Logic Masters Deutschland e.V.

Earlier this month MattYDdraig celebrated their birthday, and since they've always tested a number of my quite mathematical puzzles, I thought I'd share my appreciation by making something new, mathematical, and a little ambiguous for them. That puzzle was rushed and a little sloppier than I'd have liked, so after reworking it, I think it's worth sharing with a larger audience now.

The Rules:

1. [Sudoku]: Fill every row, column, and region with the digits from 1 to 9 once each.
2. [Greatest Product Killer Cages]: Numbers cannot repeat in a cage. The sum of the digits in a cage must equal the maximum product of any two horizontally or vertically adjacent cells within the cage.
3. [Dynamic Fog] (optional): Entering enough correct digits will reveal other parts of the puzzle hidden under the fog, guiding you along the intended solve path. If you'd rather solve on paper, you may choose the fogless option.

Example Puzzles: Here's an example puzzle, and its solution. The greatest product formed by any adjacent pairs is shown. Try This example puzzle using Sven's Sudoku Pad (estimated 2/5 stars difficulty) Try a smaller 5x5 example puzzle using Sven's Sudoku Pad (estimated 1/5 stars difficulty)

The Puzzle:

Try the Foggy version: or the Fogless version

An Extra Puzzle:

Of course, I had to also consider what about making cages with the smallest product instead. Here's a 6x6 you can try if you're interested: