Partial Manhattan Sudoku
(Published on 29. April 2020, 14:20 by Madmahogany)
Normal Sudoku rules apply. Diagonals must contain the digits 1-9 exactly once. Certain digits follow a "taxicab" restriction, that is the taxicab distance (i.e. the minimum number of orthogonal moves to go from point A to point B) between two of the same digit cannot be equal to the digit itself. That is, if there are two 6's in the grid, they obey the restriction if the taxicab distance between them is not 6.
Given here is the grid, and the red squares indicate all the violations to the taxicab restriction. That is, the digits in the red squares must be a taxicab distance from another red cell. The sum of the unique digits in the red squares is less than 15 (Originally, I had worded it as "The sum of the digits with no violations to the restriction is more than twice the sum of the remaining digits", but I decided not to put an extra roadblock in the wording).
Update: I had added some clues to the puzzle, not for disambiguation, rather to eliminate some amount of trial and error. However, I have decided to remove those clues, because the puzzle is solvable without those extraneous clues. Apologies for the inconvenience.
Solution code: The diagonals from r1c1 to r9c9, and from r1c9 to r9c1
Comments
on 27. June 2020, 00:27 by Madmahogany
Updated tags
on 25. June 2020, 02:25 by zhergan
Very nice one!
on 10. June 2020, 19:36 by Madmahogany
Clarification to the rule set
on 10. June 2020, 19:32 by Madmahogany
@Richard Thank you for the suggestion. I will reword the problem a bit.
on 10. June 2020, 06:28 by Richard
I was confused by the wording 'violations to restrictions'. That is double negative. Instead a phrase like 'all different digits in the red cells add up to...' would have made it much clearer, Similar to what Simon wrote next to the puzzle. Once I read that it was clear.
So maybe you can reconsider the phrasing of the instructions, since it might help other people as well. I think this puzzle deserves more solvers!
on 9. June 2020, 22:42 by Madmahogany
@Richard Hope the clue wasn't unnecessarily convoluted. I wanted to integrate a constraint that depends on the value of the cells alone. Thank you for trying out the puzzle!
on 9. June 2020, 20:35 by Richard
So, after I realised what is meant with that specific sentence, I picked up my old printout again. My initial pencilmark notations were helpful in definitely getting started now. I really enjoyed the taxi distance constraint; the meaning of the digits is completely different of simply having a value. No real T&E necessary for me, only very careful counting and elimininating.
Thanks for this very nice puzzle! Glad I finally tackled it.
on 9. June 2020, 08:16 by Richard
@Madmahogany: I am pretty much intrigued by this puzzle ever since you posted it, but misinterpreted this part of the rules:
'The sum of the digits that have no violations of the restriction is more than twice the sum of the remaining digits.'
Now that I have seen the first minute of the solve on CTC, I realise what this sentence means and I am eager again giving it another go. Fortunately you removed the additional clues again. It's a pity I have to work today first. :-)
on 9. June 2020, 05:49 by Madmahogany
Editing issues
on 9. June 2020, 04:19 by Madmahogany
Changes to the ruleset
on 8. June 2020, 23:21 by JGLP
I genuinely hope more people start using this constraint or a similar one, I absolutely loved the way some of the logic worked.
on 7. June 2020, 15:14 by Madmahogany
Additional clues
on 17. May 2020, 20:28 by highcelsius
Nice concept
on 4. May 2020, 09:08 by anu_chakravarti
Extremely satisfying to solve it! Great puzzle!
on 3. May 2020, 12:52 by marcmees
very nice concept - a few more hints to limit some T&E would have been great.
on 2. May 2020, 13:12 by Madmahogany
@Imperial Marcher hope you enjoyed the puzzle! It is the first one I have posted on this site.
on 2. May 2020, 02:55 by Imperial Marcher
FINALLY solved it! Took an embarrassingly long time to solve (including figuring out the exact rules as I'm a bit slow XD)
on 1. May 2020, 10:23 by Ours brun
@Imperial Marcher No, this is not valid. The taxicab distance is always the shortest possible, so in your example it would be 5 North, 1 East, for a total of 6.
on 1. May 2020, 03:37 by Imperial Marcher
Can the taxicab movement turn multiple times? For instance the 8 in R9C3, can it go north 4 cells, east 2 cells, north 1 cell and finally west 1 cell to eliminate the possibility in R4C4?
on 1. May 2020, 00:53 by Madmahogany
@ManuH the rules are the same as that of a diagonal sudoku. The added restriction is the taxicab restriction. Now, say for example r3c4 is 4. By this restriction, r4c7 cannot be 4, as it is a taxicab distance of 4 away from r3c4. Let me know if there are any other clarifications I need to offer.
on 1. May 2020, 00:35 by battuboss
Extremely fun puzzle. Really enjoyed solving it.
on 30. April 2020, 21:34 by Madmahogany
Yes, taxicab distance, also called Manhattan distance, is the minimum distance by orthogonal (left, right, up, down) movement
on 30. April 2020, 13:56 by SirWoezel
@Imperial Marcher An orthogonal move can be horizontally or vertically. So from E1 to F3 is three orthogonal moves. Taxicab restrictions mean there can't be a 3 in both these squares
on 30. April 2020, 13:03 by ManuH
Hmm. I don´t understand the rules.
on 30. April 2020, 01:00 by Imperial Marcher
If I'm not mistaken, any digit cannot be any number of orthoganol moves from itself as that breaks standard sudoku rules
on 29. April 2020, 18:04 by Madmahogany
Solution Code changed
on 29. April 2020, 15:12 by Madmahogany
Additional tags added
