The New Sudoku Players' Forum

[AnotherLife]

This is another puzzle with a symmetry of givens (thanks to Mike Metcalf for helping me to identify this pattern). Can anyone offer a one-step solution to this not very hard puzzle?

Code: Select all

.1..2.345..6.........14..2....71.45.7.......2.68.92....7..89.........5..683.7..9.

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.---------------------.-------------------.---------------------.
| 89      1      79   | 689    2    678   | 3     4      5      |
| 234589  23459  6    | 3589   35   3578  | 1789  178    1789   |
| 3589    359    579  | 1      4    35678 | 6789  2      6789   |
:---------------------+-------------------+---------------------:
| 239     239    29   | 7      1    368   | 4     5      3689   |
| 7       3459   1459 | 34568  356  34568 | 1689  1368   2      |
| 1345    6      8    | 345    9    2     | 17    137    137    |
:---------------------+-------------------+---------------------:
| 1245    7      1245 | 23456  8    9     | 126   136    1346   |
| 1249    249    1249 | 2346   36   1346  | 5     13678  134678 |
| 6       8      3    | 245    7    145   | 12    9      14     |
'---------------------'-------------------'---------------------'


[Cenoman]

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 +---------------------+--------------------+---------------------+
 | a89     1    a79    |  689   2    a678   |  3     4     5      |
 |  24     24    6     |  89    35    35    |  178   17    179    |
 |  358-9  35-9  57-9  |  1     4     78    |  68    2    c69     |
 +---------------------+--------------------+---------------------+
 |  239    239   29    |  7     1    b68    |  4     5    c68     |
 |  7      45    1     |  368   356   345   |  9     68    2      |
 |  45     6     8     |  45    9     2     |  17    137   137    |
 +---------------------+--------------------+---------------------+
 |  15     7     45    |  24    8     9     |  26-1  36-1  346-1  |
 |  129    29    249   |  36    36    14    |  5     78    78     |
 |  6      8     3     |  245   7     145   |  12    9     14     |
 +---------------------+--------------------+---------------------+

As stated by Bogdan, the puzzle has a central symmetry with the following correspondance of digits
[19] [27] [33][48]. The inferred placement +3 r5c5 doesn't solve the puzzle alone.
But the following ALS Y-wing does:
(9=786)r1c136 - (6=8)r4c6 - (8=69)r34c9 => -9 r3c123, and by symmetry -1 r7c789; ste

[AnotherLife]

Hi, Cenoman,
Congratulations on your ingenious and non-standard solution! It comes to be that the stated symmetry of the puzzle was a hint to the solution. Let me just add that we need to take account of the uniqueness of the solution. We have a direct correspondence between the givens in the upper and the lower parts of the puzzle, so we have a direct correspondence between all the cells of these parts, or else we would have more than one solution to the puzzle. You are right about the possibility to eliminate the two corresponding digits from both parts of the board.

[m_b_metcalf]

This one is nominally much harder, but has several simple paths:

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 . 8 . . 4 . 6 3 1
 . . 4 . . . . . .
 . . . 1 8 . . 5 .
 . . . 4 3 . 8 6 .
 4 . . . . . . . 5
 . 6 2 . 7 5 . . .
 . 4 . . 2 9 . . .
 . . . . . . 5 . .
 9 7 6 . 5 . . 2 .

Mike

[AnotherLife]

This one is nominally much harder, but has several simple paths...
Mike

Hello, Mike,
The solution to this puzzle is even simpler than to the one above. There is a direct correspondence between the digits in the left and the right parts of the puzzle: 1--9, 2--8, 3--7, 4--5, 6--6. Using Cenoman's logic, we can prove that r5c5=6. Firstly, digit 6 is the only one corresponding to itself, secondly, the solution is unique.
Now the puzzle is solvable by the basic methods (lcls steps, as Cenoman uses to say).
Thanks once again for this nice pattern!

Regards, Bogdan