Write a function to solve a mini-Sodoku problem as follows. On a partially-filled 3x3 board, place int instances in the range {1, 2, 3} so that no row or column contains a repeated value. Explain your reasoning.

Partially filled

_	2	_
3	1	_
_	3	_

Solved

1	2	3
3	1	2
2	3	1