Diminishing Returns
(Published on 21. May 2023, 03:55 by ul-Rhymm)
Rules
Normal Sudoku Rules and XV rules apply. In addition, the “V” is an inequality sign: the digit above the V is greater than the digit below the V.
To solve this puzzle, fill in one box at a time—at any given moment, only one box is solvable. When you finish each box, the digit in the yellow highlighted square indicates which box to solve next. The starting box must be deduced, and the highlighted digit in the final box points back to the beginning.
To begin this puzzle, all of the following constraints apply.
1. Normal sudoku rules apply.
2. Adjacent Cells may not sum to 5 unless marked with a V
3. Disjoint Groups
4. Digits may not repeat along marked diagonals
5. Cells a King’s move may not contain the same digit
6. Cells a Knight’s move may not contain the same digit
7. Adjacent Cells may not be consecutive
8. Adjacent Cells may not sum to 10 unless marked with an X
9. Adjacent Cells may not have a 1:2 ratio.
Each time you complete a box, the last rule is removed. So, the first box solved abides by all 9 constraints. The Second abides by constraints 1-8. The final box only follows constraint #1.
Solution code: Row 7 and then Column 7, with no spaces
Comments
on 30. July 2023, 03:37 by PinkNickels
This is extremely clever and was very enjoyable to solve. Really glad i found this puzzle.
on 14. July 2023, 10:18 by TheSolvingJäck
what a beautiful and unique puzzle idea its a really fun journey to work your way through the grid. Absolutely impressive piece of art
on 26. June 2023, 18:04 by Counterfeitly
I wonder if there is any way to use the fog settings on sudoku pad to make clear which rules are active - might be more trouble than it's worth, but I would be a nice way to save on the number of times people have to pause and check order
on 30. May 2023, 03:16 by KyleBaran
Seems like a nice puzzle, but I dont understand how youre meant to start. There are many permutations that make box 3, 5, and 9 valid starting boxes, for example, since they have no restrictions, and at that point it becomes a very boring exercise of bifurcation. I was able to eliminate a box as the start after 25 minutes. I know I am missing something, which is too bad because this looks like a fun puzzle.
on 23. May 2023, 07:09 by Montikulum
Not sure how the start (number, not box) could be deduced w/o trying but extremely impressive setting with the rules breaking box by box exactly as „indicated“.
on 22. May 2023, 19:08 by RedBarchetta
Once the break in was found, it flowed so well, very nice puzzle. I had the right box the first time but must have made a mistake and tried so many others for the break in. I finally went back to my first attempt and tried again. Cleverly worded by the way.
on 22. May 2023, 14:03 by LoverOfPi
Beautiful and not as hard as expected. Maybe im slowly able to do 2 stars?
on 22. May 2023, 12:30 by asp1310
Is the V also a normal "5 V", or is it ONLY an inequality sign?
on 22. May 2023, 11:52 by Snaques
It blows my mind how people are able to set puzzles like this. Very much appreciated ul-Rhymm!
This took me quite a few tries as I struggled to keep up with what rules were in play, but got there in the end and glad I did. Wasn't too bad when I worked on the correct rules. :)
on 22. May 2023, 03:05 by Paytertot
Pretty easy and straightforward solve, but the changing rules made this one a real treat to solve. Absolutely brilliant setting to make this all work.
on 22. May 2023, 01:02 by Snaques
It blows my mind how people are able to set puzzles like this. Very much appreciated ul-Rhymm!
This took me quite a few tries as I struggled to keep up with what rules were in play, but got there in the end and glad I did. Wasn't too bad when I worked on the correct rules. :)
on 21. May 2023, 21:39 by Silverscree
I found a correct solution at the end, but I found that my 6th box (order, not position) wasn't fully solvable with my remaining rules. I'm sure it must just be me, but did anyone else have two dominoes that stubbornly resisted disambiguation in their 6th box?
Edit: I went back to have another look - there was one constraint remaining that works ACROSS boxes that was the missing piece.
Regardless of that, I really enjoyed this idea. I especially loved the break-in, which tickled the same part of my brain as using uniqueness to solve but felt fairer somehow!
on 21. May 2023, 21:18 by BenTen
That is a really well-designed puzzle.
on 21. May 2023, 19:37 by Onkel_Dagobert
Pretty straight-forward for me, especially towards the end. Also, I find checking for disjoints very tedious (which is NOT criticism in any way, of course, just a matter of taste entirely).Having said all that, I can‘t help but admire how thoughtfully constructed this puzzle was. Very well done!
on 21. May 2023, 19:25 by Baklin
I kept messing up with removing the rules. After that it wasn't that hard to finish this.
Enjoyed these rules.
on 21. May 2023, 18:46 by kakstront
Love the concept of the constraints being removed as you go. Would love to see harder puzzles with this ruleset
on 21. May 2023, 17:24 by VitP
There is an inaccuracy in the rules as written.
The second paragraph should have
"only one box is PLAYABLE (or ACTIVE)", otherwise I can fill in every cell, except one cell per box, and all rules remain in force.
on 21. May 2023, 17:09 by VitP
for Guillem98
Disjoint groups means
for any given cell within a 3x3 box, no other equivalent cell within the other boxes may contain the same digit.
on 21. May 2023, 14:39 by Guillem98
What's the Disjoint Groups rule?
on 21. May 2023, 11:09 by frankpujo
Beautiful puzzle! Very nice and straight-forward solving. It was amazing to see how the rules were broken as soon as they weren't required anymore, giving confirmation that I was on the right path. Nice.
on 21. May 2023, 09:27 by annaswan
I loved this puzzle! The interplay of the rules was fantastic and the puzzle was a joy to solve.
