Logic Masters Deutschland e.V.

This puzzle was created as a collaboration with Scojo during a collaborative setting event on the Skunkworks discord. It was created to combine aspect of two great puzzles: Murder Mystery by 3good5you and Balance = Entropy by Jeremy Dover

Rules:

• Normal sudoku rules apply:
  Place the digits 1-9 once each into every row, column, and 3x3 box.
• Each circle is the fulcrum of a balance, whose balance arm is a straight line passing through it. The digits in the squares are the weights hanging from the balance. If the line that passes through a fulcrum is horizontal, then the two sides are balanced; if not, the lower side is heavier. Balance calculations are made using total torque: a weight three cells away from a fulcrum (cells can be counted horizontally on a horizontal balance arm, diagonally on a diagonal balance arm) contributes thrice the torque of the same weight hanging one cell from the fulcrum. The lines are massless and do not affect the torque calculation.
• Some fulcrums are accompanied by a clue in the top left corner of the cell. Any such clues are both sum clues and look-and-say clues. All cells on lines hanging from a clued fulcrum must sum to the number listed. Also, the first digit in a clue indicates the number of times the second digit in the clue appears within those same cells. However, and digits in square weights count twice in regards to the sum and look-and-say values.

  The cell with the fulcrum is counted for both the sum and look-and-say clues.

• Additionally, clues are encrypted. Letters A-D represent unique digits between 1-9 that must be deduced; ?'s may represent any digit between 1-9, including A-D, and different ?'s are not necessarily the same digit.

Here is an example of how the balances are calculated (taken from Balance = Entropy).

Sudokupad link: Click Here
Penpa link: Click Here