Logic Masters Deutschland e.V.

I'm very excited to finally present the 21st puzzle in the Zodiac Project, a series where setters create a puzzle based on a disjoint set given to them by the previous setter! Thank you to juggler for nominating me!

Rules:

• Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box.
• Weights: The nine diamonds all contain different digits. The weight of a diamond is the average (arithmetic mean) of the up to four digits touched by its corners (the digit in the diamond itself does not contribute to this average).
• Scales: Each small white circle is the fulcrum of a scale, whose arm is a straight line passing through it. If the line that passes through a fulcrum is horizontal, then the two sides have equal weight (taking torque multipliers into account); if not, the lower side has a greater weight.
• Scale calculations are made using torque, which is the weight times the horizontal distance from the fulcrum. This horizontal distance multiplier is provided on each diamond or hanging fulcrum, for ease of solving. For example, for the scale with its fulcrum in r1c3, the weight of r1c1 must be half the weight of r2c4, so that after the 2x torque multiplier is applied to r1c1, both sides of the scale will be balanced.
• Where one scale hangs from another, the weight of the hanging scale is the sum of any weights attached to it, centered at the hanging fulcrum. Specifically in this puzzle, this means that the weight of r5c5 must be equal to the sum of the weights of r6c8 and r8c6.

Solve in SudokuPad

The Zodiac Project

• "Chapter 1: Orion's Belt" by ViKingPrime
• "Chapter 2: Counting Castles" by Marty Sears
• "Chapter 3: Derezzed" by heliopolix
• "Chapter 4: Rodd Stevens" by 99%Sneaky
• "Chapter 5: Phase Shift" by meggen033
• "Chapter 6: Cage Decoder" by sujoyku
• "Chapter 7: Star Chart" by Flinty
• "Chapter 8: Parity Expedition" by palpot
• "Chapter 9: Suguru's Surge" by gdc
• "Chapter 10: Minefield Maneuvers" by SamuPiano
• "Chapter 11: Ponta Delgada" by Florian Wortmann
• "Chapter 12: Lost in Space" by lerroyy
• "Chapter 13: Gemini" by Christounet
• "Chapter 14: Sagittarius" by MaizeGator
• "Chapter 15: Kyklos" by sfushidahardy
• "Chapter 16: Original Sin" by Nordy
• "Chapter 17: Cluster of Galaxies" by Dorlir
• "Chapter 18: Taurus" by ThePedallingPianist
• "Chapter 19: Isolation" by vitaminz
• "Chapter 20: Space Hotel" by juggler

I'm nominating ChinStrap to be the next setter in this series! ChinStrap has done a lot of hard work for this community testing puzzles and helping the community improve readability and user-friendliness regarding line colors and presentation. He is also a fantastic setter himself of course! ChinStrap will need to use the following disjoint set in his puzzle, which I chose because it has special significance in one of my most defining puzzles!