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UR + 2?

 
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Captain Pete



Joined: 09 Jun 2007
Posts: 55
Location: Oley, PA
PostPosted: Tue Oct 21, 2008 2:05 pm    Post subject: UR + 2? Reply with quote
In a recent puzzle, I had the following pattern, six cells in two rows and three columns:

17 127 1279
17 127 127

Can I always assume the 1279 cell reduces to 9?
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ravel



Joined: 21 Apr 2006
Posts: 536
PostPosted: Tue Oct 21, 2008 2:53 pm    Post subject: Reply with quote
If the 6 cells are in 3 boxes of a band or 2 boxes of a stack, yes. Its a special form then of one of these deadly patterns:

Code:

 .   abc . | .   abc . | .   abc .
 .   abc . | .   abc . | .   abc .
 *   *   * | .   .   . | .   .   .
-----------+-----------+-----------
or
------------- 
 abc abc abc
  .   .   . 
  .   .   . 
-------------
 abc abc abc
  .   .   . 
  .   .   . 
-------------
  *   .   . 
  *   .   . 
  *   .   . 
-------------

All sub patterns, which are derived by placing one or more of the numbers somewhere outside this pattern, are deadly too (lead to 0 or more than one solutions), e.g. you get your pattern by placing b in one of the * cells.

See more about multidigit DP's in Myth Jellies thread.
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ravel



Joined: 21 Apr 2006
Posts: 536
PostPosted: Tue Oct 21, 2008 4:40 pm    Post subject: Reply with quote
On the other side a pattern like this is deadly without uniqueness arguments - it always leaves no solution.

Code:
---------------------------------------
| .  abc  . |  abc  abc  . | .  .  .  |
| .  abc  . |  abc  abc  . | .  .  .  |
| .   .   . |   .    .   . | .  .  .  |
--------------------------------------
Because of the 2 triples abc must be in row 3 in the 3rd box, therefore not in row 3 of box 1. So in box 1 only 2 cells are left for 3 numbers.

Why did i never use that ? Did anyone else?

So Captain Petes pattern (in 2 rows/3 columns) only is not deadly, if it is distributed to 4 (or 6) boxes.

Added: If it does not have a name yet, i would call this invalid pattern "deadly triples", i.e. 2 triples of the same numbers in 2 rows and 2 boxes of the same band (or 2 columns and 2 boxes of the same stack), where one of the boxes only has 2 of the triple cells.
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