The New Sudoku Players' Forum

[Jasper32]

I have been working on this puzzle for quite some time now and have given up. Just hope one of you can tell me where to go from here to solve it. Thank you.

Jasper

*-----------*
|3..|...|..2|
|.2.|...|.47|
|...|726|..1|
|---+---+---|
|..2|6.1|5..|
|.8.|.7.|.2.|
|..3|2.9|4..|
|---+---+---|
|5..|837|...|
|27.|...|.8.|
|9..|...|..5|
*-----------*


*-----------*
|3.7|...|..2|
|.2.|...|.47|
|...|726|..1|
|---+---+---|
|..2|6.1|5..|
|.8.|.7.|.2.|
|..3|2.9|4..|
|---+---+---|
|5..|837|2..|
|27.|..5|.8.|
|938|..2|7.5|
*-----------*


*-----------------------------------------------------------*
| 3 1569 7 | 1459 159 48 | 689 569 2 |
| 168 2 1569 | 1359 159 38 | 689 4 7 |
| 48 459 459 | 7 2 6 | 389 359 1 |
|-------------------+-------------------+-------------------|
| 47 49 2 | 6 48 1 | 5 379 389 |
| 146 8 1569 | 345 7 34 | 169 2 69 |
| 167 156 3 | 2 58 9 | 4 167 68 |
|-------------------+-------------------+-------------------|
| 5 146 146 | 8 3 7 | 2 169 469 |
| 2 7 146 | 19 169 5 | 136 8 346 |
| 9 3 8 | 14 146 2 | 7 16 5 |
*-----------------------------------------------------------*

[RW]

Yes, it's a toughie. I can see a few pattern based eliminations, but none that solves the puzzle. A chain will do the trick though:

Code: Select all

 *--------------------------------------------------------------------*
 | 3      1569   7      | 1459   159    48     | 689    569    2      |
 | 168    2      1569   | 1359   159    38     | 689    4      7      |
 | 48     459    459    | 7      2      6      | 389    359    1      |
 |----------------------+----------------------+----------------------|
 | 47     49     2      | 6      48     1      | 5      379    389    |
 | 146    8      14569  | 345    7      34     | 169    2      69     |
 | 167    156    3      | 2      58     9      | 4      167    68     |
 |----------------------+----------------------+----------------------|
 | 5      146    146    | 8      3      7      | 2      169    469    |
 | 2      7      146    | 19     169    5      | 136    8      346    |
 | 9      3      8      | 14     146    2      | 7      16     5      |
 *--------------------------------------------------------------------*

[r6c8]=7=[r4c8]=3=[r4c9]-3-[r8c9]=3=[r8c7]=1=[r5c7]-1-[r6c8]

This chain tells us that if r6c8<>7 => r6c8<>1, in any case r6c8<>1. One XY-wing takes care of the rest.

btw. how did you get rid of 4 in r1c5?

RW

[Jasper32]

RW, Thank you for your help. I looked all over for a chain and don't think I ever would have found it without your help.

To answer how I removed the 4 in r1c5 , I couldn't begin to tell you because I don't have any idea at which stage of working on the puzzle the 4 was removed. I spent hours over the last few days on this puzzle.

Btw, working with the digit (1), I had thought of using r2c1, r2c3, r5c1 and r5c3 as an X-Wing with r6c1 as a fin and eliminating the (1) in r6c2.
I didn't know if that was a valid finned X-Wing or not, so I didn't use it. Any comments welcomed and appreciated???

[RW]

Btw, working with the digit (1), I had thought of using r2c1, r2c3, r5c1 and r5c3 as an X-Wing with r6c1 as a fin and eliminating the (1) in r6c2.
I didn't know if that was a valid finned X-Wing or not, so I didn't use it. Any comments welcomed and appreciated???

No, it's not a valid finned X-wing, because you also have candidate one in r78c3. There is one valid finned X-wing in the puzzle, eliminating 5 from r1c4. Can you find that one?

RW

[Jasper32]

Rw wrote
No, it's not a valid finned X-wing, because you also have candidate one in r78c3. There is one valid finned X-wing in the puzzle, eliminating 5 from r1c4. Can you find that one?

I could not find the valid X-Wing you wrote about. I am really new at this and would appreciate your rely as to the location of this finned X-wing. Thanks for your help and interest.

[999_Springs]

I could not find the valid X-Wing you wrote about. I am really new at this and would appreciate your rely as to the location of this finned X-wing.

The finned x-wing is in r24c34, fin r2c5.

[Jasper32]

I did see the X-Wing mentioned but didn't try to use it because I wasn't sure if r1c4 was the fin or r2c5 was the fin. I still don't know why r2c5 is the fin. Also, I thought that r1c5 could have the (5) deleted so I was wrong there as well. Sometimes I read something and think I understand it only to read something else that explains the same solving technique a little differently, leaving me confused. I am saving your your email showing the fin as r2c5 as the fin. If I might ask, what makes r2c5 the fin rather than r1c4? Thanks for your help.[/url]

[RW]

Ok, I'll try to explain. In order to use any technique properly, you must understand WHY the elimination can be made. Just trying to memorize patterns without understanding the logic behind them will lead to confusion.

