The title suggests
The oddly-numbered squares are colored, and the few numbers we have support that theory.
This means the colored squares are 1's or 3's, the white squares are 0's or 2's.
The few numbers we have force a few of the first lines, and from there I just followed the slitherlink clockwise around the grid filling in numbers as I went.
Some rules I used:
If the line bordered a white square, it had to be a 2.
If three lines couldn't fit around a colored square, it had to be a 1. This is my first ever attempt at a slitherlink so hope I didn't miss anything! It was fun!
The starting point:
The point between the two 3's must have a line going to it from each of the 3 boxes, so these two edges are forced no matter what:
From there it was pretty easy to follow the line. It has to avoid the "0" and then just continue clockwise following the rules.
