Just the Tip (FOW arrows)
(Published on 18. August 2023, 21:29 by gdc)
This puzzle features plenty of arrow tips peaking out from the fog. Note the rotational pairs rule (example below) which is important for the break-in.
- Fog of War: The grid is covered in fog. Placing digits correctly reveals clues in the surrounding 3 by 3 area.
- Digits along an arrow sum to the digit in that arrow's circle.
- All arrows sum to a single digit number. Arrows cannot intersect, branch or overlap and no cell can belong to multiple arrows. However, circles can have multiple arrows attached to them.
- When the grid is rotated 180 degrees, the digits in the corresponding cells sum to 10 (eg. the digit in R2C3 and R8C7 sum to 10).
Rules Clarification
Here is an example of "rotational pairs" that add up to 10.
I decided to be very specific with the wording for arrows overlapping/branching etc. Some of those specifics are not necessary for the solve but included to reduce the cognitive load of the puzzle. The following arrow-shapes cannot occur based on those rules.
Hints
The following hints are sorted according to the (very linear) solve path. If you're not sure which one is relevant, reveal them in order by clicking on them to avoid spoiling future deductions.
- The rotational pairs allow you to place a 5 in the center of the grid.
- The right arrow in Box 8 needs to be exactly 2 cells long because the left arrow needs a 3 on it.
- The left arrow in Box 8 needs to be at least 3 cells long because R9C3 cannot be an 8.
- The arrow in box 3 needs a 2 on it. Where does it's counterpart (8) go in box 7?
- Putting 5 in R7C1/R3C9 would break one of the arrows it's on.
- R3C8 + R3C9 = R5C2
- There is a 578 triple in Row 4.
Difficulty
I posted this puzzle on the CtC discord for feedback with the hints and got a good amount of test-solves (thanks everyone). Therefore, I assume the puzzle has a smooth flow but don't arrest it for talking math every now and then.
Solution code: Row 1 (9 digits)
Comments
on 24. September 2024, 02:06 by seh_bas
tricky but not all too hard, thanks for the puzzle gdc!
on 16. September 2023, 00:27 by waffles_the_dog
I really enjoyed this puzzle. I found the break in cute, and the subsequent flow really nice.
on 27. August 2023, 09:48 by Nemefish
Overall smooth puzzle. For me there was one sticking point about halfway through. The fog of war mechanic does a great job of guiding the solver around the grid
on 24. August 2023, 20:17 by Nemefish
Overall smooth puzzle. For me there was one sticking point about halfway through. The fog of war mechanic does a great job of guiding the solver around the grid
on 24. August 2023, 06:05 by Nordy
Very clever and enjoyable!
on 19. August 2023, 22:58 by HumanBirdsong
Your puzzles are consistently excellent, gdc! Tricky, but satisfying. Well done!
on 19. August 2023, 03:32 by gdc
add to rules: "all arrows sum to a single digit number"
on 19. August 2023, 00:57 by antiknight
Interesting idea and not too difficult! Cool fully covered grid with fog ^^
on 19. August 2023, 00:06 by VitP
nice!
intricate interactions between the additive and subtractive properties of arrows. the "rotation" plays into that.
on 18. August 2023, 23:59 by Fisherman
This setter, GDC, has my vote for teacher of the week. The rules clarification diagram showing the X 10-X symmetry is very nice. I hope he will not mind if others use it.
---
Haha! Thanks! Feel free to reuse the images under "rules clarification". When I started solving, I always wished for those, so I made them :)
on 18. August 2023, 23:41 by PS3UDONYM
Very fun idea/ruleset!
Didn't need hint(s). Regarding hint 6: not sure if I would have understood when the grid was 'empty' (of course hindsight I see it).
---
Thanks! Yes hint 6 is a very odd implication of the ruleset :)
on 18. August 2023, 22:40 by sujoyku
Thank you for this entertaining FOW puzzle, gdc! I had to use the penultimate hint. Even after I read it I first had to get my head around why its logic holds true and I think it is a pretty cool argument. Thank you for setting and sharing!
---
Thanks! I used this short form for hint 6 because I think discovering on your own why it's true is just so delightful. That "distance preserving" argument can also be used to prove hint 5 very elegantly.
on 18. August 2023, 22:22 by gdc
fix solution code
