Logicsmith Exhibition 2: Polyominous

Would you like to try your hand at logicsmithing, and possibly be featured on my blog? Read on!

In an intriguing experiment on its online puzzle site nikoli.com, the Japanese company Nikoli asked its authors to create different Slitherlink puzzles all using the same arrangement of givens. I've decided to try a similar experiment here, using the puzzle Polyominous (link to rules, Polyominous puzzles from my blog). Your challenge is to replace each of the question marks in the grid below with an integer to create a uniquely solvable Polyominous puzzle.
For those of you who were around for the first Logicsmith Exhibition, I have followed your advice and opted for a smaller grid than last time. I noticed that the huge group of 32 unclued cells in the middle seemed to be a bit of a choke point, so I tried to avoid that. Also, this grid contains an unusually high density of givens -- 50% of the cells are givens, in fact. Finally, I'm giving you three weeks instead of just two. These factors should make it considerably easier to construct a puzzle (I hope!).

Send your puzzle (and optionally, its solution) to my e-mail address at glmathgrant@gmail.com. After three weeks (meaning the deadline is December 16), I will post the puzzle I have constructed for this layout, as well as some of my favorite submissions from other people. Good luck, and have fun!

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