Hidden Quads are so rare that we can hardly find an example. Similar to Hidden Triplet in principle, four numbers and four cells, however, are involved to be a Hidden Quad. That is, if 4 numbers only exist in four cells of a given unit while each cell contains at least 2 of these 4 numbers, then other numbers can be eliminated from these cells. For numbers 1, 2, 4 and 5, for example, if any group of cells in the same unit contains one of the combinations below is a Hidden Quad:
{1, 2, 3, 4, 5} {1, 2, 4, 5, 8} {1, 2, 4, 5} {1, 2, 4, 5, 9}, or
{1, 2, 4} {1, 5, 8} {2, 3, 5} {4, 5, 7}, or
{4, 5} {1, 2, 4, 6} {2, 5, 8} {1, 2, 3, 4, 5}, or
{1, 2, 3, 5} {1, 5} {2, 4, 8} {4, 5, 9}, or
...
Those combinations can be a great many. Here's an example:
In Row A, numbers 2, 4, 8 and 9 are only found at cells [A4], [A6], [A7] and [A8], so we can remove all other numbers from these four cells. In this example, we can also use Naked Pair Technique against cells [A3] and [A5]. But in order to illustrate Hidden Quad Technique, we give it a higher priority to be used first.
In the following example:
In Column 6, candidates 1, 4, 8, 9 exist only at the highlighted cells. Therefore, we can safely remove other numbers from these four cells.
Surely enough, we can apply Hidden Quad Technique in blocks too. Unfortunately, we are unable to find such an example yet.
See Also:
