I believe this is the unique solution for your puzzle:
Solution PicAnd I think these are the rules:
1. Each 1x3 or 3x1 bar contains one each of 1,2,3.
2. Adjacent cells (horizontally or vertically) cannot contain the same number.
3. Each row/column contain three each of 1,2,3.
Under these rules the puzzle is pretty straightforward, requiring no more than singles to solve.