The New Sudoku Players' Forum

[SteveG48]

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 *-----------*
 |...|.69|..5|
 |6.8|.5.|7.4|
 |...|...|69.|
 |---+---+---|
 |.74|1..|...|
 |3..|...|..8|
 |...|..7|45.|
 |---+---+---|
 |.85|...|...|
 |7.2|.4.|8.9|
 |1..|29.|...|
 *-----------*


[P.O.]

basics:

Hidden Text: Show

Code: Select all

( n3r2c4   n2r5c5   n5r9c7   n7r5c8   n8r9c6   n8r1c8   n9r7c1
  n9r2c2   n4r9c2   n4r7c8   n7r9c9   n9r4c7   n1r5c7 )

intersection:
((((1 0) (1 2 1) (1 2 3)) ((1 0) (1 3 1) (1 3 7))))

PAIR COL: ((4 5 5) (3 8)) ((6 5 5) (3 8)) 
(((3 5 2) (1 7 8)) ((4 6 5) (3 5 6)) ((6 4 5) (6 8 9)) ((7 5 8) (1 3 7)))

( n8r3c4 )

X-WING ROW: n1 (2 8) (6 8)
(((3 6 2) (1 2 4)) ((7 6 8) (1 3 6)))


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24    123   137   47    6     9     23    8     5             
6     9     8     3     5     12    7     12    4             
245   235   37    8     17    24    6     9     123           
258   7     4     1     38    56    9     236   236           
3     56    69    4569  2     456   1     7     8             
28    126   169   69    38    7     4     5     236           
9     8     5     67    17    36    23    4     1236           
7     36    2     56    4     1356  8     136   9             
1     4     36    2     9     8     5     36    7       

c1n5{r3 r4} => r7c4 <> 7
 r3c1=5 - r3n4{c1 c6} - r1c4{n4 n7}
 r4c1=5 - r4c6{n5 n6} - b6n6{r4c89 r6c9} - r7n6{c9 c4}
ste.


[RSW]

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 +-------------+----------------+--------------+
 |d24  123 137 |e47    6   9    | 23 8    5    |
 | 6   9   8   | 3     5   12   | 7  12   4    |
 | 245 235 37  | 8     17  124  | 6  9    123  |
 +-------------+----------------+--------------+
 |d258 7   4   | 1     38 c56   | 9 b236 b236  |
 | 3   56  69  | 459-6 2   456  | 1  7    8    |
 |d28  126 169 | 9-6   38  7    | 4  5   a236  |
 +-------------+----------------+--------------+
 | 9   8   5   |f67    17  13-6 | 23 4    123-6|
 | 7   36  2   | 56    4   135-6| 8  136  9    |
 | 1   4   36  | 2     9   8    | 5  36   7    |
 +-------------+----------------+--------------+


(6)r6c9 = r4c89 - [(6=5)r4c6 - (5=284)r146c1 - (4=7)r1c4 - (7=6)r7c4] => -6r7c9 [-6r56c4 -6r78c6]; stte
(square brackets denote subchain and subchain eliminations.)

>>>Edited to clarify subchain eliminations.

[Cenoman]

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 +--------------------+---------------------+--------------------+
 |  24    123* a137#  |  47     6    9      | B23*  8     5      |
 |  6     9     8     |  3      5    12     |  7    12    4      |
 |  245  a235#  7-3   |  8      17   124    |  6    9    C123*   |
 +--------------------+---------------------+--------------------+
 |  258   7     4     |  1      38   56     |  9    236   236    |
 |  3     56    69    |  4569   2    456    |  1    7     8      |
 |  28    126   169   |  69     38   7      |  4    5     236    |
 +--------------------+---------------------+--------------------+
 |  9     8     5     |  67     17   136*   | A23#  4     1236*  |
 |  7    y36*   2     |  56     4    1356*  |  8   x136#  9      |
 |  1     4    z36    |  2      9    8      |  5    36    7      |
 +--------------------+---------------------+--------------------+

7-link oddagon (3)r178, c269, b3 (*), having four guardians (#)
(3)r1c3|r3c2
(3)r7c7 - r1c7 = r3c9
(3)r8c8 - r8c2 = r9c3
=> -3 r3c3; ste

[SteveG48]

Nice one, RSW. I'm trying to figure out if there's another way to write it to clarify how the subchain works, but I'm not coming up with anything.

[Cenoman]

(6)r6c9 = r4c89 - [(6=5)r4c6 - (5=284)r146c1 - (4=7)r1c4 - (7=6)r7c4] => -6r7c9 [-6r56c4 -6r78c6]; stte
(square brackets denote subchain and subchain eliminations.)

...I'm trying to figure out if there's another way to write it to clarify how the subchain works...

I'm not in favour of using square brackets to delimit the endpoints of a subchain. Square brackets are already dedicated to delimit embedded chains and often used so in the forum. Using them for subchains would be much confusing.

In the present case, using '*' symbol solves the issue:
I'd write (6)r6c9 = r4c89 - (*6=5)r4c6 - (5=284)r146c1 - (4=7)r1c4 - (7=6)r7c4 => -6 r7c9, r56c4*, r78c6*; stte
or (6=7)r7c4 - (7=4)r1c4 - (4=285)r146c1 - (5=6*)r4c6 - r4c89 = (6)r6c9 => -6 r56c4*, r78c6*, r7c9; stte
(Other symbols, e.g. '^' '#' can be used in case of multiple subchains).

This not an invention of mines, but a very old practise of many players in the forum.

[SteveG48]

Very nice, Cenoman.

What I find really interesting is that the basic chain is a fully reversible AIC. It's valid when read in either direction. However, when you look at the reversed version posted by Cenoman, it's easy to see that if r7c4 is not a 6, then the starred 6 (r4r6) and the final 6 (r6c9) give the desired eliminations. If, on the other hand, if r7c4 is a 6, then that gives all the desired eliminations. If you look at the original (unreversed) chain, then the eliminations are clear if r6c9 is not at a 6, but if r6c9 is a 6, then you have to note that r4c6 must also be a 6 to see all the eliminations.

[RSW]

Thanks for the discussion. In the future, I'll use the notation suggested by Cenoman.

As for the order that I write the chain, I tend to write it in the same order that I discover it, without much regard for whether or not it would make more sense if it were reversed. I'll have to pay more attention to this when there are subchain eliminations.