The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|5..|..1|
 |8..|7..|..2|
 |491|...|.7.|
 |---+---+---|
 |..2|..8|..7|
 |...|.4.|.8.|
 |7..|2..|6..|
 |---+---+---|
 |.6.|...|324|
 |2..|..9|..8|
 |1..|..6|...|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 36    2     7      | 5     69    4      | 8     39    1      |
| 8     5    a36     | 7     69    1      | 49   b349   2      |
| 4     9     1      | 3     8     2      | 5     7     6      |
|--------------------+--------------------+--------------------|
| 36    34    2      | 69    15    8      | 49    15    7      |
| 5     1     69     | 69    4     7      | 2     8     3      |
| 7     8    d49     | 2     15    3      | 6    c1459  59     |
|--------------------+--------------------+--------------------|
| 9     6     8      | 1     7     5      | 3     2     4      |
| 2     7     5      | 4     3     9      | 1     6     8      |
| 1     34   e4-3    | 8     2     6      | 7     59    59     |
*--------------------------------------------------------------*

L2 Wing : (3) r2c3 = (3-4) r2c8 = r6c8 - r6c3 = (4) r9c3 => - 3 r9c3; stte

Leren

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 |c36    2     7     | 5     69    4     | 8    b39    1     |
 | 8     5     36    | 7     69    1     | 49    349   2     |
 | 4     9     1     | 3     8     2     | 5     7     6     |
 *-------------------+-------------------+-------------------|
 |d36   e34    2     | 69   *15    8     | 49   *15    7     |
 | 5     1     69    | 69    4     7     | 2     8     3     |
 | 7     8     9-4   | 2    *15    3     | 6   a*1459  59    |
 *-------------------+-------------------+-------------------|
 | 9     6     8     | 1     7     5     | 3     2     4     |
 | 2     7     5     | 4     3     9     | 1     6     8     |
 | 1     34    34    | 8     2     6     | 7     59    59    |
 *-----------------------------------------------------------*


(4=9)r6c8[UR 1/5 r46c58] - (9=3)r1c8 - r1c1 = r4c1 - (3=4)r4c2 => -4 r6c3 ; stte

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 36    2     7     | 5     69    4     | 8     39    1     |
 | 8     5     36    | 7     69    1     | 49    349   2     |
 | 4     9     1     | 3     8     2     | 5     7     6     |
 *-------------------+-------------------+-------------------|
 | 36    34    2     | 69   *15    8     | 49   *15    7     |
 | 5     1     69    | 69    4     7     | 2     8     3     |
 | 7     8     49    | 2    *15    3     | 6    *1459* 59*   |
 *-------------------+-------------------+-------------------|
 | 9     6     8     | 1     7     5     | 3     2     4     |
 | 2     7     5     | 4     3     9     | 1     6     8     |
 | 1     34    34    | 8     2     6     | 7     59*   59*   |
 *-----------------------------------------------------------*


How about:

UR 1/5 r46c58 => r6c8 = 9 or 4
UR 5/9 r69c89 => r6c8 = 1 or 4 => r6c8 = 4 ; stte

[StrmCkr]

Code: Select all

.------------.-----------.--------------.
| 36  2   7  | 5   69  4 | 8   39    1  |
| 8   5   36 | 7   69  1 | 49  349   2  |
| 4   9   1  | 3   8   2 | 5   7     6  |
:------------+-----------+--------------:
| 36  34  2  | 69  15  8 | 49  15    7  |
| 5   1   69 | 69  4   7 | 2   8     3  |
| 7   8   49 | 2   15  3 | 6   1459  59 |
:------------+-----------+--------------:
| 9   6   8  | 1   7   5 | 3   2     4  |
| 2   7   5  | 4   3   9 | 1   6     8  |
| 1   34  34 | 8   2   6 | 7   59    59 |
'------------'-----------'--------------'


m-wing type 1b: 4 r6c3 -4- r6c8 =4= r2c8 =3= r2c3 -3- r9c3 -4- r6c3 => r6c3<>4: stte

[bat999]

Code: Select all

.------------.-----------.--------------.
| 36b  2   7  | 5   69  4 | 8   39a   1  |
| 8    5   36 | 7   69  1 | 49f 39-4  2  |
| 4    9   1  | 3   8   2 | 5   7     6  |
:-------------+-----------+--------------:
| 36c  34d 2  | 69  15  8 | 49e 15    7  |
| 5    1   69 | 69  4   7 | 2   8     3  |
| 7    8   49 | 2   15  3 | 6   1459  59 |
:-------------+-----------+--------------:
| 9    6   8  | 1   7   5 | 3   2     4  |
| 2    7   5  | 4   3   9 | 1   6     8  |
| 1    34  34 | 8   2   6 | 7   59    59 |
'------------'-----------'--------------'

Hi
If r1c8 is not 9 then r1c1 is 6, r4c1 is 3, r4c2 is 4, r4c7 is 9, r2c7 is 4 and r2c8 is not 4.
If r2c7 is not 9 then r2c8 is not 4 again.
=> - 4 r2c8; stte

[SteveG48]

Code: Select all

.------------.-----------.--------------.
| 36b  2   7  | 5   69  4 | 8   39a   1  |
| 8    5   36 | 7   69  1 | 49f 39-4  2  |
| 4    9   1  | 3   8   2 | 5   7     6  |
:-------------+-----------+--------------:
| 36c  34d 2  | 69  15  8 | 49e 15    7  |
| 5    1   69 | 69  4   7 | 2   8     3  |
| 7    8   49 | 2   15  3 | 6   1459  59 |
:-------------+-----------+--------------:
| 9    6   8  | 1   7   5 | 3   2     4  |
| 2    7   5  | 4   3   9 | 1   6     8  |
| 1    34  34 | 8   2   6 | 7   59    59 |
'------------'-----------'--------------'

Hi
If r1c8 is not 9 then r1c1 is 6, r4c1 is 3, r4c2 is 4, r4c7 is 9, r2c7 is 4 and r2c8 is not 4.
If r2c7 is not 9 then r2c8 is not 4 again.
=> - 4 r2c8; stte

Hi, Bat. Nice chain. Notice that your first line establishes that if r1c8 is not 9, then r2c7 is 4, so r2c7 can't be a 9. stte.

