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.
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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!