The New Sudoku Players' Forum

by **papakapp** » Mon Jan 30, 2006 8:31 am

after the standard solving techniques were exhausted my board looked like this

726 3_4 _91
385 _9_ 74_
941 ___ _3_
819 437 265
57_ 9_6 _1_
63_ 51_ _79
46_ ___ 92_
298 _43 15_
15_ 2_9 _84

I was then stumped. I took a 50/50 chance and put a 3 in R9 C3 (or is it stated thus: R3 C9?) I was then able to solve the puzzle but I am still pulling my hair out over this one. I know that there must be some way to deduce the next number through logic or else the puzzle would have more than one solution. So what is the logic and how do you apply it??!

ARGH

p.s. I'm new here, so if somebody says "Well you should have used zogdors chicken-choking technique" Or something like that I will have no idea what you are talking about. Anyway, be warned, I am not yet part of the sudoku subculture so if you make obscure references, please link to a definition of them.

p.p.s. If there is more than one way to proceed from here, I'm all ears.

to all who reply, thanks for taking the time. I am amazed that some little puzzle that I got in a book last christmas can have such a devout following.

726 384 591
385 192 746
941 765 832
819 437 265
574 926 318
632 518 479
467 851 923
298 643 157
153 279 684

if anybody wants to see the solution then click the quote button

this may be a stupid thing to ask but how do you type pipes to make those nifty little ascii sudoku boards on these forums?

by **vidarino** » Mon Jan 30, 2006 8:45 am

Writing down the possible candidates for all the cells should reveal a couple of so-called naked pairs. (A naked pair is two cells that share the same two candidates, and no others. That means that each of the candidates must be in one of those two cells, and can safely be eliminated from the rest of the box/row/column that hosts the pair.) After doing those eliminations, a few more numbers can be fixed.

Then it gets a bit more complicated. You are going to run into an X-Wing, and then an XY-Wing, as far as I can see. These are explained on numerous web-sites (google is your friend), but http://angusj.com/sudoku/hints.php ought to shed some light, at least.

After that it's all singles.

Good luck!

Vidar

by **papakapp** » Mon Jan 30, 2006 9:07 am

I actually looked for some naked pairs and hidden pairs but I really don't see a specific spot where that benefits in this case. I am still missing something.

oh, and thanks for the link. I have been using x wings, (although not with the knowledge of that name) but where the heck is the logic behind a swordfish? Why would that rule out anything?

by **vidarino** » Mon Jan 30, 2006 9:19 am

papakapp wrote:I actually looked for some naked pairs and hidden pairs but I really don't see a specific spot where that benefits in this case. I am still missing something.

Here is the initial candidate list:

Code: Select all: 7 2 6 | 3 58 4 | 58 9 1 3 8 5 | 16 9 12 | 7 4 26 9 4 1 | 678 25678 258 | 568 3 268 -----------------------+-----------------------+----------------------- 8 1 9 | 4 3 7 | 2 6 5 5 7 24 | 9 28 6 | 348 1 38 6 3 24 | 5 1 28 | 48 7 9 -----------------------+-----------------------+----------------------- 4 6 37 | 178 578 158 | 9 2 37 2 9 8 | 67 4 3 | 1 5 67 1 5 37 | 2 67 9 | 36 8 4

Row 7, then Col 5.

but where the heck is the logic behind a swordfish? Why would that rule out anything?

Put short; In any NxN sized (N=2 is X-Wing, 3 is Swordfish, 4 is Jellyfish) pattern, there are only so many ways you can arrange the numbers;

Code: Select all: X.. X.. .X. .X. ..X ..X .X. ..X X.. ..X X.. .X. ..X .X. ..X X.. .X. X..

In either of these combinations, there exists one X in every vertical column involved, which would eliminate them from the columns outside of the NxN grid, even if we don't know exactly which of the patterns is the correct one.

