Programming a Sudoku Solver: Shidoku, Children Sudoku, Kids Sudoku

Shidoku, also known as Children Sudoku, is the smaller and easier 4x4 variant of Sudoku. Shidoku and Rokudoku(6x6 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 Shidoku. Fill in the grid so that every row, every column, and every 2x2 block contains the digits 1 through 4.