help with "doublet" and "triplet"

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help with "doublet" and "triplet"

Postby lioth » Tue Aug 14, 2018 5:50 am

Help,
i'm new here and in sodoku.
i'm trying to learn about resolution technique (in french doublet and triplet)
can i have some advices about this technique with my example here?
sorry for my poor english.
thanks a lot

https://imgur.com/a/OLseqT2
lioth
 
Posts: 2
Joined: 14 August 2018

Re: help with "doublet" and "triplet"

Postby champagne » Tue Aug 14, 2018 11:17 am

Hi lioth,
welcome here.

your link is to a site requiring use of cookies.

As I guess other members of the forum, I am reluctant to go on such sites unless I have a good idea of their behaviour
It would be better to load your puzzle here

(BTW I can speak french :roll: )
champagne
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Location: France Brittany

Re: help with "doublet" and "triplet"

Postby SpAce » Tue Aug 14, 2018 12:03 pm

lioth wrote:i'm trying to learn about resolution technique (in french doublet and triplet)
can i have some advices about this technique with my example here?

Hello, and welcome to the forum. I'm assuming that by "doublet" and "triplet" you mean what we call naked/hidden pairs and triples? Anyway, your puzzle doesn't require those techniques. Besides singles, it needs the two kinds of intersection techniques which we call "pointing pairs/triples" and "claiming" (or box/line reduction). You seem to be familiar with pointing pairs/triples already, as those reductions have been made in your pencil marks. There are two claiming operations available, however, after which the puzzle can be solved with singles only. (Actually just one claiming is required but I show both.)

Code: Select all
.------------------------.-----------------.--------------.
| 8       149-6   7      | 1469   2    469 | 46   3   5   |
| 45(6)   4(6)9   45(6)9 | 8      3    7   | 1    2   49  |
| 14-6    2       3      | 1469   5    469 | 467  79  8   |
:------------------------+-----------------+--------------:
| 3       46      46     | 79     79   8   | 5    1   2   |
| 57      79      59     | 2      4    1   | 8    6   3   |
| 12      8       12     | 5      6    3   | 9    4   7   |
:------------------------+-----------------+--------------:
|(1)47    3      (1)4    | 479    8    5   | 2    79  6   |
| 9       467-1   8      | 3467   17   2   | 347  5   14  |
| 2467-1  5       246-1  | 34679  179  469 | 347  8   149 |
'------------------------'-----------------'--------------'

1) Claiming: -6 b1p27 (i.e. r1c2, r3c1 <> 6)
2) Claiming: -1 b7p579 (i.e. r8c2, r9c1, r9c3 <> 1)

Claiming is similar but opposite to the pointing pair/triple technique, and typically a bit more difficult to spot. It means that if all candidates of a certain digit in a line (row or column) are within a single box, the other candidates of the same digit can be removed from the box (if any of them were true, there would be none left for the row/column). In your puzzle all candidates of the digit 6 in row 2 are inside box 1 (marked with brackets), thus all other 6s in box 1 can be eliminated (marked as -6). The same with the 1s in row 7 and box 7. (In fact, you could just do the claiming for 1s, and then a pointing pair later.)
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
SpAce
 
Posts: 680
Joined: 22 May 2017

Re: help with "doublet" and "triplet"

Postby SpAce » Tue Aug 14, 2018 1:35 pm

There is actually a hidden pair in column 3, but it doesn't really help solve the puzzle (you'll still need claiming):

Code: Select all
.---------------------.-----------------.--------------.
| 8      1469  7      | 1469   2    469 | 46   3   5   |
| 456    469  (59)-46 | 8      3    7   | 1    2   49  |
| 146    2     3      | 1469   5    469 | 467  79  8   |
:---------------------+-----------------+--------------:
| 3      46    46     | 79     79   8   | 5    1   2   |
| 57     79   (59)    | 2      4    1   | 8    6   3   |
| 12     8     12     | 5      6    3   | 9    4   7   |
:---------------------+-----------------+--------------:
| 147    3     14     | 479    8    5   | 2    79  6   |
| 9      1467  8      | 3467   17   2   | 347  5   14  |
| 12467  5     1246   | 34679  179  469 | 347  8   149 |
'---------------------'-----------------'--------------'

Hidden Pair (59)r25c3 => -46 r2c3

It means that there are only two cells in column 3 where the digits 5 and 9 can go, thus they must be reserved for them and other candidates can be removed from those two cells.

