April 30, 2014

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April 30, 2014

Postby ArkieTech » Tue Apr 29, 2014 9:13 pm

Code: Select all
 *-----------*
 |81.|6..|...|
 |...|2..|.5.|
 |...|9..|...|
 |---+---+---|
 |2.9|...|...|
 |..7|...|4..|
 |...|...|8.7|
 |---+---+---|
 |...|..5|...|
 |.4.|..8|...|
 |...|..7|.29|
 *-----------*


Play/Print this puzzle online
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Re: April 30, 2014

Postby Leren » Tue Apr 29, 2014 10:42 pm

Code: Select all
*--------------------------------------------------------------*
| 8     1     2      | 6     5     4      | 9     7     3      |
| 346   9     34     | 2     7     13     | 16    5     8      |
|c356   7    b35     | 9     8     13     | 2     4    d16     |
|--------------------+--------------------+--------------------|
| 2     8     9      | 7     4     6      | 135   13    15     |
| 135   35    7      | 8     13    9      | 4     6     2      |
| 134   6     134    | 5     13    2      | 8     9     7      |
|--------------------+--------------------+--------------------|
| 7     2     136    | 13    9     5      | 136   8     4      |
| 9     4    a56     | 13    2     8      | 7     13    5-6    |
| 135   35    8      | 4     6     7      | 135   2     9      |
*--------------------------------------------------------------*

M Wing Type 5B : (6=5) r8c3 - r3c3 = (5-6) r3c1 = (6) r3c9 => - 6 r8c9 stte

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Re: April 30, 2014

Postby SteveG48 » Tue Apr 29, 2014 11:25 pm

Code: Select all
 *--------------------------------------------------*
 | 8    1    2    | 6    5    4    | 9    7    3    |
 | 346  9    34   | 2    7   a13   |b16   5    8    |
 | 356  7   f35   | 9    8    1-3  | 2    4    16   |
 *----------------+----------------+----------------|
 | 2    8    9    | 7    4    6    | 135  13   15   |
 | 135  35   7    | 8    13   9    | 4    6    2    |
 | 134  6    134  | 5    13   2    | 8    9    7    |
 *----------------+----------------+----------------|
 | 7    2   d136  | 13   9    5    |c136  8    4    |
 | 9    4   e56   | 13   2    8    | 7    13   56   |
 | 135  35   8    | 4    6    7    | 135  2    9    |
 *--------------------------------------------------*


(3=1)r2c6 - (1=6)r2c7 - r7c7 = r7c3 - (6=5)r8c3 - (5=3)r3c3 => -3 r3c6 ; stte
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Re: April 30, 2014

Postby ArkieTech » Wed Apr 30, 2014 11:49 am

Code: Select all
 *--------------------------------------------------*
 | 8    1    2    | 6    5    4    | 9    7    3    |
 | 346  9    34   | 2    7    13   | 16   5    8    |
 |e36-5 7   a35   | 9    8    13   | 2    4   d16   |
 |----------------+----------------+----------------|
 | 2    8    9    | 7    4    6    | 135  13   15   |
 | 135  35   7    | 8    13   9    | 4    6    2    |
 | 134  6    134  | 5    13   2    | 8    9    7    |
 |----------------+----------------+----------------|
 | 7    2    136  | 13   9    5    | 136  8    4    |
 | 9    4   b56   | 13   2    8    | 7    13  c56   |
 | 135  35   8    | 4    6    7    | 135  2    9    |
 *--------------------------------------------------*
5r3c3=(5-6)r8c3=r8c9-r3c9=6r3c1 => -5r3c1; ste
Last edited by ArkieTech on Wed Apr 30, 2014 5:20 pm, edited 1 time in total.
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Re: April 30, 2014

