Spotting A Triple: What's The Logic?

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Spotting A Triple: What's The Logic?

Postby Yogi » Sat May 14, 2016 11:18 pm

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295700860031865920806000000007050006000387000500016700000500109020600350054008672 Still having trouble converting this to a readable grid image.
A program I was working with gave this analysis: 1. Naked triple {249} found at r4c467
This leads on to r3c1 = 3 and the puzzle is readily solvable after the flow-on from that and noting that r8c5 = 7 (Trying 7 at r7c5 chains to a false 2 at r8c5)
However, I did not spot the Triple at r4c467. The 2 in this row is limited to these three cells, but what identifies them as a locked triple for 2,4 and 9?
Or putting it the other way, why could the 4 and 9 not be anywhere else in this row?
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Re: Spotting A Triple: What's The Logic?

Postby Leren » Sat May 14, 2016 11:57 pm

Here is the naked Triple move:

Code: Select all
*---------------------------------------------------------------*
| 2     9     5      | 7     34    134    | 8     6      134    |
| 47    3     1      | 8     6     5      | 9     2      47     |
| 8     47    6      | 1249  2349  12349  | 45    134    13457  |
|--------------------+--------------------+---------------------|
| 3-49  18-4  7      |*249   5    *249    |*24    138-49 6      |
| 469   146   29     | 3     8     7      | 245   149    145    |
| 5     48    2389   | 249   1     6      | 7     3489   348    |
|--------------------+--------------------+---------------------|
| 367   678   38     | 5     2347  234    | 1     48     9      |
| 179   2     89     | 6     479   149    | 3     5      48     |
| 139   5     4      | 19    39    8      | 6     7      2      |
*---------------------------------------------------------------*

You can see that the three cells marked * only contain three different digits : 2, 4 and 9. So these 3 digits must occupy these three cells in some order (it doesn't matter which order).

The important point is that any cell that can see all of these three cells can have 2, 4 and 9 removed. In this case it apples to any cell in Row 4 except for the three * cells, 5 eliminations in this case.

The logic underlying these eliminations is that, if any other cell in Row 4 solved to 2, 4, or 9 there wouldn't be enough digits to fill the three * cells, and at least one of them would be empty - that's bad !

Note that the three cells must be in the same row, column or box for this move to apply.

Also, here is the puzzle in . line format : 2957..86..3186592.8.6........7.5...6...387...5...167.....5..1.9.2.6..35..54..8672

Links to good teaching sites that explain the naked triple move can be found here and here.

Leren

PS thanks to Jason for showing me how to change the URL gobbldegook into nice labels. Only took me 4 years to get around to asking him how to do it but better late than never.
Last edited by Leren on Sun May 15, 2016 9:14 am, edited 3 times in total.
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Re: Spotting A Triple: What's The Logic?

Postby JasonLion » Sun May 15, 2016 1:03 am

To add a few words to what Leren said:

The marked cells each must contain one of the digits. Since the three cells share a house, none of the digits can repeat in two or more cells. Thus the three marked cells together use up the digits, three cells, three digits, no other options.
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Re: Spotting A Triple: What's The Logic?

Postby Yogi » Mon May 16, 2016 7:30 am

Thanx guys. I think I've got it. I seem to have a different way of processing or explaining these things.
Is it right to say that the reason these three cells form a locked triple is that they ONLY have candidates from that group of 2, 4 and 9?
Therefore they encompass between them all possible arrangements of those three candidates and therefore no other cells in that House (in this case a row) could be a 2, 4 or 9.
I think an easy way to conceptualise this is to say that because the candidates are locked into these particular cells, they are locked OUT of everywhere else in that House.
Or simply - 'They MUST be in there, so they CAN'T be anywhere else.'
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Re: Spotting A Triple: What's The Logic?

Postby Leren » Mon May 16, 2016 7:56 am

Hi Yogi, there is nothing wrong with what you are saying, I thought I said all this in my post in different words, but if you understand your own words better then mine, that's OK.

For similar reasons you can get a locked quad - four cells in a house with only four different digits in them, with eliminations possible in the other cells in the house.

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Re: Spotting A Triple: What's The Logic?

Postby enxio27 » Tue May 17, 2016 4:01 pm

Yogi wrote:Is it right to say that the reason these three cells form a locked triple is that they ONLY have candidates from that group of 2, 4 and 9?
Therefore they encompass between them all possible arrangements of those three candidates and therefore no other cells in that House (in this case a row) could be a 2, 4 or 9.
I think an easy way to conceptualise this is to say that because the candidates are locked into these particular cells, they are locked OUT of everywhere else in that House.
Or simply - 'They MUST be in there, so they CAN'T be anywhere else.'

Exactly.
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