subsets: how to identify the target and solve?

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subsets: how to identify the target and solve?

Postby Riddick51PB » Tue Sep 16, 2008 4:48 pm

i'd like to see you solve this using the most elementary tool, which should be from the "Subsets" theory. page 33 of the workbook provided below. after your initial groundwork (scanning and the like), you should have 9 cells filled in. the 10th cell is what i'm interested in.

or, if you prefer, just solve the darn thing using your preferred course of action.

my specific questions:
  1. what is the 10th cell you filled in?
  2. what is the value of the 10th cell?
  3. tersely, what did you employ to arrive at the answer for the 10th blank cell? meaning, how did you target the 10th cell to fill in. can subsets theory lead you to the targeted 10th cell?


Mensa Guide to Solving Soduku
by Peter Gordon, Frank Longo
[Puzzle: #48]

Code: Select all
. . . | 9 . . | . 5 .
7 9 4 | . . . | . . .
. . . | . 3 6 | . . 1
------+-------+------
. . . | 6 . . | . . 5
. 4 3 | . . . | 8 7 .
8 . . | . . 4 | . . .
------+-------+------
9 . . | 3 5 . | . . .
. . . | . . . | 1 8 3
. 2 . | . . 7 | . . .




or, if you trust me:
Code: Select all
1236   168    1268   | 9      1247   128    | 2467   5      24678
7      9      4      | 1258   12     1258   | 236    236    268
25     58     258    | 4578   3      6      | 2479   249    1
---------------------+----------------------+---------------------
12     17     1279   | 6      12789  12389  | 249    1249   5
1256   4      3      | 125    129    125    | 8      7      269
8      1567   125679 | 1257   1279   4      | 2369   12369  269
---------------------+----------------------+---------------------
9      1678   1678   | 3      5      128    | 2467   246    2467
456    567    567    | 24     2469   259    | 1      8      3
13456  2      168    | 148    146    7      | 4569   469    469
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Postby Luke » Tue Sep 16, 2008 11:42 pm

Hi, Riddick,

This puzzle has so many "subsets" that choosing any one of them would likely solve the puzzle. There are no rules that lay down in what order or how a puzzle should be solved.

I'd put the pamphlet aside and go to Sudopedia and search for
-Naked pair
-Naked triple
-Hidden pair
-Hidden triple

No Mensa membership required!:)
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Postby daj95376 » Wed Sep 17, 2008 12:02 am

This smells like a homework assignment, but maybe not.

I suspect that all possible Locked Candidate moves along the way must be ignored.

Luke451 should have included Naked/Hidden Quads for completeness.

The first nine assignments are Naked/Hidden Singles. Then there are a number of Subset eliminations before the tenth assignment can be performed. I reversed the hierarch of applying Subsets, but arrived at the same tenth assignment. Probably a property of Subsets that I'm not aware exists.

Bottom Line: I see no indication that Riddick51PB tried to solve this problem him/herself.
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Postby Luke » Wed Sep 17, 2008 12:25 am

Not another riddle! You imply this is deeper than it appears.

But if so, why....
or, if you prefer, just solve the darn thing using your preferred course of action.
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re: Mensa Guide to Solving Soduku -- puzzle 48

Postby Pat » Wed Sep 17, 2008 4:58 am


      is it possible that Riddick51PB copied the question directly from the book?

      (Mensa Guide to Solving Soduku
      -- i haven't seen the book, perhaps that's their style of questions)
can subsets theory lead you to the targeted 10th cell?
Code: Select all
 . . . | 9 . . | . 5 .
 7 9 4 | . . . | . . .
 . . . | . 3 6 | . . 1
-------+-------+------
 . . . | 6 . . | . . 5
 . 4 3 | . . . | 8 7 .
 8 . . | . . 4 | . . .
-------+-------+------
 9 . . | 3 5 . | . . .
 . . . | . . . | 1 8 3
 . 2 . | . . 7 | . . .


evidently the puzzle was selected to provide an exercise in subsets --
  • box-line interactions (without subsets): will not solve the puzzle
  • subsets (without box-line interactions): will solve the puzzle

Luke451 wrote:This puzzle has so many subsets
that choosing any one of them would likely solve the puzzle
many, yes,
but not quite that easy
the 10th cell --
"hidden" duo in b1 + "naked" duo in b7
combine to create "naked" trio in c3



daj95376 wrote:I reversed the hierarch of applying Subsets, but arrived at the same tenth assignment. Probably a property of Subsets that I'm not aware exists.

i'll trust you that it does happen in the present example --
but generally, no such property
    different solution-paths, both using subsets,
    may solve different cells
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Postby daj95376 » Wed Sep 17, 2008 5:59 am

Update on my earlier reply:

Even if Locked Candidates are used, the same tenth assignment occurs.

