Every cell in a Sudoku puzzle is shared by three houses (one row, one column, and one 3 x 3 block). This is an extremely important concept to get about Sudoku puzzles. As an example, we are going to concentrate on cell R3C5 (row 3, column 5) outlined in black below:
The three houses shared by cell R3C5 are shown above highlighted in gray. It is important to understand how each cell is shared by three different houses. The idea of a cell participating in three houses is key in determining what possible numbers can go into a blank cell.
Notice the tiny numbers in cell R3C5. These are called “possible candidates”. What this means is the tiny numbers showing up in cell R3C5 are the possible numbers the cell could be. Our job is to narrow this list down to a single number so we can select it as the value for the cell.
It is important to understand how these tiny numbers are determined. These tiny numbers are determined by the intersection of the three shared houses of cell R3C5. If you look at the house making up row 3 it has the numbers 1, 3, 7, and 9. The house making up column 5 has the number 6. And the house making up block 2 has the numbers 1 and 2. The tiny numbers that go into cell R3C5 are whatever is left missing from the numbers 1 through 9. In this case, the numbers 4, 5, and 8.
A 9 x 9 grid has 81 cells. Each of the 81 cells is shared by the intersection of three houses. By considering the location of every given we can fill out all the possible candidates for all the cells in the puzzle:
