by Nick67 » Thu Oct 06, 2005 9:41 pm
You present a nice example!
Let's consider cells 4,6, and 9 first.
The candidates for these cells are:
(1,3,6) (1,3,6) (1,6)
This is a "naked triple".
Among the 3 cells, there are only 3 candidates.
So, in the final solution, these 3 numbers
*must* appear in those 3 cells!
So, we can eliminate those candidates (1,3,6) from
all other cells in the row.
Let's consider cells 1,3, and 7 next.
The candidates for these cells are:
(3,6,8,9) (3,5,8,9) (1,3,5,9)
This is a "hidden triple."
The candidates 5, 8, and 9 appear *only* in
these 3 cells, and nowhere else.
So clearly, in the final solution, these 3 numbers
must appear in these 3 cells. There is no
room for any other number in these cells, so
we can eliminate numbers besides 5,8, and 9
as candidates in these 3 cells.
Notice the naked triple is much easier to spot, because
we can see it by looking at *just* the 3 involved cells.
To spot the hidden triple, we have to look at all 9 cells.
Let me end with a quote from Sudoku expert Angus Johnson:
"Hidden triples are generally extremely hard to
spot but fortunately they're rarely required to solve a puzzle."