice piece of logic to avoid using it, which feels better than only using the rule constraint.
on 23. November 2023, 03:03 by rameshsrivats
Extremely enjoyable. I could be wrong, but I think I didn't need the rule of the box number not appearing in the hidden arrow.
on 22. November 2023, 23:55 by Myxo
Lovely puzzle! Very smooth and fun :)
on 22. November 2023, 23:24 by vitaminz
Amazing puzzle, and not too terribly difficult. These types of rulesets (assign constraints to "lines") always seem quite daunting to me, especially when the (seeming) level of symmetry is so high. It takes some patience and thinking about each constraint but the path was surprisingly clear. Well done.
on 22. November 2023, 20:23 by heliosfant
This sounds interesting. Since my English is not so good can you confirm or negate the fact that each constraint does only appear once? Or can several arrows be e.g. a whisper line or only one arrow?
~ Hello helios! There is no limitation on how many times a constraint appears, some arrow configurations may fulfil more than one constraint. The important thing is that if you wrote all 8 constraints into a list and the 8 arrows into another, you would be able to assign each constraint to each arrow in some way. So there is at least one of each, but technically more can appear. Hope that clarifies!
on 22. November 2023, 19:39 by MicroStudy
only OGs remember dynamic formations
on 22. November 2023, 19:09 by Qodec
Challenging and loads of fun, thanks!
on 22. November 2023, 18:44 by lerroyy
Very cool puzzle, thanks!