Vidar

by **papakapp** » Mon Jan 30, 2006 9:36 am

vidarino wrote:
papakapp wrote:I actually looked for some naked pairs and hidden pairs but I really don't see a specific spot where that benefits in this case. I am still missing something.

Here is the initial candidate list:
Code: Select all
7 2 6 | 3 58 4 | 58 9 1 3 8 5 | 16 9 12 | 7 4 26 9 4 1 | 678 25678 258 | 568 3 268 -----------------------+-----------------------+----------------------- 8 1 9 | 4 3 7 | 2 6 5 5 7 24 | 9 28 6 | 348 1 38 6 3 24 | 5 1 28 | 48 7 9 -----------------------+-----------------------+----------------------- 4 6 37 | 178 578 158 | 9 2 37 2 9 8 | 67 4 3 | 1 5 67 1 5 37 | 2 67 9 | 36 8 4

Row 7, then Col 5.

Code: Select all: 7 2 6 | 3 58 4 | 58 9 1 3 8 5 | 16 9 12 | 7 4 26 9 4 1 | 678 25678 258 | 568 3 268 -----------------------+-----------------------+----------------------- 8 1 9 | 4 3 7 | 2 6 5 5 7 24 | 9 28 6 | 348 1 38 6 3 24 | 5 1 28 | 48 7 9 -----------------------+-----------------------+----------------------- 4 6 37 | 18 58 158 | 9 2 37 2 9 8 | 67 4 3 | 1 5 67 1 5 37 | 2 67 9 | 36 8 4

okay, I modified the board to look like what I think it should look like after implementing naked pairs but that didn't really tell me squat. I must be missing something. :?:

but where the heck is the logic behind a swordfish? Why would that rule out anything?

Put short; In any NxN sized (N=2 is X-Wing, 3 is Swordfish, 4 is Jellyfish) pattern, there are only so many ways you can arrange the numbers;

Code: Select all
X.. X.. .X. .X. ..X ..X .X. ..X X.. ..X X.. .X. ..X .X. ..X X.. .X. X..

In either of these combinations, there exists one X in every vertical column involved, which would eliminate them from the columns outside of the NxN grid, even if we don't know exactly which of the patterns is the correct one.

Vidar

Aahhhh You're a genius. You finally were somone that explained swordfish in a way that made sense. thanks.

by **vidarino** » Mon Jan 30, 2006 11:56 am

papakapp wrote:
Code: Select all
7 2 6 | 3 58 4 | 58 9 1 3 8 5 | 16 9 12 | 7 4 26 9 4 1 | 678 25678 258 | 568 3 268 -----------------------+-----------------------+----------------------- 8 1 9 | 4 3 7 | 2 6 5 5 7 24 | 9 28 6 | 348 1 38 6 3 24 | 5 1 28 | 48 7 9 -----------------------+-----------------------+----------------------- 4 6 37 | 18 58 158 | 9 2 37 2 9 8 | 67 4 3 | 1 5 67 1 5 37 | 2 67 9 | 36 8 4

okay, I modified the board to look like what I think it should look like after implementing naked pairs but that didn't really tell me squat. I must be missing something.

Correct so far. Now look in column 5 for a newly revealed naked pair, and the rest should be a walk in the park from there.

Aahhhh You're a genius. You finally were somone that explained swordfish in a way that made sense. thanks.

Hehe, happy to be of assistance.

Vidar

by **tso** » Mon Jan 30, 2006 7:34 pm

From this point, here are some ways to proceed:

Puzzle as posted:

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

Candidate lists:

CL 1 -- I've left out the solved cells for clarity.