[Ngisa]

Code: Select all

+----------+---------+------------+
| 36 2  7  | 5  69 4 | 8  39   1  |
| 8  5  d36 | 7  c69 1 | b49 349  2  |
| 4  9  1  | 3  8  2 | 5  7    6  |
+----------+---------+------------+
| 36 34 2  | 6-9 15 8 | a49 1459 7  |
| 5  1  e69 | f69 4  7 | 2  8    3  |
| 7  8  49 | 2  15 3 | 6  1459 59 |
+----------+---------+------------+
| 9  6  8  | 1  7  5 | 3  2    4  |
| 2  7  5  | 4  3  9 | 1  6    8  |
| 1  34 34 | 8  2  6 | 7  59   59 |
+----------+---------+------------+


(9=4)r4c7-(4=9)r2c7-(9=6)r2c5-r2c3=r5c3-(6=9)r5c4 => -9r4c4; stte.

[bat999]

... so r2c7 can't be a 9. stte.

Yes, I should have thought it through...
If r1c8 is not 9, then r2c7 is 4 (first line).
and
If r2c7 is not 9, then r2c7 is 4.

=> - 9 r2c7; stte

[SteveG48]

... so r2c7 can't be a 9. stte.

Yes, I should have thought it through...
If r1c8 is not 9, then r2c7 is 4 (first line).
and
If r2c7 is not 9, then r2c7 is 4.

=> - 9 r2c7; stte

Yes, but you still don't need the second line, because if r1c8 is a 9, then r2c7 still can't be a 9. This is a general rule. If you can establish a strong link from one candidate in one cell to a different candidate in a second cell in the same house, then you can eliminate the first candidate in the second cell. Further, since strong links work in both directions, you can eliminate the second candidate in the first cell if it hasn't already been eliminated. It's a powerful tool.

[bat999]

... If you can establish a strong link from one candidate in one cell to a different candidate in a second cell in the same house, then you can eliminate the first candidate in the second cell. Further, since strong links work in both directions, you can eliminate the second candidate in the first cell if it hasn't already been eliminated....

Hi
Trying to digest that statement, waiting for the penny to drop.


With hindsight, my solution would probably have been better expressed using Leren's "Kraken cell" layout.
Something like this...
Using r1c8.
If r1c8 is 9 then r2c7 is 4.
If r1c8 is 3 then r2c7 is 4 (through the chain).
=> - 9 r2c7; stte

I'm still not comfortable with that Eureka notation, seems weird.
When I see an expression such as "(4=9)" it makes me want to cry.
It's as though somebody tried to tell me an apple is the same as an orange, or 4Kg of rice weighs the same as 9Kg of rice.
Using the equals sign to do something it's not supposed to.

I'll get there eventually, maybe.

[ArkieTech]

When I see an expression such as "(4=9)" it makes me want to cry.
It's as though somebody tried to tell me an apple is the same as an orange, or 4Kg of rice weighs the same as 9Kg of rice.
Using the equals sign to do something it's not supposed to.

I'll get there eventually, maybe.

= means a strong link.. If a cell contains a 4 and 9 only (4=9)cell means one must be true. Not 4 then 9 or backwards not 9 then 4.

I went through the same struggle .. when you get there you never go back.

[SteveG48]

= means a strong link.. If a cell contains a 4 and 9 only (4=9)cell means one must be true. Not 4 then 9 or backwards not 9 then 4.

I went through the same struggle .. when you get there you never go back.

Yup. You just need to accept that the symbols as used here don't mean the same thing that they mean in math class.

[eleven]

I went through the same struggle .. when you get there you never go back.

Peer pressure.
Bat, you will see, that it has some advantages (e.g. for finding the eliminations to a loop), and some drawbacks (sometimes things which can be described clearly with simple words, look terribly complicated).

[gurth]

When I see an expression such as "(4=9)" it makes me want to cry.
It's as though somebody tried to tell me an apple is the same as an orange, or 4Kg of rice weighs the same as 9Kg of rice.
Using the equals sign to do something it's not supposed to.

I'll get there eventually, maybe.

One could of course replace the ambiguous (to the uninitiated) '=' ( which in an AIC means 'OR', nothing more and nothing less) with something else, for instance a slash '/' which has a common meaning of 'OR'. This is called a 'strong link'. Then there is a third type of link, called the 'conjugate link' : this means Exclusive Or (EOR), which means one but NOT both sides of the link are true. A weak link '-' means that both sides of the link are NOT true, though both sides may be false.
A Conjugate Link is both strong and weak, but a Strong Link is not necessarily a weak link, though it usually is in AICs.

It can be fun to draw strong links on a diagram with a double line between the candidates, and a weak link with a single line. This is perhaps where the '=,-' notation comes from. A 'spaghetti diagram'. On the whole, I would favour retaining this notation, as I find it the most aesthetically pleasing.