Double Dip
(Published on 21. June 2022, 19:38 by zetamath)
Jay Dyer Deconstruction rules apply: Place nine disjoint 3x3 regions into the grid. Each region must contain the digits 1-9 once each. The digits 1-9 may not repeat within a row or column. Cells not within regions are to be left empty.
The clues in the grid are double arrow clues. The digits along a line have the same sum as the digits at either end of the line. For example, if the circles contained 4 and 8, the line could contain 1227.
If a circle or line segment on a double arrow clue is not a part of a region, it simply does not count. For example, if one of the circles of a double arrow clue is empty and the other contains an 8, the line could contain 134. In essence it becomes a single arrow clue.
No double arrow clue is left entirely empty. In other words, anywhere that a line connects two circles, at least one cell of the line and at least one of the two circles is part of a region.
Lastly, if you have not worked with these deconstruction rules before, it is a consequence of the stated rules that each cell marked with an asterisk in the image above is part of a region in the final solution. The asterisks do not appear at the solve link below.
Have fun, leave a comment if you enjoy the puzzle!
Solution code: Row 3 followed by Column 3. Write X for cells which do not contain a digit.
Comments
on 26. April 2024, 05:16 by Mr.CHEN
I hope these link can add answer verification so that the timer can stop in time to determine the record and prevent errors.
on 3. May 2023, 12:30 by OldCaptainWZJ
Enjoyable and approachable if you have experienced deconstruction puzzles. I was not fast but I enjoy slowly but surely reaching the final solution!
on 17. October 2022, 19:08 by ddx2407
That one was a challenge!
There was a part I was sure I broke the puzzle, until I finally found the way out.
Thank you, zetamath, for a very thorough mental workout. I enjoyed it a lot.
on 5. August 2022, 17:22 by StephenR
Lovely doubly jubbly stuff, thank you.
on 9. July 2022, 04:59 by Agent
Great puzzle! I liked how the regions were being built continuously as the puzzle unfolds.
on 3. July 2022, 10:59 by Sumyrda
Interesting, I usually tend to rate puzzles slightly higher than this community, but this was more a 3 than a 4 for me on difficulty. Maybe it's because I got the break in quite quickly and just kept applying the same kind of reasoning, so I never really felt stuck.
Very enjoyable puzzle.
on 25. June 2022, 07:47 by Crusader175
Very nice puzzle! Flow very nicely.
on 23. June 2022, 00:31 by Christounet
Very nice ! Very well balanced, I love the fact you need sudoku logic to delineate the regions progressively and vice versa. Great puzzle again !
on 22. June 2022, 20:59 by Snookerfan
Great puzzle! A little bit easier than usual. Very lovely and intricate logic.
on 22. June 2022, 19:02 by farodin64
Not easy for me, but with a lot of fun, thx!
on 22. June 2022, 11:13 by twobear
Very nice! It actually feels a bit more approachable than some of your double arrow puzzles :) thank you!
on 22. June 2022, 09:38 by henrypijames
When you say "it simply doesn't count", do you mean it counts as 0, or as if the cell isn't part of the grid? If it's the former, then R10-11C1-3 can't be all empty because the line inside doesn't sum up to R9C3. But if it's the latter then those cells can be all empty because the line inside simply doesn't matter and can be ignored.
EDIT: Having solved the puzzle, it seems "counts as 0" is what you mean, and I suggest you rephrase the rules that way as it's much clearer.
[Isn't this completely clarified by the rule that immediately follows? I worried "counts as zero" would be confusing with the next rule.]
<<<
No, "the next rule" clarifies what happens to an empty circle, but no rule clarifies what happens to empty line cells.
Imagine "doesn't count" as an blackout marker (or eraser) that blacks out (or deletes) circles and lines from every non-counting cell - i.e. making it completely empty, not just empty of digit. That would allow R10-11C1-3 to be all discounted (which doesn't violate your next rule because the circle in R9C3 remains non-empty).
Your version of "doesn't count" is "doesn't count as digit, but still counts as a clue". That needs to be clarified.
on 22. June 2022, 02:36 by twototenth
Gorgeous! Very challenging, yet highly logical at every step.
on 21. June 2022, 22:21 by KNT
Enjoyed that a lot, thanks
on 21. June 2022, 21:04 by Jesper
A very nice Deconstruction variant. Thanks, zeta!
on 21. June 2022, 20:52 by JayForty
Great puzzle! The mid-part of the solve is just beautiful and very nice flow throughout!
on 21. June 2022, 19:53 by Vebby
Very nice flow! Also got to learn about the asterisk-cell placement which never occurred to me before. Thanks zetamath! :)
on 21. June 2022, 19:41 by LittleBallOfPurr
What a masterfully crafted puzzle. Could feel how intentionally every deduction was built into it, like breadcrumbs in a trail. Must admit, it was pretty tricky! Thanks Zeta, this was an absolute pleasure to test.
