Madrigal
(Published on 1. January 2023, 17:41 by Fafrd)
Madrigal
Draw nine non-overlapping 3x3 boxes, and place the digits 1-9 in each box. Digits cannot repeat in a row or column. Cells outside the boxes should remain empty. Digits within a cage must sum to the given total. Orthogonally adjacent digits can never be consecutive, be in a 1:2 ratio, sum to 5, or sum to 10.
This puzzle is fairly hard, but these mini puzzles should make it approachable, they will help if you get stuck.
Hint puzzle 1:
Hint puzzle 2:
Solution code: Row 6 (ignoring blank cells)
Comments
on 17. January 2025, 06:30 by fellanh
I feel like this this puzzle has multiple unique solutions. Could someone confirm? I found a solution by putting the 2 and 9 in the cage.
on 5. December 2024, 12:22 by TheNineElements
Solve Time: 63:29
I rated this 4/5 difficulty.
This puzzle is genuinely astonishing. Such a cool combination of rules. I spent about 15-20 mins figuring out the 3*3 cage logic and all possible cases, and quickly understood how to use the cage. That was probably 2-3/5 difficulty. It was very nice to see how the rules all restricted boxes to really only 1 possible arrangement, with mirroring & rotation subcases.
The difficult part for me was figuring out which case was valid for box 9 (bottom right) was valid. That was probably 4-5/5 difficulty for me. Looking back it should have been obvious, but during the solve it took me quite a while to understand what was going on.
Once I could place the boxes, rest of puzzle was very straightforward. Determining which subcases could work for each of the boxes was easy (1-2/5 difficulty)
Very cool puzzle - I still am shocked that such a simple ruleset can create a unique deconstruction sudoku that is actually feasible to find by a human.
on 15. March 2023, 22:42 by wisty
I love love LOVE the inclusion of mini-puzzles that teach you the main puzzle. I really appreciate when puzzles can teach themselves (grkles' sadism is a good example of this with the top three boxes being somewhat approachable) but when the main puzzle has such a minimal grid this is such an elegant way to do it. Thank you for putting this together!
on 25. February 2023, 03:32 by HalfBakedLunatic
@Fafrd - absolutely wonderful puzzle, thank you! When I saw the solve on Cracking The Cryptic, my first thought was "this solution path would work with Magic Squares as well" ... so I've posted a "Variation on a Theme" based on your puzzle (full kudos and credits to you): https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=000D3C
on 16. February 2023, 18:10 by OGRussHood
This puzzle is mad.
on 16. February 2023, 02:56 by BMEP
Very nice puzzle! I'm amazed that it works! Not that hard, tho…
on 16. February 2023, 00:06 by apiyo
It feels unjust that this didn't get a higher rating. Even though the logic boils down to a fairly uncomplicated end game, it's amazing that you thought of this idea and found such a minimalist starting point. Well done Fafrd!
on 3. January 2023, 02:08 by drbs
The mini puzzles are helpful. At first I was wondering what the second one might be good for, but it became clear later. Sometimes I need to think for a long time to realize something is obvious.
on 2. January 2023, 23:47 by JennaStella
Really clever puzzle - loved the entire concept! I also really liked the 2 hint puzzles which you provided as they helped me both understand the logic more and come to a solution quicker than I think I would have otherwise done, therefore making the main puzzle more enjoyable :)
on 2. January 2023, 17:33 by DVFrank
Very cute! :^)
