From Sun 11/12 Boston Globe

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From Sun 11/12 Boston Globe

Postby WABJABUSC$UC » Tue Nov 14, 2006 2:50 pm

Stuck on the following puzzle

x1x 2xx x8x
2x6 xx8 x95
8xx 64x xxx

x62 xxx 81x
x81 xxx xxx
x97 xxx x5x

xxx x62 xx1
123 4xx 768
6xx xx3 x2x

HELP Please!!![/list]
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Postby RW » Tue Nov 14, 2006 3:15 pm

Code: Select all
 *-----------*
 |.1.|2..|.8.|
 |2.6|..8|.95|
 |8..|64.|...|
 |---+---+---|
 |.62|...|81.|
 |.81|...|...|
 |.97|...|.5.|
 |---+---+---|
 |...|.62|..1|
 |123|4..|768|
 |6..|..3|.2.|
 *-----------*

In row 8, there's 2 empty cells. These cells must hold digits 5 and 9 in any order. These two digits cannot go anywhere else in that box, which leaves only two cells in column 4 that can have any of these values - r4c4 and r4c5. These two cells must also have the 2 values in any order. Both of the cells are in box 5, so '5' and '9' cannot go anywhere else in that box. This leaves only one cell in column 5, apart from r8c5, that can hold any of the two values - r1c5 - r1c5 and r8c5 must have the two digits '5' and '9'. Now you have a unique rectangle in r18c56 that tells you that if this is a valid sudoku with an unique solution, then r1c6 cannot have any of the values '5' or '9'. This leaves only one possible value for that cell.

RW
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Re: From Sun 11/12 Boston Globe

Postby QBasicMac » Tue Nov 14, 2006 11:46 pm

WABJABUSC$UC wrote:Stuck


Start here

Code: Select all
+------------------+---------------------+--------------------+
| 34579  1    459  | 2      3579   579   | 346    8    3467   |
| 2      347  6    | 137    137    8     | 134    9    5      |
| 8      357  59   | 6      4      1579  | 123    37   237    |
+------------------+---------------------+--------------------+
| 345    6    2    | 3579   3579   4579  | 8      1    3479   |
| 345    8    1    | 3579   23579  45679 | 23469  347  234679 |
| 34     9    7    | 138    1238   146   | 2346   5    2346   |
+------------------+---------------------+--------------------+
| 4579   457  4589 | 5789   6      2     | 3459   34   1      |
| 1      2    3    | 4      59     59    | 7      6    8      |
| 6      457  4589 | 15789  15789  3     | 459    2    49     |
+------------------+---------------------+--------------------+



r8c5=r8c6=59. So one of those two cells is 5 and the other is 9. Erase those pencilmarks from all other cells in box 8.

r4c4 and r5c4 contain the only 5's and 9's in column 4. One must be 5 and the other 9. Erase other pencil marks from those two cells and erase 5 and 9 from all other cells in box 5.

r4c1, r5c1 and r6c1 contain pencilmarks 3,4 and 5. Those numbers must fall somewhere there. Erase those values from all other cells in column 1.

r1c5 and r8c5 contain the only 5's and 9's in column 5. Erase the other numbers in r1c5.

r2c4 and r2c5 contain the only 3's in box 2. Erase the 3's from other cells in row 2.

FINALLY! r3c2 has the only 3 in box 1. Place that 3, erasing all other 3's in row 3. Now everything is pretty easy.

Mac


Code: Select all
+----------------+-----------------+--------------------+
| 79   1    459  | 2    59    579  | 346    8    3467   |
| 2    47   6    | 137  137   8    | 14     9    5      |
| 8    3    59   | 6    4     1579 | 12     {7}  27     |
+----------------+-----------------+--------------------+
| 345  6    2    | 59   37    47   | 8      1    3479   |
| 345  8    1    | 59   237   467  | 23469  347  234679 |
| 34   9    7    | 138  1238  146  | 2346   5    2346   |
+----------------+-----------------+--------------------+
| 79   457  4589 | 78   6     2    | 3459   34   1      |
| 1    2    3    | 4    59    59   | 7      6    8      |
| 6    457  4589 | 178  178   3    | 459    2    49     |
+----------------+-----------------+--------------------+
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