Hint on a puzzle

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Hint on a puzzle

Postby Snap » Thu Feb 05, 2015 3:57 pm

Hello there! I'm sort of new to Sudoku and I've been struggling for quite some time with this puzzle:

Code: Select all
9     2    3    | 6    5     7   | 14    48     18
5    67    4    | 8    9     1   | 2     67      3
67    1    8    | 4    3     2   | 9    567     57
------------------+--------------------+-------------------
2    47    9    | 1   67     5   | 8      3     46
47    3    1    | 2   67     8   | 56     9    456
8     5    6    | 9    4     3   | 17    27     12
------------------+--------------------+-------------------
3     9    2    | 5    8     4   | 67     1     67
1    48    5    | 7    2     6   | 3     48      9
46  468    7    | 3    1     9   | 45    25     28


I've done all elimination that I could. Help would be appreciated!
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Re: Hint on a puzzle

Postby JasonLion » Thu Feb 05, 2015 5:22 pm

I see an XY Chain and then singles to the end.

(4=7)R5C1 - (7=6)R5C5 - (6=5)R5C7 - (5=4) R9C7 => R9C1<>4
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Re: Hint on a puzzle

Postby daj95376 » Thu Feb 05, 2015 5:32 pm

There are numerous short chains available. However, There's also a BUG+3 present. A BUG occurs when all of the unsolved cells contain bivalue candidates and can't be reduced any further (e.g., by a Hidden Single). A BUG is unacceptable!!!

A BUG is being prevented by the possibility of r3c8=7, and/or r5c9=6, and/or r9c2=4. So, do they produce a common elimination?

Code: Select all
 +-----------------------------------------------------+
 |  9    2    3    |  6    5    7    |  14   48   18   |
 |  5    67   4    |  8    9    1    |  2    67   3    |
 |  67   1    8    |  4    3    2    |  9    56+7 5-7  |
 |-----------------+-----------------+-----------------|
 |  2    47   9    |  1    67   5    |  8    3    46   |
 |  47   3    1    |  2    67   8    |  56   9    45+6 |
 |  8    5    6    |  9    4    3    |  17   27   12   |
 |-----------------+-----------------+-----------------|
 |  3    9    2    |  5    8    4    |  67   1    67   |
 |  1    48   5    |  7    2    6    |  3    48   9    |
 |  46   68+4 7    |  3    1    9    |  45   25   28   |
 +-----------------------------------------------------+
 # 30 eliminations remain

 r3c8=7                      =>  -7 r3c9

 r5c9=6 -> r7c9=7            =>  -7 r3c9

 r9c2=4 -> r9c1=6 -> r3c1=7  =>  -7 r3c9

_
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Re: Hint on a puzzle

Postby Leren » Thu Feb 05, 2015 8:10 pm

Code: Select all
*--------------------------------------------------------------*
| 9     2     3      | 6     5     7      | 14    48    18     |
| 5     67    4      | 8     9     1      | 2     67    3      |
|b67    1     8      | 4     3     2      | 9     567  a57     |
|--------------------+--------------------+--------------------|
| 2     47    9      | 1     67    5      | 8     3     46     |
|c47    3     1      | 2     67    8      | 56    9    d46-5   |
| 8     5     6      | 9     4     3      | 17    27    12     |
|--------------------+--------------------+--------------------|
| 3     9     2      | 5     8     4      | 67    1     67     |
| 1     48    5      | 7     2     6      | 3     48    9      |
| 46    468   7      | 3     1     9      | 45    25    28     |
*--------------------------------------------------------------*

The simplest move that I found that solves this puzzle is the following: Since you say you are new to Sudoku I'll describe this in words. Look at the cells I've marked a, b, c and d.

Suppose r3c9 (cell a) was not 5. Then it must be 7. So r3c1 (cell b) must not be 7. So r5c1 (cell c) must be 7 (since there are only two 7's in Column 1), so it must not be 4.

So cell r5c9 (cell d) must be 4 (since there are only two 4's in Row 5).

So summarizing, if r3c9 is not 5 then r5c9 is 4. In particular it is not 5. On the other hand if r3c9 is 5 then r5c9 is obviously not 5.

Since in r3c9 the 5 must only be either True or False then we have shown that in both cases r5c9 can't be 5. So you can remove the 5 from r5c9. This means that r3c9 is 5 and the puzzle solves easily after that.

The standard notation (gobbledegook) for this move is : (5=7) r3c9 - r3c1 = (7-4) r5c1 = (4) r5c9 => - 5 r5c9

Notice that the notation only describes the longer leg of the move (cells abcd). The obvious leg (cells a & d only) is usually left out because, well, it's obvious !

Leren
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Re: Hint on a puzzle

Postby pjb » Fri Feb 06, 2015 12:40 am

Another take on the BUG+3
Code: Select all
*--------------------------------------------------------------*
| 9     2     3      | 6     5     7      | 14    48    18     |
| 5    q67    4      | 8     9     1      | 2     67    3      |
|r67    1     8      | 4     3     2      | 9   s56-7  57     |
|--------------------+--------------------+--------------------|
| 2  pAa47    9      | 1    B67    5      | 8     3    C46     |
| 47    3     1      | 2     67    8      | 56    9    D45-6   |
| 8     5     6      | 9     4     3      | 17    27    12     |
|--------------------+--------------------+--------------------|
| 3     9     2      | 5     8     4      | 67    1     67     |
| 1     48    5      | 7     2     6      | 3     48    9      |
| 46   b68-4  7      | 3     1     9      | 45    25    28     |
*--------------------------------------------------------------*


(7=4)r4c2 => -4 r8c2
(7)r4c2 = (7-6)r4c5 = (6)r4c9 => -6 r5c9
(4=7)r4c2 - (7=6)r2c2 - (6=7)r3c1 => -7 r3c8

Therefore if r4c2 = 4, the above 3 eliminations leaves us with a BUG as described above, so r4c2 cannot be 4.

Phil
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