Logic Masters Deutschland e.V.

This puzzle was set as a Secret Satan gift to yttrio, and published here with his encouragement.

For those unfamiliar, “Secret Satan” is a more intense and complex version of “Secret Santa”. I would not usually set a puzzle with such an extensive ruleset, but this is the fun and appeal of Secret Satan.

I admire Yttrio for his sudoku/shading/loop hybrid puzzles, so I thought it would be fun to emulate his style for this challenge. One puzzle didn’t seem like enough, so I set four. But that wasn’t evil enough, so I combined them into a single large grid and allowed them to possibly overlap.

The title "Cyclone" is a tribute to Yttrio’s alma mater, Iowa State, and aptly describes the chaotic look of the blank grid, as if a cyclone had just torn through it.

RULES:

The overall 19x19 grid contains 4 (possibly overlapping) standard sudoku grids. Each grid has a different shading rule, which the solver must deduce. Possibilities are Nurikabe, Cave, Yin-Yang, and Snake-Egg (explained below).

Additionally, draw a single, closed, non-branching, non-crossing loop that moves orthogonally and visits each sudoku grid exactly once. Within each grid, a different rule applies for the loop, which the solver must deduce. Possibilities are: Modular (each set of 3 cells along the line has one of each from the sets [147], [258], and [369]), Entropic (each set of 3 cells along the line has one of each from the sets [123], [456], and [789]), Parity (digits along the line alternate odd and even), and Regional 3-Whisper (adjacent cells along the line that are in the same 3x3 sudoku box must differ by at least 3).

The Cardinal-colored letter clues from “IOWA ST U” are ciphered givens; they each represent a unique digit from 1-9. Cells outside of all Sudoku grids do not contain digits, even if they contain a letter clue.

Each grid has unique rules for circle clues and loop movements:

• Nurikabe: Unshaded cells represent water and must all be connected, but may not cover any 2x2 area. Areas of shaded cells represent islands (note the shading is OPPOSITE normal convention). Each island has exactly one circle clue, indicating the size of the island. Exactly one cell in each island is visited by the loop.

• Cave: Each group of shaded cells (wall) must connect to the edge of the grid. All unshaded cells (cave) form a single connected area. Circle clues are always unshaded (cave), and indicate the total number of unshaded cells seen in the four orthogonal directions (including itself), where shaded cells block vision. The loop is only allowed to visit cave cells (but does not need to visit all cave cells).

• Yin-Yang: All shaded cells are connected and all unshaded cells are connected, while no 2x2 is entirely shaded or unshaded. Circle clues indicate the number of shaded cells in the (up to) 9 cells surrounding the clue and itself. The loop must alternate shaded cells and unshaded cells.

• Snake-Egg: A snake (1-cell wide path) of unshaded cells slithers around the grid, without branching or touching itself orthogonally. Areas of cells that are not on the snake are shaded, and each area size from 1-8 appears exactly once, and each area has exactly one circle clue, which indicates the size of the shaded area. The loop follows the snake.

The loop cannot enter circle clues outside of all sudoku grids or cells marked with a gold “X”. It may otherwise enter empty cells.

Clarification: Sudoku grid borders block vision for circle clues (as they apply in that grid). In other words, each sudoku grid, with shading and loop must be valid when viewed in isolation (except the loop does not have to close within each grid).

I hope you have fun solving, and please reach out to me on Discord if you need a nudge!