Intermediate technique · 08
Four numbers are hiding in four cells of a house.
The idea
A Hidden Quad occurs when four numbers in a house can appear only in four cells, allowing every other candidate in those cells to be removed.
The question: Which four numbers are confined to four cells in this house?
Walkthroughs
Hidden Quad most likely happens in a house with eight or nine empty cells.
Walkthrough
Digits 2, 6, 7 and 9 in row 4 are restricted to cells r4c1, r4c2, r4c4 and r4c6, no other cell in row 4 can have these four numbers; also these four cells contain other numbers, so this is a Hidden Quad and rest of numbers, in this example, number 1, 3 and 4 can be removed from these four cells.
What to notice: Look at houses that have eight or nine empty cells and you may find one like this.
Walkthrough
In this example, a Hidden Quad is in box 6, where numbers 4, 5, 6 and 9 are restricted to cells r5c7, r5c9, r6c7 and r6c9, no other cell in box 6 can have these four numbers, so rest of numbers, in this example, number 1, 2 and 7 can be removed from these four cells.
What to notice: Hidden Quad could happen in a row, column or box that has most of cells unsolved.
How it works
The four numbers are hidden because the cells may contain extra candidates. Once their shared restriction is proven, those extras are no longer possible.
Look at a house with most of cells unfilled, then choose four numbers, and track the possible locations of each number within the house.
If all four numbers are confined to four cells in this house, a Hidden Quad is present.
Keep only the four hidden numbers in those four cells.
A useful reminder
Hidden Subset, 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.
