Logic Masters Deutschland e.V.

A recall from my 3 Battle With The Archers puzzles in the past that used 3 different types of line: Between Line, Lockout Line, Double Arrow.


In this puzzle, I revisited the concept of ambiguous lines in the past (see this link) and attempted to combine all 3 types of line - Between line, Lockout line, Double arrow - into something that compares the strength of each of them. The puzzle is quite hard but I think the amount of surprising interactions in here will surely worth your experience!

I decided to share this one earlier than planned because I'm currently preparing for the big things in real life in the next 2 weeks, and I surely need to focus more on that instead of puzzling here. Don't be upset, I shall be back in mid-April! :)


Rules:

- Normal Sudoku rules apply: every row, column and 3x3 box contains digits from 1 to 9 each once.

- Each line in the grid has two circles as its endpoints. Each line must obey at least one of the three following properties, which has to be deduced throughout:

+ Between Line: Digit[s] along the line that has two circles as its ends must lie between the digits in the circles, i.e. digit in one circle is greater than all digits along the line, while digit in other circle is smaller than all digits along the line.
+ Lockout Line: Digits in the circles must have difference by at least 4, and also digit[s] along the line must be different than endpoint values and must not lie between them.
+ Double Arrow: Digit[s] along a line that has two circles as its ends must have the same total as the total of two digits in those circles.

For the sake of the entire rule set, digits along a line can repeat if allowed by other rules.

Puzzle: (for f-puzzle link, turning off highlight conflicts is required)

F-puzzle link

Penpa plus (alt. link)

CTC app (alt. link)

Good luck and have fun solving!