This technique is less used than Naked Triplet Technique, but their principles are quite similar. Any group of four cells in the same unit that contain in total four candidates (while each cell must contain at lease two candidates) is a Naked Quad. For a number set {1, 2, 4, 5}, for example, the combinations of a Naked Quad can be one of the followings:
{1, 2, 4, 5} {1, 2, 4, 5} {1, 2, 4, 5} {1, 2, 4, 5}, or
{1, 2, 4} {1, 4, 5} {2, 5} {1, 2}, or
{1, 2, 4, 5} {2, 5} {2, 4, 5} {1, 2, 4, 5}, or
{2, 5} {4, 5} {1, 2, 5} {1, 2, 4}, or
{1, 2, 5} {1, 2, 4, 5} {1, 2, 4, 5} {2, 4}, or
...
However, cells containing the following combination do not form a Naked Quad:
{1, 2, 4, 5} {2, 4} {2, 5} {2, 4, 5}
Among the candidates above, {2, 4} {2, 5} {2, 4, 5} form a Naked Triplet, so that after applying Naked Triplet Technique, only sole number 1 is left in the first number set {1, 2, 4, 5}, and then Naked Single Technique can be used.
In the following example:
cells [D1], [D4], [D6] and [D8] in Row D which contain {3, 5, 6}, {2, 5, 6}, {2, 5, 6} and {3, 5, 6} respectively form a Naked Quad of numbers {2, 3, 5, 6}. So we can remove these values from other cells ([D3] and [D7] in this example) in this row.
Here is another example:
In Column 9, candidates at cells [C9], [D9], [E9] and [G9] form a Naked Quad of numbers {1, 6, 7, 8}. So candidates in cells [A9] and [B9] must not contain any of these numbers.
The same can happen in blocks:
In Block at [A7], cells [B9], [C7], [C8] and [C9] contain {6, 7}, {1, 6, 8}, {7, 8} and {1, 6, 7, 8} respectively, which are subsets of number quad {1, 6, 7, 8}. Therefore, these values cannot occur in the other cells in Block at [A7].
See Also:
