Intermediate technique · 07
Four cells collectively reserve four candidates.
The idea
A Naked Quad occurs when four cells in one house collectively contain only four candidates. The four cells do not need identical candidate lists.
The question: Do these four cells contain exactly four candidates between them?
Walkthroughs
Each of those four cells does not have to be exact four candidates, but must be exact four numbers combined.
Walkthrough
Digits 2, 3, 5 and 7 forms a Naked Quad in column 8 because those four numbers are restricted to four column 8 cells r1c8, r3c8, r4c8 and r5c8, no other cells in column 8 can contain those four numbers and no other numbers are candidates of those four cells.
What to notice: Those four numbers must fill the four cells in a house and none can appear elsewhere in that house. Note that each individual of those four cells does not have to contain all four numbers.
Walkthrough
In this example, a Naked Quad is found in row 1, where numbers 2, 3, 7 and 9 are restricted to four row 1 cells r1c1, r1c2, r1c3 and r1c5, no other cells in row 1 can contain those four numbers and no other numbers are candidates of those four cells, therefore those four numbers can be removed from rest of cells in row 1.
What to notice: Look at houses that have eight or nine empty cells and you may find one like this.
Also note that similar to the example 01 above, the other four cells actually form a Hidden Quad.
How it works
In a house, those four numbers must fill the four cells in some order, so none can appear elsewhere in that house.
Look at a house with eight or nine cells unsolved
Find four cells whose combined candidate set contains exactly four numbers.
Remove those four numbers from every other cell of the same house.
A useful reminder
Naked Subset, Naked Quadruple are related terms you may encounter while learning this technique. The important part is understanding the constraint and why the elimination follows from it.
Watch & learn
Comming soon...
Practice
Once you can explain why the pattern is valid, practice finding it in a few real puzzle positions before moving on.