Code: Select all: *--------------------------------------------------------------------* | . . . | . 58 . | 58 . . | | . . . | 16 . 12 | . . 26 | | . . . | 678 25678 258 | 568 . 268 | |----------------------+----------------------+----------------------| | . . . | . . . | . . . | | . . 24 | . 28 . | 348 . 38 | | . . 24 | . . 28 | 48 . . | |----------------------+----------------------+----------------------| | . . 37 | 178 578 158 | . . 37 | | . . . | 67 . . | . . 67 | | . . 37 | . 67 . | 36 . . | *--------------------------------------------------------------------*

1) In box 8 there is a naked pair of [67][67] that excludes 6s and 7s from the rest of the box.
2) After these exclusions, there is a naked pair [58][58] in column 5 that excludes 5s and 8s from the rest of the column.
3) After this, there are several naked singles.

The situation now looks like this:

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

CL2

Code: Select all: *--------------------------------------------------* | . . . | . 58 . | 58 . . | | . . . |[16] . 12 | . . [26] | | . . . |x678 67 25 | 568 . 2x68 | |----------------+----------------+----------------| | . . . | . . . | . . . | | . . . | . . . | 38 . 38 | | . . . | . . . | . . . | |----------------+----------------+----------------| | . . 37 | 18 58 15 | . . 37 | | . . . |[67] . . | . . [67] | | . . 37 | . 67 . | 36 . . | *--------------------------------------------------*

4a) The four cells in [brackets] form an "x-wing" in 6s. These are the only two cells in rows 2 and 8 that can hold a 6; therefore, exclude all other 6s in columns 4 and 9, marked with 'x'.

There are now (at least) two obvious ways to finish the puzzle.
CL3

Code: Select all: *--------------------------------------------------* | . . . | . [58] . | 5x8 . . | | . . . | 16 . 12 | . . 26 | | . . . | 7x8 67 [25] | 568 . [28] | |----------------+----------------+----------------| | . . . | . . . | . . . | | . . . | . . . | 38 . 38 | | . . . | . . . | . . . | |----------------+----------------+----------------| | . . 37 | 18 58 15 | . . 37 | | . . . | 67 . . | . . 67 | | . . 37 | . 67 . | 36 . . | *--------------------------------------------------*

One way is:
5a1) There is an "xy-wing" in [brackets]. Any value in any of these three cells forces r3c4<>8 and r1c7<>8.

(Alternately, there is another xy-wing: r1c7-r3c9-r3c6 is an xy-wing in 5s. Any value in any of these three cells forces both r1c5<>5 and r3c7<>5. An xy-wing is the shortest possible forcing chain. There are dozens of longer forcing chains that will also solve the puzzle.)

The rest of the puzzle is solved with singles.

Another solution from the same postition is "BUG" or "Bivalue Universal Grave".

5a2) All but one of the undecided cells have only two candidates. The other one (r3c7=568) has three candidates. One of the candidates (the 8) appears three times in the row, column and box that the cell is in. The BUG theory allows you to place this digit -- 8 -- into the cell -- just like that.

The rest of the puzzle is solved with singles.

One last solution that solves the puzzle *before* the x-wing.

CL2b

Code: Select all: *--------------------------------------------------* | . . . | . 58 . | 58 . . | | . . . | 16 . 12 | . . 26 | | . . . |[678] 67 25 |[568] . [268] | |----------------+----------------+----------------| | . . . | . . . | . . . | | . . . | . . . | 38 . 38 | | . . . | . . . | . . . | |----------------+----------------+----------------| | . . 37 | 18 58 15 | . . 37 | | . . . | 67 . . | . . 67 | | . . 37 | . 67 . | 36 . . | *--------------------------------------------------*

4b) There are THREE cells that have three candidates, marked in [brackets].
To avoid a BUG at least ONE of these three statements must be true:
-- r3c4=6
-- r3c7=8
-- r3c9=6

However, if r3c7=6, then NONE of these three will be true. Therefore, r3c7<>6.

After this, the puzzle can be solved with singles alone -- no x-wing or xy-wings required.

by **eclark** » Tue Jan 31, 2006 4:40 am

I found two subsets, one x-wing, and one xy-wing then after that it was all singles

The New Sudoku Players' Forum

what solving technique should have been applied here?

what solving technique should have been applied here?