Postby SteveG48 » Wed Apr 30, 2014 1:41 pm

ArkieTech wrote:
Code: Select all
 *--------------------------------------------------*
 | 8    1    2    | 6    5    4    | 9    7    3    |
 | 346  9    34   | 2    7    13   | 16   5    8    |
 |e36-5 7   a35   | 9    8    13   | 2    4   d16   |
 |----------------+----------------+----------------|
 | 2    8    9    | 7    4    6    | 135  13   15   |
 | 135  35   7    | 8    13   9    | 4    6    2    |
 | 134  6    134  | 5    13   2    | 8    9    7    |
 |----------------+----------------+----------------|
 | 7    2    136  | 13   9    5    | 136  8    4    |
 | 9    4   b56   | 13   2    8    | 7    13  c56   |
 | 135  35   8    | 4    6    7    | 135  2    9    |
 *--------------------------------------------------*
5r3c3=(5-6)r8c3=r8c9-r3c9=5r3c1 => -5r3c1; ste


Dan, should this read:

5r3c3=(5-6)r8c3=r8c9-r3c9=(6-5)r3c1 => -5r3c1 ?
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Re: April 30, 2014

Postby Sudtyro2 » Wed Apr 30, 2014 2:58 pm

Code: Select all
 *--------------------------------------------------*
 | 8    1    2    | 6    5    4    | 9    7    3    |
 | 346  9    34   | 2    7    13   | 16   5    8    |
 | 365  7    35   | 9    8    13   | 2    4    16   |
 |----------------+----------------+----------------|
 | 2    8    9    | 7    4    6    |b135  13  c15   |
 | 135  35   7    | 8    13   9    | 4    6    2    |
 | 134  6    134  | 5    13   2    | 8    9    7    |
 |----------------+----------------+----------------|
 | 7    2    136  | 13   9    5    |a136  8    4    |
 | 9    4    56   | 13   2    8    | 7    13  d5-6  |
 | 135  35   8    | 4    6    7    | 135  2    9    |
 *--------------------------------------------------*

Alternate to Leren's elimination, from easy-to-spot Almost-DP: (13)[r4c78,r7c47,r8c48] => strong inference: (6)r7c7=(5)r4c7

AIC: (6)r7c7=(5)r4c7-(5)r4c9=(5)r8c9 => r8c9<>6

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Re: April 30, 2014

Postby Marty R. » Wed Apr 30, 2014 2:59 pm

Code: Select all
+------------+----------+-----------+
| 8   1  2   | 6  5  4  | 9   7  3  |
| 346 9  34  | 2  7  13 | 16  5  8  |
| 356 7  35  | 9  8  13 | 2   4  16 |
+------------+----------+-----------+
| 2   8  9   | 7  4  6  | 135 13 15 |
| 135 35 7   | 8  13 9  | 4   6  2  |
| 134 6  134 | 5  13 2  | 8   9  7  |
+------------+----------+-----------+
| 7   2  136 | 13 9  5  | 136 8  4  |
| 9   4  56  | 13 2  8  | 7   13 56 |
| 135 35 8   | 4  6  7  | 135 2  9  |
+------------+----------+-----------+

Play this puzzle online at the Daily Sudoku site

XY-Chain, another solution similar to Leren's.

(5=3)r3c3-(3=1)r3c6-(1=6)r3c9-(6=5)r8c9=>r8c3<>5
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Re: April 30, 2014

Postby SteveG48 » Wed Apr 30, 2014 3:27 pm

Sudtyro2 wrote:Alternate to Leren's elimination, from easy-to-spot Almost-DP: (13)[r4c78,r7c47,r8c48] => strong inference: (6)r7c7=(5)r4c7

AIC: (6)r7c7=(5)r4c7-(5)r4c9=(5)r8c9 => r8c9<>6

SteveC


Nice one, Steve!
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Re: April 30, 2014

Postby daj95376 » Wed Apr 30, 2014 4:23 pm

SteveG48 wrote:
ArkieTech wrote:
Code: Select all
 *--------------------------------------------------*
 | 8    1    2    | 6    5    4    | 9    7    3    |
 | 346  9    34   | 2    7    13   | 16   5    8    |
 |e36-5 7   a35   | 9    8    13   | 2    4   d16   |
 |----------------+----------------+----------------|
 | 2    8    9    | 7    4    6    | 135  13   15   |
 | 135  35   7    | 8    13   9    | 4    6    2    |
 | 134  6    134  | 5    13   2    | 8    9    7    |
 |----------------+----------------+----------------|
 | 7    2    136  | 13   9    5    | 136  8    4    |
 | 9    4   b56   | 13   2    8    | 7    13  c56   |
 | 135  35   8    | 4    6    7    | 135  2    9    |
 *--------------------------------------------------*
5r3c3=(5-6)r8c3=r8c9-r3c9=5r3c1 => -5r3c1; ste


Dan, should this read:

5r3c3=(5-6)r8c3=r8c9-r3c9=(6-5)r3c1 => -5r3c1 ?

