Logic Masters Deutschland e.V.

The following puzzle is the direct follow-up of my previous Modern Art puzzle in the past and it also belongs to one of my three main projects aimed towards the later half of this year.

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Modern Art took a look into a large variety of different constraints with a common property between them (all being line constraints, in that case) and then mixed them in such a way so that each of those constraints would only be used once and also play some needed role in the solve, and all of that were also confined under my signature symmetry theme as well.

Till this day it's still one of my most unique puzzles both in terms of logical creativity and artistic value, and when I heard that this month will celebrate 4 years anniversary of Lockout line (that old already, holy crap), I figured out the following sequel should try to mix some more line constraints but with endpoint gimmick since Lockout line is among that group of constraints too.

This sequel also features some recently invented line constraints I've never touched or set with before, but I never really expected those would come together so nicely at the end of the setting here, especially since I set most of the things by hands as well (I only relied to extra software at the end to search for the most efficient ending for this).

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The puzzle isn't really very hard overall but there are rather plenty of stuff to take into account in terms of solving and understanding the implications so on here, I put this at around high 3 - low 4 difficulty range. I hope more people will enjoy this too :)


    



Rules:

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

- Constraints included in this puzzle are: Between Line (thicker dark gray line with two circles), Product Line (thicker brown line with two circles), Circle Sum/Arrow (diamond line shape in box 5 with a circle), Split Peas (green line with two circles), Double Arrow (red line with two circles), Lockout Line (blue line with two circles), Odd/Even Parity Counter (golden line with two circles), Index Line (lighter blue line with a diamond endpoint), Flexible Difference Line(pink line with a diamond endpoint).

A detailed explanation of every constraint can be found below.



Puzzle:  Penpa plus  -  Sudokupad





1) Between Line: The digit along the dark gray line with two circles must be between two digits in those two circles, i.e. that digit must be smaller than the digit in one circle and also must be bigger than the digit in the other circle.

2) Product Line: The digit along the brown line with two circles is equal to the product of two digits in those two circles.

3) Circle Sum/Arrow: Along the diamond line shape in box 5, the digit in the circle cell is equal to the sum of the rest of the digits.
(For example, 8 in the circle can be 8 = 1+2+5.)

4) Split Peas: Along the green line with two circles, the sum of the digits is equal to the concatenation of two digits in those two circles in some order.
(For example, 2-[345]-1 is a valid split pea line because 3+4+5 = 12, which is a concatenation of two endpoint digits 1 and 2.)

5) Double Arrow: The sum of the digits along the red line with two circles is equal to the sum of two digits in those two circles.

6) Lockout Line: The digits along the blue line with two circles must *not* be between the two digits in those two circles. Additionally, the two digits in those two circles have the difference of at least 4.

7) Odd/Even Parity Counter: Consider the entire golden line with two circles, the digit in one circle is equal to how many even digits there are on that entire line (including itself), while the digit in the other circle is equal to how many odd digits there are on that entire line (including itself).

8) Index Line: Along the light blue line with a diamond endpoint, starting from the diamond, the digit in the Nth cell indicates the 'position cell' where the digit N has to appear.
(For example, if the diamond contains a 2 then the 2nd cell along that line (R4C1 in this case) has to contain digit 1.)

9) Flexible Difference Line: Along the pink line with a diamond endpoint, starting from the cell right after the diamond (starting from R4C9 in this case), every pair of two adjacent cells contains two digits with the difference value being equal to or bigger than the digit in that diamond, and this digit also must be bigger than 1.
(For example, if the diamond contains a 3 then the difference between R3C9 and R4C9 has to be equal to or bigger than 3, the same for the difference between R3C8 and R3C9 and so on.)

Good luck and have fun solving!