Sudoku Solving Techniques

Hidden Quad

The Hidden Quad technique is similar to the Hidden Triplet technique. Instead of three cells and three digits for the Hidden Triplet technique, the Hidden Quad technique involves four cells and four digits.

In a 9-cell unit (a row, a column, or a 3x3 block) of a Sudoku puzzle, if four certain digits appear only in four cells as candidates, that is, only four cells in a 9-cell unit contain some of these four candidate digits, and the other cells do not have any of them, then these four digits have nowhere to go in the 9-cell unit but these four cells. They must each occupy one of these four cells, and other candidate digits cannot occupy any of these cells. So if other digits appear in these four cells as candidates, they can be removed.

Please note that:

• It is not necessary that each of these four cells have all these four digits as candidates.
• These four cells may have candidate digits other than these four certain digits.
• Also, it is not necessary for each of the four digits to be a candidate for all four cells.
• It is only required that, in a 9-cell unit, only these four cells each have some of these four certain digits as candidates.

We will demonstrate this technique visually with the following examples.

Example 1 - Hidden Quad in a Row

In row R1 of the puzzle in Figure 1a, the four digits 3, 6, 8, and 9 (marked in red) may appear only in four cells (R1,C3), (R1,C5), (R1,C6), and (R1,C7) (marked in orange) as candidates, but nowhere else. These four cells are the only choices for the four digits in this row. In this situation, the digits 3, 6, 8, and 9 each will occupy one of these four orange cells, and no other candidate digits can occupy any of them. As a result, other candidate digits in the orange cells can be removed, as shown in Figure 1b below.

Example 2 - Hidden Quad in a Column

In column C5 of the puzzle in Figure 2a, the four digits 2, 5, 6, and 7 (marked in red) may appear only in four cells (R1,C5), (R3,C5), (R4,C5), and (R5,C5) (marked in orange) as candidates, but nowhere else. These four cells are the only choices for the four digits in this column. In this situation, the digits 2, 5, 6, and 7 each will occupy one of these four orange cells, and no other candidate digits can occupy any of them. As a result, other candidate digits in the orange cells can be removed, as shown in Figure 2b below.

Example 3 - Hidden Quad in a Block

In block B9 of the puzzle in Figure 3a, the four digits 4, 6, 8, and 9 (marked in red) may appear only in four cells (R7,C7), (R7,C8), (R9,C7) and (R9,C8) (marked in orange) as candidates, but nowhere else. These four cells are the only choices for the four digits in this block. In this situation, the digits 4, 6, 8, and 9 each will occupy one of these four orange cells, and no other candidate digits can occupy any of them. As a result, other candidate digits in the orange cells can be removed, as shown in Figure 3b below.