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A Uniqueness Elimination

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sun Jul 15, 2007 12:12 pm    Post subject: A Uniqueness Elimination Reply with quote
Here is one I thought interesting. It is a Brain Basher's Super Hard:
Code:

Puzzle: BB070307sh
+-------+-------+-------+
| . . . | 4 . 5 | . . . |
| . 8 . | 9 . 2 | . 4 . |
| . 4 2 | . 8 . | 5 9 . |
+-------+-------+-------+
| 2 9 . | . . . | . 7 3 |
| . . 4 | . . . | 9 . . |
| 5 3 . | . . . | . 6 2 |
+-------+-------+-------+
| . 2 9 | . 4 . | 7 3 . |
| . 5 . | 7 . 3 | . 8 . |
| . . . | 1 . 9 | . . . |
+-------+-------+-------+

Basic methods get you to here:
Code:
+-------------------+-------------------+-------------------+
| 9     16    1367  | 4     167   5     | 12368 12    1678  |
| 1367  8     5     | 9     167   2     | 136   4     167   |
| 167   4     2     | 3     8     16    | 5     9     167   |
+-------------------+-------------------+-------------------+
| 2     9     168   | 56    156   146   | 148   7     3     |
| 1678  16    4     | 2     3     167   | 9     15    158   |
| 5     3     17    | 8     9     147   | 14    6     2     |
+-------------------+-------------------+-------------------+
| 16    2     9     | 56    4     8     | 7     3     156   |
| 4     5     16    | 7     26    3     | 126   8     9     |
| 38    7     38    | 1     256   9     | 26    25    4     |
+-------------------+-------------------+-------------------+

You can continue with an X-wing, etc., but the solution still has a number of steps.

Or, notice the <26> UR in R89C57. To avoid the deadly pattern, either R8C7 is <1>, and/or R9C5 is <5>.

Looking in R9 and B9, if R9C5 is <5>, R8C7 is <1>. Thus, R8C7 must be <1>, and the puzzle is solved.

Keith
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
PostPosted: Thu Sep 27, 2007 2:58 pm    Post subject: Reply with quote
This UR elimination comes from the recent VH from 26 Sept

For avoiding the deadly [15] pattern in R29C12

a) R2C1 must contain a <6>, <7>, or a <9>

OR

b) R2C2 must contain a <6> or a <7>

In both ways it results in a naked [679] triple in the first four cells in R2, which erases the <6> in R2C9, though it didn't crack the puzzle, i found it a rather nice step.

Code:

+-----------------+----------------+-------------+
| 1235679 8    23 | 3679 13679 137 | 4  1569 156 |
|*15679  *1567 69 | 679  8     4   | 3  2   15-6 |
| 1369    136  4  | 5    1369  2   | 7  169  8   |
+-----------------+----------------+-------------+
| 39      2    5  | 8    39    6   | 1  47   47  |
| 8       4    69 | 279  1279  157 | 26 56   3   |
| 367     367  1  | 4    23    35  | 9  8    256 |
+-----------------+----------------+-------------+
| 4       36   8  | 1    236   9   | 5  67   267 |
| 236     9    23 | 367  5     37  | 8  14   14  |
|*15     *15   7  | 26   4     8   | 26 3    9   |
+-----------------+----------------+-------------+
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