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Empty Rectangle

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Empty Rectangle

Postby strmckr on Sun May 10, 2009 4:02 am

this stratagy has two names depending on where you may learn it from.

it is commonly known as the Empty Rectangle {er} and obscurly known as a Hinge:

Code: Select all
/  N  / | . . . | . / .
N  N  N | . . . | . N .
/  N  / | . . . | . / .
--------+-------+-------
.  .  . | . . . | . / .
.  .  . | . . . | . / .
.  .  . | . . . | . / .
--------+-------+-------
.  .  . | . . . | . / .
.  X  . | . . . | . N .
.  .  . | . . . | . / .


KEY: '/' <=> cells void of candidate 'N'
'N' <=> cells with candidate 'N'; not all are required in the box.
"-X" <=> potential eliminations of candidate 'N'


there is several way to exend the elimination of an empty rectangle here is one for example.

Grouped ER:
Code: Select all
/  N  / | . . . | / N /
N  N  N | x x x | N N N
/  N  / | . . . | / N /
--------+-------+-------
.  x  . | . . . | . x .
.  x  . | . . . | . x .
.  x  . | . . . | . x .
--------+-------+-------
.  x  . | . . . | . x .
/  N  / | / / / | / N /
.  x  . | . . . | . x .
Last edited by strmckr on Sun May 10, 2009 5:30 pm, edited 5 times in total.
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Grand Guru strmckr
 
Posts: 188
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Re: Empty Rectangle {Hinge}

Postby strmckr on Sun May 10, 2009 4:05 am

Example: Empty Rectangle

Code: Select all
.---------------.------------.----------------.
| 4   1     5   | 7    39  2 | 8    369  36   |
| 9-2  2369  369 | 8    1   4 | 279@  5   237@ |
| 7   239   8   | 5    39  6 | 1    239@  4   |
:---------------+------------+----------------:
| 1   8     2   | 6    4   3 | 5    7    9    |
| 5   39    39  | 1    8   7 | 26   4    26   |
| 6   4     7   | 2    5   9 | 3    8    1    |
:---------------+------------+----------------:
| 29@  7     1   | 39   6   5 | 4    239@  8    |
| 8   569   469 | 349  2   1 | 679  369  3567 |
| 3   2569  469 | 49   7   8 | 269  1    256  |
'---------------'------------'----------------'


2 in b3 (r7c18) => r2c1<>2
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Grand Guru strmckr
 
Posts: 188
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