Bottom Line: Luke451's suggestion still seems best -- go study Subsets.
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Postby Glyn » Wed Sep 17, 2008 6:59 am

I have managed to deliberately avoid making the placement of an 8 at r2c9 (I guess that's the one we all end up with most easily) and placed the 8 at r3c2 first instead. Just keep ignoring column 9 until the triple in column 3 is revealed.
Incidentally r1c6=8 is a singles backdoor for the puzzle. (corrected cell address)

can subsets theory lead you to the targeted 10th cell?


Is the implication here that the vulnerability of that cell could be identified before the application of any subsets? Now that might be clever. Does the book cover ALS or similar? If so is this where they get introduced, I guess a Mensa book might have a fast learning curve.
Last edited by Glyn on Wed Sep 17, 2008 7:19 am, edited 1 time in total.
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Postby daj95376 » Wed Sep 17, 2008 10:25 am

Hmmmmm. My solver placed [r3c2]=8 before [r2c9]=8 was available.
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Postby Glyn » Wed Sep 17, 2008 11:16 am

Daj Here's my manual route to both placements starting from here

Code: Select all
.---------------------.---------------------.---------------------.
| 126    3      1268  | 9      1247   128   | 2467   5      24678 |
| 7      9      4     | 158    12     1258  | 236    236    268   |
| 25     58     258   | 4578   3      6     | 2479   249    1     |
:---------------------+---------------------+---------------------:
| 12     17     1279  | 6      8      3     | 249    1249   5     |
| 1256   4      3     | 15     129    125   | 8      7      269   |
| 8      1567   125679| 157    1279   4     | 2369   12369  269   |
:---------------------+---------------------+---------------------:
| 9      1678   1678  | 3      5      18    | 2467   246    2467  |
| 4      57     57    | 2      6      9     | 1      8      3     |
| 3      2      168   | 148    14     7     | 5      469    469   |
'---------------------'---------------------'---------------------'


Locked candidates 7 Row 8 in Box 7.
Naked triple 258 in r3c123
Naked triple 168 in r179c3 => Hidden single r3c2=8. (10th placement)

Locked candidate 4 Box 8 Row 9
Naked triple 269 r569c9 => Naked single r2c9=8. (10th placement)

Now to find a way to get r1c6=8 as the 10th placement, which is proving more tricky.
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Postby Riddick51PB » Wed Sep 17, 2008 1:43 pm

Luke451 wrote:Hi, Riddick,

This puzzle has so many "subsets" that choosing any one of them would likely solve the puzzle. There are no rules that lay down in what order or how a puzzle should be solved.

I'd put the pamphlet aside and go to Sudopedia and search for
-Naked pair
-Naked triple
-Hidden pair
-Hidden triple

No Mensa membership required!:)


ok, sounds like you all agree on following this advice. so i'll go there.

evidence (beginner strats gave me):
  1. r1,c2=3
  2. r4,c5=8
  3. r4,c6=3
  4. r8,c1=4
  5. r8,c4=2
  6. r8,c5=6
  7. r8,c6=9
  8. r9,c1=3
  9. r9,c7=5

gawd i want to use r0,c0 notations. but r1-9,c1-9 is sensible.

i spent quite some time staring that thing down --- after those 9 were filled in. you might find that humorous:D


workbook: here's a link to the book on amazon

i'll set that aside and go to the sudopedia as mentioned.
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Postby Riddick51PB » Wed Sep 17, 2008 2:45 pm

my doubt is kicking in. i am a newcomer to sudoku.

would you all say that 1) or 2) is true?

1): this puzzle in the OP is a good learning exercise for a beginner. forge ahead and continue ice breaking.

