Sudoku Solver conceptual doubt

#1

I am not able to understand the subproblems in this q. From what I have learnt ,we normally divide the original problem into SIMILAR kind of subproblems , for example : in N queen problem , we placed the queen in one row and moved to the next row , so the problem reduced to a subproblem having one less row from original and this goes until we traverse all the rows . But in this question , we are moving cell to cell , how does moving from cell to cell divide the original problem into smaller grids( subproblems ) ?

#2

in n queen also you were moving cell to cell , but placing the queen only in one of the cells .
in this question you move to every cell and fill that cell with the suitable number from one to 9.
here the subproblems are of three types
1- fill a cell with x and fill the remaining row with S={ 1 to 9 - x};
2-fill a cell with x and fill the remaining column with S={ 1 to 9 - x };
3- fill a cell with x and fill the 3*3 matix with S= { 1 to 9 - x};

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#3

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