PSE Advent Calendar 2021 (Day 17): That's the way the cookie crumbles

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.

Step by step walkthrough

Step 1

The first step of the solution is realizing that piece o only fits at the top right of the grid. There are 3 permutations in which it could fit but we can eliminate the upright permutation since it violates the empty cells being adjacent rule. We are left with 2 possible permutations of piece o as shown below

Step 2

The next step is realizing that piece b can only fit somewhere at the top left of the puzzle. Now if piece b goes at the top left then piece t can only fit at the bottom right of the grid. This leaves the only possible option for piece C is to go to the bottom left of the puzzle and it only fits there in one permutation

Step 3

We can actually determine where each piece would fit at this point. Pieces b and g cannot fit together at the top left of the puzzle so pieces b and c must be at the top left which leaves pieces t and g at the bottom right. There's only one way where each pair would fit together without breaking any rules as shown below

Step 4

The last part of the puzzle was just determining which is the correct permutation of piece o. It has to be pointing to the left since pointing it downwards would block the empty cells at the bottom right and they wouldn't be orthogonally adjacent with the rest. With this, we have solved the puzzle

• Great job...that's correct! Thanks for the nice write-up! Just one quick note: you've left the bottom square off of the tree piece. Doesn't affect your answer, just an aesthetic thing. Commented Dec 17, 2021 at 15:03
• My bad, must have forgot to paint that in. I fixed it now Commented Dec 17, 2021 at 15:46