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logic

 
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Don Odone



Joined: 18 Aug 2006
Posts: 2

PostPosted: Sat Aug 19, 2006 4:37 pm    Post subject: logic Reply with quote

How does the naked triple work?
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Aug 19, 2006 5:04 pm    Post subject: Reply with quote

Don,

You should have posted this in the same thread as your original question, to make it easier for others to follow. Just click on the 'post reply' button at the bottom under the last post.

Look at column 2 in the puzzle.
Code:

 *---------------------------------------------------------------------------*
 | 14579  57     2       | 8       6       39      | 3579    4579    3479    |
 | 45679  567    4567    | 1       2349    239     | 35679   8       234679  |
 | 46789  3      4678    | 2479    249     5       | 1       2479    24679   |
 |-----------------------+-------------------------+-------------------------|
 | 3      25678  5678    | 269     289     269     | 4       1       26789   |
 | 268    4      68      | 5       1289    7       | 689     3       2689    |
 | 2678   9      1       | 246     2348    236     | 678     27      5       |
 |-----------------------+-------------------------+-------------------------|
 | 24578  2578   9       | 3       125     12      | 578     6       1478    |
 | 25678  1      35678   | 269     259     4       | 35789   579     3789    |
 | 456    56     3456    | 69      7       8       | 2       459     1349    |
 *---------------------------------------------------------------------------*


You'll notice that r1c2, r2c2 & r9c2 contain only the digits (5,6 & 7). One of these cells must be 5, one must be 6 and one must be 7. You don't know which digit goes in what cell but those three cells must contain one of those three numbers. Therefore no other cells in that column can contain any of those three digits and they can be excluded from all other cells in that column.
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Marty R.



Joined: 12 Feb 2006
Posts: 5159
Location: Rochester, NY, USA

PostPosted: Sat Aug 19, 2006 5:13 pm    Post subject: Re: logic Reply with quote

Don Odone wrote:
How does the naked triple work?

It involves three numbers that can occupy only three cells in a row, column or box, though you don't know which number goes in which cell. Let's use 123 as an example.

Three cells contain only 123 in some combination. The three cells could be 123-123-123 or 12-123-123 or 12-13-23 or any combination of 123. These three cells cannot contain any number other than the 123 and none of 123 can go in any other cell.

The value lies in the fact that since 123 must go in those three cells in some combination, 123 can be eliminated as possibilities from all other cells in that row, column or box. Eliminating those possibilities can open up many other possibilities, including the direct solving of a cell.

The same principle applies to a naked pair, quad, etc.

Hope this makes sense.

P.S. I wrote this out not being aware of Tracy's post.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Aug 19, 2006 10:48 pm    Post subject: Reply with quote

You did a more thorough job than I did.
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