Archery Target
(Published on 24. April 2022, 15:48 by Nahileon)
Normal Sudoku rules apply.
The grey line in the central box is a thermometer. Digits along that thermometer must increase from the bulb to the tip, but the positions of the bulb and the tip are hidden.
Starting from the position of any 9 on one of the three outer rings and adding up the digits along that ring until you hit another 9, must always give the same total.
Example: With this arrangement of 9s, all of the green lines would have to add to the same total.
Hint: (Not every ring has to have a 9 in it. Think about what that means in terms of the rules.)
Solution code: Row 5 in the Sudoku.
Comments
on 25. January 2025, 19:07 by TheNineElements
Solve Time 101:01
I rated this 5/5 difficulty.
Wow that was an extremely hard puzzle but also very elegant and rewarding. This is definitely one of the hardest puzzles I have ever solved, but it was worth the effort in the end. There was a lot of arithmetic involved, and I ended up jotting down several notes to keep track of my findings. It took quite a while for me to complete, but it was worth it!
The break-in, expectedly, was BY FAR the hardest part of the puzzle for me. From the beginning I had assumed something that was untrue and it set me back for quite a while, as my math just wasn't working no matter what I tried. I had assumed the logical negation of the statement provided in the hint (will not state it here to avoid spoilers), and I spent around 40-45 minutes just totally stuck. I nearly gave up on the solve, but I'm glad I persevered! I eventually took a step back and re-read the rules carefully. I realized that my assumption was not stated by (or necessitated by) the rules.
After I figured that out, I was finally able to begin progressing and at least make some useful pencilmarks. That is where I the 'break-in' phase ended for me, and it was definitely 5/5 difficulty - and on the harder end for other 5* puzzles I have done.
The midgame was slightly easier (still very hard), as I had learned a lot while experimenting early on in the solve. Once I determined the sums between '9's, the puzzle finally began 'clicking' for me. The placement of the givens was very clever, and once I realized how to use them, the rest of the puzzle felt smooth and I seemed to make steady progress until completion.
The center-box thermo logic was a (pleasantly) straightforward element once I was able to use it. I thought the idea was clever and the placement of the bulb was a neat way to disambiguate the final digits. I don't think I have ever solved a puzzle with both a solver-deduced bulb placement and direction (given it is a loop), but it was cool and a rewarding end to my solve. The mid-game to endgame phase(s) started out 5/5 difficulty, but once I finally grasped the big ideas the actual sudoku/ring digit logic was around 4-5/5 difficulty.
Overall, this was undoubtedly 5/5 difficulty for me. I have no idea how you came up with this idea and executed/demonstrated it in such an elegant way, but it is definitely one of best and hardest puzzles I have solved. Very unique and challenging sudoku, thanks for sharing!
on 4. July 2022, 17:36 by Niverio
What an arithmetic journey.
on 26. May 2022, 22:29 by michelkraemer
Wow! This is probably the hardest puzzle I've ever solved. Although in hindsight, the solve path is extremely clear and logical. What a beautiful puzzle!
on 24. May 2022, 18:22 by cristophermoore
Amazing. This is the kind of puzzle I like to return to over the course of a few days, as I understand a little more each time. What a beauty!
on 18. May 2022, 22:11 by wpolly
A 51-minute solve for this extraordinary puzzle. The calculation for the "sums between 9s" is absolutely beautiful.
on 29. April 2022, 03:37 by Crusader175
This is definitely count as one of the best puzzle I've ever solved. That break-in was insane but absolutely brilliant!
on 26. April 2022, 22:05 by Qodec
Goodness me what a ride. Whew!
on 26. April 2022, 11:43 by Nahileon
I've added a hint for everyone who gets stuck at the very beginning.
on 25. April 2022, 09:00 by polar
Took me a little while to figure out the start, but once I (eventually) did, it was a joy to solve :)
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It is a bit tricky. Thanks :)
on 25. April 2022, 06:32 by kolot
This puzzle is a gem!
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Thanks!
on 24. April 2022, 23:23 by noname1477
Okay, I normally don't comment here, but this masterpiece deserves it! This is probably in the top five puzzles I've ever solved, both in terms of difficulty and quality. Thanks for this 90-minute fight and the very... precise phrasing of the rules, which tripped me up for like 20 mins. Loved it!
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Thank you! I'm glad you enjoyed the challenge.
