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."