Logic Masters Deutschland e.V.

Millstone, by James Sinclair

Schrodinger's cell rules apply: fill the grid with the digits 0-9 so that digits do not repeat in a row, column, or 3x3 box, and exactly one cell in each row, column, and box contains two digits.
A cell's value is equal to the sum of its digits.
A cage's product is equal to the value of each of its cells multiplied together.
Each cage's product is consecutive with that of exactly one other cage in the puzzle, and no two cages have the same product. Some cage products are given, others must be deduced.
Digits cannot repeat within a cage (but values can).
The sum of the values along an arrow is equal to the value in the connected circle.
Values in cells with a shaded square must be even.

Play online

Edit: apologies to everyone who attempted this puzzle in the first day or so, I completely missed a (pretty obvious) possibility that caused it to be tougher than it's meant to be. I've added a clue to fix this.

I think my comment below is still valid so I'm leaving it in, with one small addition.

Edit, again: one more small change. Now I'm done tinkering, I promise. Probably.

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Quick comment on this puzzle (not really a spoiler, but I'm hiding it anyway for folks who want to go in completely cold). Highlight to read: This is one of my favorite puzzles that I've set. It's difficult, but it can be solved fully logically, and—now that I've fixed the mistake I made and somehow didn't catch sooner—I'm confident that no single step (including the math) is beyond the ability of the folks here to comfortably do in their heads or with minimal notes.

Several test-solvers, however, found a different path which involved using a calculator and/or lots of note-taking. Maybe there's more I could've done to make my "intended" path more forced, but I couldn't find a way to do it without hurting the puzzle in some other way, and I think there's an extent to which the central concept of this puzzle makes an alternate, math-heavy solve path unavoidable. Whichever path you take, I hope you enjoy the puzzle! Please feel free to reach out here or on the CtC Discord if you want help.