Logic Masters Deutschland e.V.

Normal Sudoku rules apply. Clues outside the grid are either Sandwich clues, or X-Sum clues. You will need to determine which during the solve. If a row or column has two clues given outside the grid, there is always one Sandwich clue, and one X-Sum clue. For convenience, you may solve on Penpa.

This puzzle has a narrow solve path, and may be artificially difficult because of it. Familiarity with at least one rule set at a minimum is encouraged.

Sandwich Rules: The number given outside the grid is the sum of the digits between the positions of the numbers 1 and 9. Do not include 1 and 9 in the sum.

X-Sum Rules: The number given outside the grid is the sum of the first X digits from that direction (the direction the clue is given from, for example 'left'), where X is the value of the first digit from that direction. Include that first digit in the sum.

Inspired by Shye's "Unknown Values Sudoku" and Cracking the Cryptic.