Here's how the 5s are located in the grid when the elimination occurs:

Code: Select all

*-----------------------*
| . 5 . |-5 5 . | . 5 . |
| . .*5 |*5#5 . | . . . |
| . 5 5 | . . . | . 5 . |
|-------+-------+-------|
| . . . | . . . | 5 . . |
| . .*5 |*5 . . | . . . |
| . 5 . | . 5 . | . . . |
|-------+-------+-------|
| 5 . . | . . . | . . . |
| . . . | . . 5 | . . . |
| . . . | . . . | . . 5 |
*-----------------------*

The finned X-wing in r25c34, fin r2c5. Now let's examine the pattern. In row 5 digit 5 must be either in column 3 or column 4. In row 2 the 5 must be either in column 3, 4 or 5, r2c4 and r2c5 are both in box 2. So what are the options here? Either r5c4=5 or r5c3=5 => r2c3<>5 => r2c45=5. So either r5c4=5 or r2c45=5. Any cell that can see all those cells must not be 5 => r1c4<>5.

If you are not sure if an elimination is valid or not, you may always check it by assuming that the potentially eliminated candidate is true. When you make an elimination based on a pattern, the eliminated candidate would always cause a contradiction within the pattern. In this case: if r1c4=5 => r5c4<>5 => r5c3=5 => no 5 in row 2 = contradiction. If you use this aproach, you will also notice that the 5 from r1c5 cannot be eliminated: if r1c5=5 => r2c45<>5 => r2c3=5 => r5c3<>5 => r5c4=5 = no contradiction but a perfectly valid solution to the pattern cells.

Hope this helped.

RW

[Jasper32]

Thank you for your detailed reply. It was quite easy to grasp the concept of pattern elimination but not be too well versed in mathmatical concepts, I did have a problem with the logical part of your explanation.

I have been using pattern recognition when working with X-Wing's rather than logic. You wrote, "Either r5c4=5 or r5c3=5 =>r2c3 <>5=>r2c45=5" which left me confused. In plain English I read this to be..... either r5c4=5 or r5c3=5 if this is the case, then r2c3 cannot equal (5) and r2c5 or r2c4 will equal (5).

Perhaps I don't iinterpret Eureka notation properly but I cannot understand this logic . In this puzzle, r2c3 does equal 5 as does r5c4. Perhaps some of my problems with Sudoku is that I don't understand the logic that is expressed with Eureka notation. I wonder if my problem is my misunderstanding of " => "?

I know this forum isn't to explain some very basic concepts of Eureka notation. I do appreciate your help and your patience and I will prod on...I am addicted to Sudoku. Thank you.

[daj95376]

Cutting to the chase for your puzzle.

If the 5's in your puzzle occupied just the cells shown below, then there would be an X-Wing pattern in the '*' cells and eliminations in the '-' cells. Rows 2 & 5 are the Base Set and columns 3 & 4 are the Cover Set. Eliminations always occur in the Cover Set.

Code: Select all

+-----------------------------------+
|  .  5  .  | -5  5  .  |  .  5  .  |
|  .  . *5  | *5  .  .  |  .  .  .  |
|  .  5 -5  |  .  .  .  |  .  5  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  5  .  .  |
|  .  . *5  | *5  .  .  |  .  .  .  |
|  .  5  .  |  .  5  .  |  .  .  .  |
|-----------+-----------+-----------|
|  5  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  5  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  5  |
+-----------------------------------+


Fin cells are additional cells in the Base Set. In your case, [r2c5] is a fin '#' cell. However, it only sees the [r1c4] elimination cell from the original X-Wing eliminations, so that's the only elimination allowed for your finned X-Wing.

Code: Select all

+-----------------------------------+
|  .  5  .  | -5  5  .  |  .  5  .  |
|  .  . *5  | *5 #5  .  |  .  .  .  |
|  .  5  5  |  .  .  .  |  .  5  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  5  .  .  |
|  .  . *5  | *5  .  .  |  .  .  .  |
|  .  5  .  |  .  5  .  |  .  .  .  |
|-----------+-----------+-----------|
|  5  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  5  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  5  |
+-----------------------------------+


If there are more fin cells, then all of the fin cells must see any final elimination cell(s).

[Pat]

In order to use any technique properly, you must understand WHY the elimination can be made. Just trying to memorize patterns without understanding the logic behind them will lead to confusion.

Here's how the 5s are located in the grid when the elimination occurs:

Code: Select all

*-----------------------*
| . 5 . |-5 5 . | . 5 . |
| . .*5 |*5#5 . | . . . |
| . 5 5 | . . . | . 5 . |
|-------+-------+-------|
| . . . | . . . | 5 . . |
| . .*5 |*5 . . | . . . |
| . 5 . | . 5 . | . . . |
|-------+-------+-------|
| 5 . . | . . . | . . . |
| . . . | . . 5 | . . . |
| . . . | . . . | . . 5 |
*-----------------------*



The finned X-wing in r25c34, fin r2c5. Now let's examine the pattern. In row 5 digit 5 must be either in column 3 or column 4. In row 2 the 5 must be either in column 3, 4 or 5, r2c4 and r2c5 are both in box 2. So what are the options here? Either r5c4=5 or r5c3=5 => r2c3<>5 => r2c45=5. So either r5c4=5 or r2c45=5. Any cell that can see all those cells must not be 5 => r1c4<>5.

