Naked quad
The naked quad is a basic sudoku solving technique that you need to master.
Principle
If you have already mastered the naked pair and naked triple techniques, then you should easily understand the naked quad technique. The principle is the same for four cells and four numbers.
A naked quad is a set of four cells belonging to the same row, column, or region, and whose set formed by their combined candidate values contains four distinct numbers in total.
Each cell of the naked quad can contain either all four candidates values, or only two or three among the four, as long as on the whole of the quad the preceding condition is respected (four distinct numbers in total).
In the grid solution, these four numbers will necessarily be in these four cells. Therefore, they can be eliminated as candidates from all other cells of the row, column, or region shared by the quad.
Examples
Example 1 : naked quad on region
On region 1, cells A2, A3, B3, and C3 have four distinct numbers as combined candidates : 2, 6, 7, and 9. These four numbers can be eliminated as candidates from all other cells of region 1, here B1, B2, C1 and C2.
Example 2 : naked quad on row
On row B, cells B1, B3, B7, and B9 have four distinct numbers as combined candidates : 2, 3, 4, and 5. These four numbers can be eliminated as candidates from all other cells of row B, here B2, B4, B5 and B6.
Example 3 : naked quad on column
On column 5, cells A5, D5, E5, and K5 have four distinct numbers as combined candidates : 2, 4, 5, and 6. These four numbers can be eliminated as candidates from all other cells of column 5, here B5, C5, G5 and H5.
Exercises
The sudoku grids below require, to be solved, to use the naked quad technique, as well as some naked pairs and naked triples :
- Sudoku n°76034 (Medium)
- Sudoku n°96324 (Medium)
- Sudoku n°450178 (Medium)
- Sudoku n°237890 (Medium)
- Sudoku n°145816 (Medium)
Naked quads are much rarer than naked pairs and naked triples. Perhaps you will meet some in our daily sudokus of medium and higher levels.