Anyone found sudoku with the following "Uniqueness&quot

Advanced methods and approaches for solving Sudoku puzzles

Anyone found sudoku with the following "Uniqueness&quot

Postby bennys » Sat Oct 29, 2005 3:05 am

Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . a b | . . . | . . . |
+-------+-------+-------+
| . b . | a . . | . . . |
| . . a | b . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
bennys
 
Posts: 156
Joined: Wed Sep 28, 2005 4:00 pm

Postby DanO » Sat Oct 29, 2005 4:53 am

It shows up all the time if one or more of the a's or b's is fixed as a clue. Otherwise it could be permuted to an alternate solution making the sudoku invalid.

Another configuration is:
Code: Select all
+-------+-------+-------+
| . . . | . b . | a . . |
| . . a | . . . | b . . |
| . . b | . a . | . . . |
+-------+-------+-------+


I've been watching for these configurations to show up where the uniqueness rules could be applied but since the basic form would require 5 of the 6 cells to reduce down to the same naked pair it's not going to be very common.
DanO
 
Posts: 40
Joined: Tue Oct 18, 2005 4:00 pm

Postby PaulIQ164 » Sat Oct 29, 2005 1:03 pm

I've almost seen it a few times, but I guess it's probably very unlikely to ever actually occur for some statistical reason. It's certainly a theoretical possibility though.
PaulIQ164
 
Posts: 533
Joined: Sat Jul 16, 2005 4:00 pm


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