Logic Masters Deutschland e.V.

Many thanks to cyddrdrd and DylanRay for testing!

This idea was inspired by this puzzle, which introduced limit ordinals. Unfortunately, that puzzle is only published in the Chinese community.

However, the concept of infinity used in this puzzle is actually not mathematically rigorous. Just treat infinity in the usual way: positive infinity is bigger than any finite number, positive infinity plus any finite number (or plus positive infinity) is positive infinity, and positive infinity minus any finite number is positive infinity. Solvers don't have to consider the result of infinity minus infinity.

Another idea I wanted to try was to use each clue type only once, so I'm sorry for the long rules. Happy solving!

Rules:

• Normal Sudoku rules apply.
• Infinity Cells: Place nine Infinity Cells in the grid: one in each row, column, and 3×3 box, each containing a different digit from 1-9. For all puzzle constraints below, the value of an Infinity Cell is considered positive infinity, regardless of the digit written in it. The value of a normal cell is simply its digit.
• Kropki : The values of two cells joined by a white dot are consecutive. The values of two cells joined by a black dot are in a 1:2 ratio. Not all possible dots are given.
• XVs: Values in cells separated by an X sum to 10. Not all possible Xs are given.
• Arrow: Values along an arrow must sum to the value in the attached circle.
• Thermometer (The): Values must strictly increase from the bulb end of the thermometer.
• German Whisper (GW): Adjacent values on a green line must differ by at least 5.
• Renban (Ren): The values on a purple line must form a set of consecutive, non-repeating values, in any order.
• Region Sum Line (RSL): A blue line is divided into segments by region borders. The sum of the values in each segment must be equal.
• Skyscraper (Sky): Clues outside the grid indicate how many values are visible from that direction, treating values as building heights (larger values block the view of smaller ones behind them).
• Sandwich (Sand): The clues outside the grid give the sum of the values between the highest and lowest value in that row or column. (The highest and lowest values themselves are not included in the sum.)

Play on SudokuPad

This puzzle is also solvable without the given X clue, but the Sudoku part becomes much harder.