The New Sudoku Players' Forum

[re'born]

The following is Ruud's One-Trick Pony from February 16, 2007:

Code: Select all

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


The idea behind the One-Trick Pony collection of puzzles is that there should only be one 'advanced' step in the puzzle, where advanced means beyond "singles, locked candidates, subsets, basic fish, simple colors, XY-Wing, UR 1 and BUG," but not "tabling or 3D Medusa with weak links". Help me find the one trick for this puzzle.

[ronk]

No help here, as I need a finned x-wing, a finned swordfish and an ALS xz-rule to solve.

[re'born]

Thanks for looking at. That was the best I could do as well.

[_m_k]

r9c4=59, and the puzzle can be solved using only elimination and hidden singles starting with r9c4=9. To make it a little more logical, we can show that r9c4<>5 in two stpes.

Step 1: r9c2=39.
Claim: r9c2=3.
Proof:
[r9c2=9] =>
[r9c4=5 & r1c6=3 (hidden single in r9)] =>
[r5c4=78 & r1c4=679 & r1c6=5] =>
[r1c8=6] => [r1c7=9] => [A: & B:]
A:[r1c4=7] => [r5c4=8] => [r5c2=4] => [r2c2=8]
B:[r2c9=58 && r4c7=15] =>
[r4c9=9 (hidden single r4 & c9)] =>
[r4c7=1 (hidden single r4)] =>
[r3c7=2] => [r2c8=58]
However, r2c2=8 & r2c8=58 & r2c9=58 is a contradiction.

Step 2: r9c4=59.
Claim: r9c4=9.
Proof: r9c4=5 alone does not give a contradiction (using elimination and hidden singles only), but r9c2=3 above & r9c4=5 cause a contradiction similar to the above. Hence, r9c4=9.

I know that this is probably not what you were expecting.

M.K.

[StrmCkr]

yip thats not where doing...

where looking for moves that show the deduction and the contradiction at the same time

rather then apply a "guess" at a bivavled cell. then look for the contradiction buried in a chain of events = true/false of the tested number.

even though a guess is still logic in a sence. (if then else )

[re'born]

r9c4=59, and the puzzle can be solved using only elimination and hidden singles starting with r9c4=9. To make it a little more logical, we can show that r9c4<>5 in two stpes.

Step 1: r9c2=39.
Claim: r9c2=3.
Proof:
[r9c2=9] =>
[r9c4=5 & r1c6=3 (hidden single in r9)] =>
[r5c4=78 & r1c4=679 & r1c6=5] =>
[r1c8=6] => [r1c7=9] => [A: & B:]
A:[r1c4=7] => [r5c4=8] => [r5c2=4] => [r2c2=8]
B:[r2c9=58 && r4c7=15] =>
[r4c9=9 (hidden single r4 & c9)] =>
[r4c7=1 (hidden single r4)] =>
[r3c7=2] => [r2c8=58]
However, r2c2=8 & r2c8=58 & r2c9=58 is a contradiction.

Step 2: r9c4=59.
Claim: r9c4=9.
Proof: r9c4=5 alone does not give a contradiction (using elimination and hidden singles only), but r9c2=3 above & r9c4=5 cause a contradiction similar to the above. Hence, r9c4=9.

I know that this is probably not what you were expecting.

M.K.

I am hoping for a pattern based exclusion, but thank you for looking at the problem and for your solution. Perhaps knowing this cell's value will lead me towards an elegant one-step pattern based solution.

[ravel]

Hi _m_k,

nice solution, but i prefer Ron's:

Code: Select all

 *--------------------------------------------------------------------*
 | 1     x3679   2      | 5679   8      35     |x569   x56     4      |
 | 36     8      469    | 1      3459   45     | 7      2      569    |
 | 67     5      4679   | 2679   479    24     | 1      8      3      |
 |----------------------+----------------------+----------------------|
 | 578    2      57     | 4     *157    6      | 59     3     *1589   |
 | 9      4      3      | 578    157    158    |x56    x1567   2      |
 | 5678   1      567    | 3      2      9      | 4      57     58     |
 |----------------------+----------------------+----------------------|
 | 4     @67     1567   | 258    135    1258   | 23     9     #156    |
 | 35-6  x69     8      | 259   *13459  7      | 23   x-1456  *156    |
 | 2      39     159    | 59     6      1345   | 8      145    7      |
 *--------------------------------------------------------------------*


Finned x-wing(* and # for the fin) and finned swordfish (x and @ for the fin) eliminate 1 from r8c8 and 6 from r8c1.
x/xy-wings and a turbot fish later

Code: Select all

 *-----------------------------------------------------------*
 | 1     679   2     | 567   8     3     | 59    56    4     |
 | 3     8     469   | 1     459   45    | 7     2     569   |
 | 67    5     4679  | 2679  479   24    | 1     8     3     |
 |-------------------+-------------------+-------------------|
 | 78    2     57    | 4     1     6     | 59    3     589   |
 | 9     4     3     | 578   57    58    | 6     1     2     |
 | 68    1     56    | 3     2     9     | 4     7     58    |
 |-------------------+-------------------+-------------------|
 | 4     67    167   |B258  B35   B1258  |B23    9     56    |
 | 5     69    8     | 29    349   7     | 23    46    1     |
 | 2     3    A19    |A59    6     145   | 8     45    7     |
 *-----------------------------------------------------------*


A={159}, B={12358}, x=5, z=1
In A 5 is locked to r9c4 by a 1, in B to r7c456. A 1 in r7c3 locks both and can be eliminated.