Logic Masters Deutschland e.V.

This puzzle was inspired by a cosmic class masterpiece called Crowd Control, published about 3 years ago by Allagem.

It has been designed to showcase a variety of standard clue types all of which are ambiguous. Namely, they are utterly insensitive to a polarity switch (y = 10 – x) applied throughout the grid. They are so many that I doubt you will need to use them all, but I hope you will enjoy testing their insensitivity.

Warning: Since I forgot to include a disambiguator, this puzzle turned out to be ambiguous❗️ It seems to have two valid solutions, that can be transformed into each other by switching polarity. However, only one of them has been included in SudokuPad's checker. Your goal is getting SudokuPad's joyful "Yay, congrats" message, but the only way to do that is by trial and error. If you get the "Uh oh" warning instead, you will need to switch polarity.

Hint 1: You can switch polarity in the blink of an eye (about 40 seconds) if you use this trick:

• Switch from 9, 8, 7, 6 to A, B, C, D
• Switch from 1, 2, 3, 4 to 9, 8, 7, 6
• Switch from A, B, C, D to 1, 2, 3, 4

Hint 2: Use <double click> or <double tap > to select multiple instances of the same digit. For instance, you can select all 9s at once by double clicking any 9. Then you can press A to overwrite all of them at the same time.

Spoiler: See this playlist to learn more about ambiguous or quasi-ambiguous puzzles.

Other clues that share the same kind of ambiguity:

• Any type of Whisper lines, including Expanding Whispers
• Texas Holler lines
• Tentropic lines
• Equal Difference, Sequence, and Lockout lines
• Any region containing sets of distinct digits (e.g. Disjoint Sets or Diagonals)
• Normal 3×3 Magic Squares❗
• Anti-King, Anti-Knight, Anti-Queen, and Anti-Camel (Tigger Bounce) constraints
• A given digit 5

Other kinds of ambiguity:

• Rotational symmetry
• Mirror symmetry

Click on the image to solve this puzzle online

Rules:

• Normal sudoku rules apply.
• German Whispers: Adjacent digits along a green line have a difference of at least 5.
• Dutch Whispers: Adjacent digits along an orange line have a difference of at least 4.
• Between lines: Digits along a thin grey line must have values strictly between the digits in the attached circles.
• Renbans:Digits along a purple line form a set of consecutive digits in any order.
• Nabners: Digits along a yellow line form a set of non-consecutive digits in any order.
• Parity lines: Adjacent digits along a red line have opposite parity; one of them is odd and the other is even.
• Entropic lines: Any run of three sequential cells on a peach line must contain one digit from each of the sets {1,2,3}, {4,5,6}, and {7,8,9}.
• Modular lines: Any run of three sequential cells on a teal line must contain one digit from each of the sets {1,4,7}, {2,5,8}, and {3,6,9}.
• Palindromes: Digits along a grey line read the same in both directions.
• White Dots: Digits in cells joined by a white dot are consecutive.
• Xs: Digits in cells joined by an X sum to 10.
• This puzzle has two valid solutions, but only one of them will trigger Sudokupad's "congrats." You will need to switch polarity if you get its "Uh, oh" warning instead (see above for details).