Logic Masters Deutschland e.V.

This is the fifth puzzle in the Zippular Lines series. It also features ambiguous Psycho Look-and-Say Killers, which are notably complex all on their own. This puzzle is very hard, and has some deductions that are quite difficult to spot. You can get a hint for one of the deductions in the lore at the bottom. The puzzle is unique and solvable without the hint, if you prefer not to use it.

Zippular Lines were inspired by the Zipper Lines created by Jaze and the many excellent puzzles featuring them created by the community. I wanted to expand the possible pairs of digits on a line, so I chose to modify the constraint to compare the sum’s Modular Line remainders (0, 1, or 2) instead of the full sum. This creates a line which is less constrained but still has lots of potential.

Thanks to all the testers who gave their time and feedback to this puzzle, including: Dumediat, LMDemasi, Roger Wrightshoe, Josh Johnson, Applesauce, Simoons, and Scojo.

Zippular Lines Series

1. The Prophecy (Zippular Lines #1)
2. The Magic Potion (Zippular Lines #2)
3. The Roc’s Shadow (Zippular Lines #3)
4. The Ankheg (Zippular Lines #4)
5. The False Tautology (Zippular Lines #5)

Ziffular Lines Series

1. The Humble Beginning (Ziffular Lines #1)

Rules:

• Normal Sudoku and Kropki Pairs rules apply, along with Zippular Lines and Psycho Look-and-Say Killers.
• Sudoku: Place the digits 1-9 once each in every row, column, and 3x3 box.
• Zippular Lines: Each pair of digits an equal distance from the central spot on a Zippular line have the same SUM MODULO 3 (the remainder when the digits are summed and then divided by 3). The digit in the central spot has the same remainder when divided by 3.
• For example, 658 is a valid Zippular line, because 6+8=14, and 14 and 5 have the same remainder (2) when divided by 3.
• Psycho Look-and-Say Killers: Digits in pink cages may not repeat. Each digit in a cage indexes a cell in the grid. The cell is located in the *box* with the digit's number, in the *same position* within the box as the cell containing the digit. A digit may index its own cell. The cage clue should be read as a look-and-say clue that counts the number of times a digit appears in all the indexed cells.
• Cage clues are two digit numbers which must be determined by the solver. Each ? in the clue must match a digit in the cage. Both ? may match the same digit.
• Each cage must have only *one* valid clue. Different cages may have the same clue.
• For example, a cage containing the digits 238 would have a clue containing only 2's, 3's, and 8's. If the clue was 28, then there would be exactly two 8's in the cells indexed by the digits in the cage.
• Kropki Pairs: Digits separated by a white dot are consecutive. Digits separated by a black dot are in a 2:1 ratio. Not all dots are necessarily given.

Streamers have permission to use this puzzle.

Play in SudokuPad

Psycho Look-and-Say Killers Example:

• In the example image, there must be two 8’s in the cells indexed by the 28 cage in box 2.
• The digit 1 in that cage indexes to *box* 1, and then to the cell in the *same position* in that box as the digit 1 in its box (the top-middle cell).
• The digit 3 in that cage indexes to *box* 3, and then to the cell in the *same position* in that box as the digit 3 in its box (the middle-middle cell).
• Since there must be two 8’s in the indexed cells, both indexed cells must contain an 8.

I am a big fan of fantasy adventures, so I decided to add a bit of lore to this puzzle series. The lore is completely optional and will come in the form of a hint for one of the puzzles in the series (not necessarily the current puzzle). All puzzles are unique and solvable without using a hint. The hint will make some difficult deduction a bit easier, but it will not make the puzzle trivial.

“The mad wizard's prison is awash with an overwhelming array of sights and sounds. The impossible geometry of the interlocking staircases twists at your mind, and you can feel madness bashing at the bounds of your sanity like the great caged beasts imprisoned here. You draw out the Magic Potion you obtained from the cheerful peddler, and eye it dubiously. Lacking another good option, you quaff the bitter liquid and hope for the best!”