This is a variant on the anti-taxicab restriction I introduced in my Partial Manhattan Sudoku. After that puzzle was featured on CTC, I was very happy to see people experimenting with the restriction. I had realized that I would require computer assistance to make a complete Manhattan sudoku (since the Partial Manhattan Sudoku was the furthest extent I could reach by hand). I am very grateful to the people on the CTC Discord server, particularly RealShaggy, for finding completed grids with the restriction.
Now, there are examples of anti-taxicab sudokus, such as this one by JGLP. I wanted to introduce some more interplay between the digits. Thus, I made this consecutive sudoku with that restriction. The solution was generated by RealShaggy. Now, onto the puzzle!
Normal Sudoku X rules apply (that is, diagonals contain the digits 1-9 exactly once). If two consecutive digits are adjacent in the completed grid, the edge between them is marked with a white circle. Similarly, if two digits along the two main diagonals are consecutive, they have been separated by a grey dot. All possible white and grey dots are provided.
Additionally, there is an anti-taxicab restriction. That is, if two cells contain the same digit, the taxicab distance (minimum number of orthogonal moves from point A to point B) cannot be equal to that digit. For example, if there is a 4 in R3C4, then there cannot be a 4 in R2C7, since it takes a minimum of 4 moves to go from R3C4 to R2C7.
Here is a Penpa-edit link to try it out online. Hope you enjoy it!
Lösungscode: Row 8, followed by Column 9
am 27. Juni 2020, 11:25 Uhr von Madmahogany
@panthchesh The Penpa link should be working now
am 27. Juni 2020, 11:02 Uhr von Madmahogany
@BigTiger sorry for the confusion. It is as @stefliew says, all the consecutive adjacent digits are marked with circles.
am 27. Juni 2020, 05:03 Uhr von panthchesh
Your Penpa link doesn't work.
am 27. Juni 2020, 02:44 Uhr von Big Tiger
Ahh, so "if two >consecutive< digits are adjacent"...
am 27. Juni 2020, 01:49 Uhr von stefliew
If two consecutive digits are adjacent orthogonally, there is a white circle between them. If two consecutive digits along the main diagonals are adjacent diagonally, there is a grey circle between them.
am 27. Juni 2020, 01:25 Uhr von Big Tiger
I'm stuck on "If two digits are adjacent" ... EVERY digit is adjacent to another on this. Clarification of this particular rule?