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Is it grammatically correct to say:

"I have all the pieces to the colorful puzzle."

vs

"I have all the pieces of the colorful puzzle."

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    Yeah, either one's OK. To tends to indicate that the puzzle is completely disassembled, and the separate parts all must move together (to somewhere), but for simply means they are somehow associated with the puzzle by its makers (for the purpose of the puzzle). – John Lawler Jun 22 '18 at 23:24
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The preposition to usually carries a sense of movement; of usually refers to ownership or being part of a whole. Both are used in "piece __ the puzzle," but "of" is much more common.

Interestingly, examining the examples for "piece to the puzzle", or "pieces to the puzzle", these usages with to tend to be figurative and refer to a missing or out of place piece that has to be searched for.

e.g., in the NCI Grading Guide

For the newcomer, the process of grading coins can be likened to a jigsaw puzzle. No one book holds all the pieces to the puzzle.

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