Non-consecutive sudoku and roping

Just putting this little discovery here in case it helps anyone else with the same question. Somehow I got hooked on Variant Sudoku lately, which is Sudoku plus some twist. The variant rules can get quite elaborate, and the result is that most puzzles present novel logic problems within the usual Sudoku framework. Check out Cracking the Cryptic on YouTube for an introduction.

One of the variations is a non-consecutive rule also called anti-consecutive. It means no two consecutive digits can occur next to each other horizontally or vertically. So 3 cannot occur next to a 2 or a 4.

After doing a few of those, it seemed they always exhibited something called roping or braiding, which can occur in any sudoku puzzle. It’s when the same triplet of digits appears together in the rows or columns of three consecutive boxes.

Below is an example of a non-consecutive sudoku solution with lots of roping, and highlighting the roping in the top three boxes.

I wondered if roping always occurs when there is a non-consecutive constraint. If I knew that was the case, I could speed up some solves.

I know there exists some deep sudoku research community somewhere, who have proven things like what’s the minimum number of digits needed for a unique solution in regular sudoku (I think I read it’s 19). But I had no luck finding any results for my query, perhaps partly because sudoku is so popular and the search engines are overloaded with sudoku content.

However, I did stumble upon a nice online sudoku solver, and set out to create a non-consecutive solution myself without roping. After a few tries, I succeeded! I entered the black digits, and the solver derived these blue digits.

So, yes, it is possible to have a non-consecutive/anti-consecutive constraint without roping/braiding in sudoku.