Programming a Sudoku Solver: Rokudoku

Rokudoku is the 6x6 variant of Sudoku. Rokudoku and Shidoku(4x4 variant) are known as Kids Sudoku. All variants of Sudoku which has a smaller grid than the normal Sudoku are collectively known as Sub Doku.

Below is a sample puzzle of Rokudoku. Fill in the grid so that every row, every column, and every 2x3 block contains the digits 1 through 6.