## Hint on a puzzle

Post the puzzle or solving technique that's causing you trouble and someone will help

### Hint on a puzzle

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     185    67    4    | 8    9     1   | 2     67      367    1    8    | 4    3     2   | 9    567     57------------------+--------------------+-------------------2    47    9    | 1   67     5   | 8      3     4647    3    1    | 2   67     8   | 56     9    4568     5    6    | 9    4     3   | 17    27     12------------------+--------------------+-------------------3     9    2    | 5    8     4   | 67     1     671    48    5    | 7    2     6   | 3     48      946  468    7    | 3    1     9   | 45    25     28`

I've done all elimination that I could. Help would be appreciated!
Snap

Posts: 1
Joined: 05 February 2015

### Re: Hint on a puzzle

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

JasonLion
2017 Supporter

Posts: 640
Joined: 25 October 2007
Location: Silver Spring, MD, USA

### Re: Hint on a puzzle

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`

_
daj95376
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Posts: 2624
Joined: 15 May 2006

### Re: Hint on a puzzle

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
Leren

Posts: 3319
Joined: 03 June 2012

### Re: Hint on a puzzle

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
pjb
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