## naked triples

Advanced methods and approaches for solving Sudoku puzzles

### naked triples

I find this topic to be the most difficult to visualize and employ. Here is an example with a row of entries:

(3,6,8,9),(4),(3,5,8,9),(1,3,6)(2),(1,3,6),(1,3,5,9),(7),(1,6)

Now someone will say there are two naked triples above, (5,8,9) and (1,3,6), but it's unclear to me why that's the case. Please explain and also explain how one can see this.

Thanks.
rp

Posts: 1
Joined: 07 August 2005

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."
Nick67

Posts: 113
Joined: 24 August 2007

I can see one hidden triple 589 - only three places in the row where these 3 numbers can go. One naked triple 136 - three places in the row where only these 3 numbers can go. Subtle difference. Do you see it?

Edit : Oops Paul beat me to it!
emm

Posts: 987
Joined: 02 July 2005

em wrote:Edit : Oops Paul beat me to it!

But you said it so much more concisely! Nicely done.
Nick67

Posts: 113
Joined: 24 August 2007

But I called you Paul! Sorry - it's the post-nomimal numbers that are confusing me. Your IQ'a not 67 is it?
emm

Posts: 987
Joined: 02 July 2005

em wrote:Your IQ'a not 67 is it?

Heh heh ... well, my utter failure to come up with a repartee points that way!
Nick67

Posts: 113
Joined: 24 August 2007