It should read:

5r3c3=(5-6)r8c3=r8c9-r3c9=6r3c1 => -5r3c1; ste
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Re: April 30, 2014

Postby ArkieTech » Wed Apr 30, 2014 5:21 pm

SteveG48 wrote:
ArkieTech wrote:
Code: Select all
 *--------------------------------------------------*
 | 8    1    2    | 6    5    4    | 9    7    3    |
 | 346  9    34   | 2    7    13   | 16   5    8    |
 |e36-5 7   a35   | 9    8    13   | 2    4   d16   |
 |----------------+----------------+----------------|
 | 2    8    9    | 7    4    6    | 135  13   15   |
 | 135  35   7    | 8    13   9    | 4    6    2    |
 | 134  6    134  | 5    13   2    | 8    9    7    |
 |----------------+----------------+----------------|
 | 7    2    136  | 13   9    5    | 136  8    4    |
 | 9    4   b56   | 13   2    8    | 7    13  c56   |
 | 135  35   8    | 4    6    7    | 135  2    9    |
 *--------------------------------------------------*
5r3c3=(5-6)r8c3=r8c9-r3c9=5r3c1 => -5r3c1; ste


Dan, should this read:

5r3c3=(5-6)r8c3=r8c9-r3c9=(6-5)r3c1 => -5r3c1 ?


Thanks Steve I have corrected it. :oops:
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Re: April 30, 2014

Postby SteveG48 » Wed Apr 30, 2014 10:29 pm

daj95376 wrote:
SteveG48 wrote:Dan, should this read:

5r3c3=(5-6)r8c3=r8c9-r3c9=(6-5)r3c1 => -5r3c1 ?


It should read:

5r3c3=(5-6)r8c3=r8c9-r3c9=6r3c1 => -5r3c1; ste


I think I'm about to learn something (again).

Danny, I understand that the weak link to 5 in the last term isn't, strictly speaking, necessary, but why isn't it preferred? After all, the whole point of the logic is that r3c1 can't be a 5 whether or not r3c3 is a 5. Doesn't including the weak link to 5 make that clearer?
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Re: April 30, 2014

Postby daj95376 » Thu May 01, 2014 12:30 am

SteveG48 wrote:
daj95376 wrote:
SteveG48 wrote:Dan, should this read:

5r3c3=(5-6)r8c3=r8c9-r3c9=(6-5)r3c1 => -5r3c1 ?


It should read:

5r3c3=(5-6)r8c3=r8c9-r3c9=6r3c1 => -5r3c1; ste


I think I'm about to learn something (again).

Danny, I understand that the weak link to 5 in the last term isn't, strictly speaking, necessary, but why isn't it preferred? After all, the whole point of the logic is that r3c1 can't be a 5 whether or not r3c3 is a 5. Doesn't including the weak link to 5 make that clearer?

Steve, there's nothing wrong with adding the weak link. It was probably done a lot back when NL notation was common. Now that Eureka notation is more common, most people use the AIC constraint/logic to determine eliminations. As an AIC, the trailing weak link is superflous.

One additional point. If there had been a <6> in r3c3, then the AIC logic would have (clearly) allowed for its elimination as well. If you add the weak link to the chain, then the r3c3<>6 elimination becomes embedded in the chain and could easily be overlooked.

Note: a continuous AIC loop is the only instance (that I'm aware of) when an AIC is followed by a weak link -- as in "- loop".

_
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Re: April 30, 2014

Postby SteveG48 » Thu May 01, 2014 1:01 am

I was right; I learned something.

Thanks, Danny!
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