You wrote, "Either r5c4=5 or r5c3=5 =>r2c3 <>5=>r2c45=5" which left me confused. In plain English I read this to be..... either r5c4=5 or r5c3=5 if this is the case, then r2c3 cannot equal (5) and r2c5 or r2c4 will equal (5).

Perhaps I don't iinterpret Eureka notation properly but I cannot understand this logic . In this puzzle, r2c3 does equal 5 as does r5c4. Perhaps some of my problems with Sudoku is that I don't understand the logic that is expressed with Eureka notation. I wonder if my problem is my misunderstanding of " => "?

hi Jasper32


where RW wrote "Either r5c4=5 or r5c3=5 => r2c3<>5 => r2c45=5", this means --

either r5c4=5
or r5c3=5;
the 2nd possibility would exclude 5 at c3,
forcing the r2 5 into c45

-- which you did understand properly.

nobody is saying that r5c3 is 5,
we're merely discussing the 2 possibilities and their implications.

[daj95376]

where RW wrote "Either r5c4=5 or r5c3=5 => r2c3<>5 => r2c45=5", this means --

either r5c4=5
or r5c3=5;
the 2nd possibility would exclude 5 at c3,
forcing the r2 5 into c45

-- which you did understand properly.

nobody is saying that r5c3 is 5,
we're merely discussing the 2 possibilities and their implications.

Either (r5c4=5) or (r5c4<>5 => r5c3=5 => r2c3<>5 => r2c45=5) might have been a clearer way to reach RW's conclusion So either r5c4=5 or r2c45=5.

[Pat]

where RW wrote "Either r5c4=5 or r5c3=5 => r2c3<>5 => r2c45=5", this means --

either r5c4=5
or r5c3=5;
the 2nd possibility would exclude 5 at c3,
forcing the r2 5 into c45

-- which you did understand properly.

nobody is saying that r5c3 is 5,
we're merely discussing the 2 possibilities and their implications.

Either (r5c4=5) or (r5c4<>5 => r5c3=5 => r2c3<>5 => r2c45=5)
might have been a clearer way to reach RW's conclusion So either r5c4=5 or r2c45=5.

i beg to differ

in my view,
Either (r5c4=5) or (r5c4<>5 => r5c3=5 => r2c3<>5 => r2c45=5)
is poor notation

the expression in the 2nd parentheses is itself always true

the combined expression "either A or B" is useless

[wintder]

I firmly agree with RW that understanding the pattern (and the logic thereof) is critical. I have found that expressing a topic in more than one way helps, so I'll jump in on showing how this x-wing (finned) works. If you grasp it, it explains x-wings, finned-x and sashimi-x.

Below you can see that in column 3 it isn't possible that both "*"marked cells are 5. At least one of them is not, given a valid puzzle.

Code: Select all

*-----------------------*
| . 5 . | 5 5 . | . 5 . |
| . .*5 | 5 5 . | . . . |
| . 5 5 | . . . | . 5 . |
|-------+-------+-------|
| . . . | . . . | 5 . . |
| . .*5 | 5 . . | . . . |
| . 5 . | . 5 . | . . . |
|-------+-------+-------|
| 5 . C | . . . | . . . |
| . . O | . . 5 | . . . |
| . . L | . . . | . . 5 |
*-----3-----------------*

Now, because we know that at least one of the question marks IS NOT a 5 we also know that one of the "*"cells in row2 or row5 is a 5.

In every such case row1 column4 is exposed to at least one of them, thus cannot be a 5.

Code: Select all

*-----------------------*
| . 5 . |-5 5 . | . 5 . |
| . . ? |*5*5 . |  . . .|
| . 5 5 | . . . | . 5 . |
|-------+-------+-------|
| . . . | . . . | 5 . . |
| . . ? |*5 . . | . . . |
| . 5 . | . 5 . | . . . |
|-------+-------+-------|
| 5 . . | . . . | . . . |
| . . . | . . 5 | . . . |
| . . . | . . . | . . 5 |
*-----------------------*

daj pointed out a huge flaw in my next "guess". Sorry if you saw it, it is gone.

[daj95376]

i beg to differ

in my view,
Either (r5c4=5) or (r5c4<>5 => r5c3=5 => r2c3<>5 => r2c45=5)
is poor notation

the expression in the 2nd parentheses is itself always true

the combined expression "either A or B" is useless

I agree that the 2nd patentheses is always true. In my attempt to justify [r5c3]=5, I introduced too much information. Is the following acceptable to you?

Either (r5c4=5) or (r5c3=5 => r2c3<>5 => r2c45=5)

-or- the more formal

(5) [r5c4]=[r5c3]-[r2c3]=[r2c45]; => [r1c4]<>5

with its implied either.