Manhattan Loop
(Published on 21. August 2024, 22:45 by Arlo Lipof)
In this puzzle a taxicab drives in a loop around Manhattan.
The taxicab distance from cell A to cell B is the minimum number of orthogonal steps to get from A to B, e.g. if A and B are a chess knight's move away from each other, they have a taxicab distance of 3, since a chess knight goes 2 cells in one direction and 1 cell in an orthogonal direction.
Rules:
- Normal 6x6 Sudoku rules apply.
- Draw a single one-cell-wide loop of orthogonally connected cells (= the taxicab's path in Manhattan). The loop may not touch itself, not even diagonally. The loop must enter each box of the grid. A cell with a digit X is part of the loop if and only if it is a taxicab distance of X away from at least one other cell with an identical digit X.
Link: CTC
Please enjoy! Ratings and comments are welcome of course.
Solution code: Sum of all the digits in the loop, then Column 6
Comments
on 23. August 2024, 14:57 by luisdias412
Really enjoyed this set of rules! Hoping for a full 9x9. Great work!
on 22. August 2024, 20:05 by lordovol
Nice puzzle. But the rules was confusing. I wasn't sure if cells not in the loop count as taxicab cells for allowing another cell to be on the loop
on 22. August 2024, 13:16 by Platinum
Great concept, like others would love a 9x9 version
on 22. August 2024, 12:32 by permafrostyx
yay
on 22. August 2024, 11:13 by nearestneighbour
Awesome puzzle, loved the logic and would like to see a full sized version.
About the rules, I think for many people here it would be clearer if you use a term like negative constraint, because it's more commonly used on this site.
Also, solution code was too much work lol. Maybe something like "row 6 and column 6, loop cells only"
But again I love this puzzle
A: Thank you for your nice words and your advice.
on 22. August 2024, 06:58 by Hajuhn
Great puzzle, like GrumpyMan said would've been great if it was clearer in the ruleset that numbers not on the loop cannot be a taxicab difference away
A: That is precisely the meaning of ‘if and only if’.
on 22. August 2024, 03:22 by thrutch
A really fun and interesting rule set, look forwards to seeing a 9x9 version!
A: Thank you. Maybe one day I’ll give it a try. :-)
on 22. August 2024, 03:19 by kdkirby
The backwards direction of the iff was wonderful to work with. Great puzzle!
A: Thank you, glad you liked it!
on 22. August 2024, 00:04 by JasonRobards
Nice puzzle! Thank you :)
A: Thanks!
on 21. August 2024, 23:38 by GrumpyMan
It could have been clearer in the instructions that not only are all parts of the loop taxicab cells, but all non-loop cells are not taxicab cells.
A: That is precisely the meaning of ‘if and only if’.
