Logic Masters Deutschland e.V.

I ended up making two versions of this puzzle. The pictured version I think is slightly easier to execute on despite having fewer clues, but I think the harder version (click here to play) actually slightly better telegraphs the opening idea. Feel free to try either puzzle - though they have different solutions, the section for the solution code is the same. Please leave a comment if you enjoy it!


RULES:

Normal Sudoku Rules Apply

1/9 Column Indexing: The digit in row X of column (1/9) indicates the position of (1/9) in row X.
Killer Cages: Digits in a killer cage sum to the total in the top-left corner of the cage.

Balancers: You have a bag of 9 coins which each bear a digit from 1-9. All of these coins weigh exactly the same weight, except for one which is a counterfeit, and is lighter or heavier (to be deduced) than the others.

You find the counterfeit coin in a series of weighings. Each weighing has 3 coins on each side, and the results are shown. Each time, the lower side indicates that the 3 coins on that side have a combined weight greater than those on the other side.

Each weighing groups coins by one of three properties: entropy, polarity, or residue mod 3. Each property is used in one of the weighings.

The coins on one side will all share a property and differ from the coins on the other side with regards to the same property.

Full property descriptions:
Entropy: 1,2,3 vs. 4,5,6 vs. 7,8,9.
Residue class (mod 3): 1,4,7, vs. 2,5,8. vs. 3,6,9.
Parity: 1,3,5,7,9 vs. 2,4,6,8.
Example: if the weighing is grouping by entropy then the coins on one side might be 456 and the coins on the other side might be 123.