Intermediate technique · 06
Three numbers are hiding in three cells of a house.
The idea
A Hidden Triple occurs when three numbers in a house can appear only in three cells, even though those cells contain extra candidates.
The question: Which three numbers are confined to three cells in this house?
Walkthroughs
A Hidden Triple usually appears in houses with six or more unsolved cells.
Walkthrough
Only three numbers 2, 3 and 8 in box 6 are restricted to cells r4c7, r6c7 and r6c9, no other cell in box 6 can have these three numbers, so this is a Hidden Triple and rest of numbers, in this example, number 1 and 4, can be removed from these three cells.
What to notice: Look at houses that have six or more empty cells in which most likely a Hidden Triple will present.
Walkthrough
In column 7, three numbers 1, 3 and 5 are restricted to cells r1c7, r7c7 and r9c7, no other cell in column 7 can have these three numbers, since number 7 appears in cell r7c7, so this is a Hidden Triple and number 7 can be removed from cell r7c7.
What to notice: Hidden Triple can happen in any row, column or box that have six or more empty cells.
How it works
The useful information is attached to the numbers rather than the cells. Once the three numbers are identified in only three cells in a house, every other candidate in those cells can be removed.
Choose three numbers, and track their possible positions through one house.
If all three numbers are confined to three cells in this house, the hidden triple is present.
Keep only the three hidden numbers in those three cells, remove every other candidate from those three cells.
A useful reminder
Hidden Subset, Hidden Triple 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.