The same eliminations could be achieved with the corresponding naked quad which is seen in the other four cells in that column. Depending on one's solving style it might be actually easier to spot. It means that there are four cells in that column (rows 4,6,7,9) which share only the same four candidates (1,2,4,6); thus those digits must go into those four cells (in some yet unknown order) and can be eliminated from other cells in that column.

Naked Quad (1246)r4679c3 => -46 r2c3
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
SpAce
 
Posts: 680
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Re: help with "doublet" and "triplet"

Postby lioth » Tue Aug 14, 2018 1:43 pm

both many thanks for your time and explanations.
it's very easy to understand thanks to your exemple.

i have just to apply claiming now to progress !

thanks!!
lioth
 
Posts: 2
Joined: 14 August 2018

Re: help with "doublet" and "triplet"

Postby SpAce » Tue Aug 14, 2018 10:55 pm

lioth wrote:both many thanks for your time and explanations.
it's very easy to understand thanks to your exemple.

Glad if I could help!

i have just to apply claiming now to progress !

Yep. Claiming situations can be a bit tricky to spot for a pencil&paper solver (software helpers have single-digit filters that make them obvious), but they can sometimes be detected more easily indirectly. I show now how I often see them or the equivalent eliminations, even though they're usually considered more advanced techniques.

First the 1s:
Code: Select all
.------------------------.-----------------.--------------.
|  8       1469    7     | 1469   2    469 | 46   3   5   |
|  456     469     4569  | 8      3    7   | 1    2   49  |
| x46-1    2       3     | 1469   5    469 | 467  79  8   |
:------------------------+-----------------+--------------:
|  3       46      46    | 79     79   8   | 5    1   2   |
|  57      79      59    | 2      4    1   | 8    6   3   |
|*(1)2     8     *(1)2   | 5      6    3   | 9    4   7   |
:------------------------+-----------------+--------------:
|*(1)47    3     *(1)4   | 479    8    5   | 2    79  6   |
|  9       1467    8     | 3467   17   2   | 347  5   14  |
| x2467-1  5      x246-1 | 34679  179  469 | 347  8   149 |
'------------------------'-----------------'--------------'

Notice the cells with *(1). There are only two candidate 1s in rows 6 and 8 and they happen to share the same columns 1 and 3. That's an X-Wing. It means that all other 1s can be eliminated from those columns, because either r6c1&r7c3 or r6c3&r7c1 must be 1s. Compared to the claiming, it gives a bit different eliminations initially but the end result is the same as the (1)r1c2 is left as a hidden single in both cases. (This is not really easier than direct claiming, but it's another way to see the same eliminations.)

The 6s in box 1 can also be eliminated in another way:
Code: Select all
.----------------------.-------------------.----------------.
| 8     x149-6   7     |*14(6)9  2  *4(6)9 |*4(6)   3   5   |
| 456    469     4569  | 8       3   7     | 1      2   49  |
|x14-6   2       3     |*14(6)9  5  *4(6)9 |*4(6)7  79  8   |
:----------------------+-------------------+----------------:
| 3      46      46    | 79     79   8     | 5      1   2   |
| 57     79      59    | 2      4    1     | 8      6   3   |
| 12     8       12    | 5      6    3     | 9      4   7   |
:----------------------+-------------------+----------------:
| 147    3       14    | 479    8    5     | 2      79  6   |
| 9      1467    8     | 3467   17   2     | 347    5   14  |
| 12467  5       1246  | 34679  179  469   | 347    8   149 |
'----------------------'-------------------'----------------'

If we look at boxes 2 and 3, we notice that the 6s (starred) are located in rows 1 and 3 only. One of those boxes will have its 6 in row 1 and the other in row 3, which means any 6s in those rows can be eliminated from box 1. It's basically the same logic as with the earlier X-Wing even though it looks different (it's actually a Franken X-Wing). It's just another way of seeing that row 2 is the only place for 6s in box 1.
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
SpAce
 
Posts: 680
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