This puzzle is part of the Puzzling StackExchange Advent Calendar 2021. The accepted answer to this question will be awarded a bounty worth 50 reputation.
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In our house, one of our big traditions during Advent is baking Christmas cookies. Eggnog sandwiches, spritz cookie trees, Russian tea cookies, and raspberry thumbprints are just a few of our favorites. And how can you have Christmas without cutout sugar cookies? I have a special set of cutters that I use every year, with six shapes: bell, candle, candy cane, gingerbread person, ornament, and tree.
But this year, I dropped the box they come in, and many of the posts that hold the cutters in place broke off. I know none of the cutters touch side-to-side, because I don't want them to scratch, and I remember that all of the area outside the cutters is connected, because I'm nerdy like that. But I don't remember which side goes up on each cutter, because I'm forgetful like that. Can you please help me put the cookie cutters back in place?
There is a logical path through this puzzle; please answer ONLY if you include a description of the logic used to place shapes. I hope you enjoy!
SOLVER NOTES
Unwrapping the holiday dressing, this is a Statue Park puzzle. Specifically, you need to place the given shapes into the grid such that:
- No shape may go on a cell with an empty circle.
- A shape must go on each cell with a filled circle; note that this puzzle has no filled circles.
- Two distinct shapes may not lie in cells that are orthogonally adjacent, though diagonally adjacent cells are allowed.
- The set of all empty cells must be connected orthogonally.
- The shapes may be rotated or flipped to be placed in the grid.
Penpa link for interested solvers.