-or-

2): this puzzle is not the best introduction to learning subsets. most likely too advanced for a beginner. i (you) recommend studying an easier puzzle to learn subsets.


a few of you check in and tell me what you think. i'll keep looking at it until i see a few replies on the recommended course of action. thanks for your input.
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Postby Riddick51PB » Wed Sep 17, 2008 3:40 pm

continuing until i hear otherwise:


in r8,c2=57
in r8,c3=57

and
in r7,c2=1678
in r7,c3=1678

===================
define the house as box 7:
so i can remove the "7" from both r7,c2 and r7,c3


now i have
in r7,c2=168
in r7,c3=168

[edit]this part is in error i believe

====================
define the house as row 7:
strip 168 from the rest of row 7.
now we have r7,c6=2

[/edit]
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Postby Glyn » Wed Sep 17, 2008 5:54 pm

Riddick51PB The first step is ok. Stripping the 7's from r7c2 and r7c3 is the application of Locked candidates 7 Row 8 in Box 7 that I used above. You have done it slightly differently by identifying a naked pair {57} in r8c23.

The section you highlighted that you thought to be in error is in fact wrong.

Look at Box 1 to see if you can find the naked triple. Apply it then find another one in Column 3.
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re: Mensa Guide to Solving Soduku -- puzzle 48

Postby Pat » Thu Sep 18, 2008 4:13 am

Pat wrote:
can subsets theory lead you to the targeted 10th cell?

evidently the puzzle was selected to provide an exercise in subsets---subsets (without box-line interactions) will solve the puzzle

the 10th cell --
"hidden" duo in box 1 + "naked" duo in box 7
combine to create "naked" trio in column 3


taking this as an exercise in subsets (deliberately avoiding any box-line interactions),
the 10th cell is the 8 in box 1


Riddick51PB wrote:i am a newcomer to sudoku.

would you all say that 1) or 2) is true?
    1) this puzzle in the OP is a good learning exercise for a beginner. forge ahead and continue ice breaking.

    2) this puzzle is not the best introduction to learning subsets. most likely too advanced for a beginner. i (you) recommend studying an easier puzzle to learn subsets.


Riddick51PB, this puzzle requires multiple applications of subsets -- is that too much? you tell me. (presumably you've done some simpler examples.)
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Postby daj95376 » Thu Sep 18, 2008 10:46 am

I too felt that the main emphasis of this puzzle was to use Subsets. However, Glyn's solution is thissss close to using them, and his/her solution is far better than the one produced by my solver.

Code: Select all
 *-----------------------------------------------------------------------------*
 | 126     3       1268    | 9       1247    128     | 2467    5       24678   |
 | 7       9       4       | 158     12      1258    | 236     236     268     |
 | 25      58      258     | 4578    3       6       | 2479    249     1       |
 |-------------------------+-------------------------+-------------------------|
 | 12      17      1279    | 6       8       3       | 249     1249    5       |
 | 1256    4       3       | 15      129     125     | 8       7       269     |
 | 8       1567    125679  | 157     1279    4       | 2369    12369   269     |
 |-------------------------+-------------------------+-------------------------|
 | 9       1678    1678    | 3       5       18      | 2467    246     2467    |
 | 4       57      57      | 2       6       9       | 1       8       3       |
 | 3       2       168     | 148     14      7       | 5       469     469     |
 *-----------------------------------------------------------------------------*

Glyn wrote:Locked candidates 7 Row 8 in Box 7.
Naked triple 258 in r3c123
Naked triple 168 in r179c3 => Hidden single r3c2=8. (10th placement)

Can also be viewed as:

Code: Select all
57  Naked  Pair   [r8c23]  => [r7c23]<>7
258 Naked  Triple [r3c123] => [r1c23]<>28
168 Naked  Triple [r179c3] => [r34c3]<>168
    Hidden Single          => [r3c2]=8      (10th placement)

Glyn wrote:Locked candidate 4 Box 8 Row 9
Naked triple 269 r569c9 => Naked single r2c9=8. (10th placement)

Can be expanded and viewed as:

Code: Select all
57  Naked  Pair   [r8c23]  => [r7c23]<>7
247 Hidden Triple [r7c789] => [r9c89]<>247
269 Naked  Triple [r569c9] => [r127c9]<>269
    Naked  Single          => [r2c9]=8      (10th placement)

Both paths use the same number of Subsets and arrive at alternate assignments. Nice work Glyn!
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