Santoitchi: Introduction

Question

Santoitchi is yet another genre involving trominoes. It appears to be invented by Inaba Naoki, and then picked up by Bram de Laat, who uses the name Sandwich (blame Google Translate for the possible mistranslation, as the genre apparently has nothing to do with sandwiches). The name seems to mean Three-and-One in Japanese with a deliberate misspelling (イッチ instead of the usual イチ for "one").
Here is an example puzzle with solution:
 
Rules:

Shade some cells. The shaded cells are not allowed to share an edge.
Divide the unshaded cells into trominoes (contiguous group of three cells).
Each tromino must contain exactly one number.
The number indicates how many shaded cells share an edge with the region. (Not to be confused with "how many edges of the region are shared with shaded cells")

Now solve the following puzzle, which features only threes and ones (as in the name of the genre). A question mark represents one number between zero (inclusive) and infinity.

Deusovi · Accepted Answer

First,

Now, since every tromino must have exactly one clue in it,

Next we can look at a different area of the puzzle:

And finally, one argument finishes it off:

Santoitchi: Introduction

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