The Effortless Extremes thread

Everything about Sudoku that doesn't fit in one of the other sections

Postby RW » Mon Sep 24, 2007 6:39 pm

re'born wrote:Perhaps this transported wxyz-wing will fare better. An assist goes to JPF for more or less finding this puzzle

Sorry, but in this case I'd say the XY chain [r2c4]-5-[r1c6]-1-[r4c6]-5-[r5c5] (r3c5 and r6c4<>7) is definitely easier. It considers fewer cells and only bivalue cells. If I recall correctly someone has actually given this particular pattern (two 'ab' bivalue cells connected by two 'ac' bivalue cells) a name because it's so easy to find.

RW
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Postby re'born » Mon Sep 24, 2007 11:12 pm

I don't know whether to be happy I've gotten so good at finding xyz-wings, or sad that I've gotten so bad at spotting xy-chains. Here is my next attempt:
Code: Select all
. 9 4|7 . 5|. . .
5 . 8|. 6 .|. . .
. . .|. 8 .|4 . .
-----+-----+-----
. . .|. . .|. . 6
. . 6|8 9 .|2 3 .
. 1 .|3 7 .|. . 5
-----+-----+-----
. . .|. 2 .|. 9 8
. . .|5 . .|. . 3
1 . .|. . .|. 7 .

After basics we get to
Code: Select all
.------------------.------------------.------------------.
| 23    9     4    | 7     13    5    | 8     6     12   |
| 5     27    8    | 1249  6     1249 | 3     12    79   |
| 236   2367  1    | 29    8     239  | 4     5     79   |
:------------------+------------------+------------------:
| 3489  348   39   | 124   5     124  | 7     148   6    |
| 7     5     6    | 8     9     14   | 2     3     14   |
| 48    1     2    | 3     7     6    | 9     48    5    |
:------------------+------------------+------------------:
| 346   346   357  | 16A   2     137  | 156B  9     8    |
| 2689  268   79   | 5     14    1789 | 16    24    3    |
| 1     2368  359  | 69    34    389  | 56C   7     24   |
'------------------'------------------'------------------'

where the xyz-wing eliminates nothing. But we can transport C to A via:
[r7c4 = 6 = r9c4 - 6 - r9c7]
and hence we can eliminate everything that sees A and B, i.e., r7c12<>6, reducing the puzzle to basics.
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