The New Sudoku Players' Forum

[deecee]

Having trouble with this puzzle from a local paper. I must have missed something obvious. I would appreciate some help.

Original puzzle:

- 7 - | 9 3 - | 8 5 -
---------------------
9 - 5 | - - - | - - -
---------------------
- - - | 4 - - | 9 - -
============
- - 1 | 7 - - | - - 6
---------------------
- 8 - | 1 - 4 | - 2 -
----------------------
6 - - | - - 8 | 5 - -
============
- - 8 | - - 9 | - - -
----------------------
- - - | - - - | 6 - 4
----------------------
- 6 2 | - 4 7 | - 9 -

This is as far as I have got:



24 | 7 |46 || 9 | 3 |126 || 8 | 5 | 12
-------------------------------------------------------------
9 | 123| 5 || 28 | 278|126 || 1347 |1346 |1237
-------------------------------------------------------------
8 | 123| 36 || 4 |257 |1256|| 9 |136 |1237
==================================
234 |2349| 1 || 7 |259 |235 || 34 | 8 | 6
-------------------------------------------------------------
5 | 8 | 37 || 1 | 6 | 4 || 37 | 2 | 9
-------------------------------------------------------------
6 |2349|347|| 23 |29 | 8 || 5 | 134 |137
==================================
347 |34 | 8 || 6 | 1 | 9 || 2 | 37 | 5
-------------------------------------------------------------
17 | 5 | 9 || 238| 28 |23 || 6 | 17 | 4
-------------------------------------------------------------
13 |6 | 2 || 5 | 4 | 7 || 13 |9 | 8

[daj95376]

Code: Select all

 *-----------*
 |.7.|93.|85.|
 |9.5|...|...|
 |...|4..|9..|
 |---+---+---|
 |..1|7..|..6|
 |.8.|1.4|.2.|
 |6..|..8|5..|
 |---+---+---|
 |..8|..9|...|
 |...|...|6.4|
 |.62|.47|.9.|
 *-----------*


Code: Select all

*--------------------------------------------------------------------*
|  24     7      46    |  9      3      126   |  8      5      12    |
|  9      123    5     |  28     278    126   |  1347   1346   1237  |
|  8      123    36    |  4      257    1256  |  9      136    1237  |
|----------------------+----------------------+----------------------|
|  234    2349   1     |  7      259    235   |  34     8      6     |
|  5      8      37    |  1      6      4     |  37     2      9     |
|  6      2349   347   |  23     29     8     |  5      134    137   |
|----------------------+----------------------+----------------------|
|  347    34     8     |  6      1      9     |  2      37     5     |
|  17     5      9     |  238    28     23    |  6      17     4     |
|  13     6      2     |  5      4      7     |  13     9      8     |
*--------------------------------------------------------------------*


Maybe someone else will find something simpler than a Skyscraper in <3> and (later) an XY-Chain on <6> at [r1c3]. For sure, you need to find a newspaper with easier puzzles.

[udosuk]

Code: Select all

 *-----------------------------------------------------------*
 | 24    7     46    | 9     3     126   | 8     5     12    |
 | 9     123   5     | 28    278   126   | 1347  1346  1237  |
 | 8     123   36    | 4     257   1256  | 9     136   1237  |
 |-------------------+-------------------+-------------------|
 |-234   2349  1     | 7     259   235   | 34    8     6     |
 | 5     8    *37    | 1     6     4     |*37    2     9     |
 | 6     2349  347   | 23    29    8     | 5     134   137   |
 |-------------------+-------------------+-------------------|
 | 347   34    8     | 6     1     9     | 2     37    5     |
 | 17    5     9     | 238   28    23    | 6     17    4     |
 |*13    6     2     | 5     4     7     |*13    9     8     |
 *-----------------------------------------------------------*

Skyscraper/Turbot fish on 3s:
Strong links in r5c37+r9c17 -> r4c1<>3

After a few more basic moves (including a triple on r6), we reach this position:

Code: Select all

 *-----------------------------------------------------------*
 |@24    7    @46    | 9     3     126   | 8     5    @12    |
 | 9     123   5     | 28    278   126   | 47    146   1237  |
 | 8     123  -36    | 4     257   1256  | 9    #16    1237  |
 |-------------------+-------------------+-------------------|
 | 24    239   1     | 7     259   235   | 34    8     6     |
 | 5     8     37    | 1     6     4     | 37    2     9     |
 | 6     239   47    | 23    29    8     | 5     14    17    |
 |-------------------+-------------------+-------------------|
 | 7     4     8     | 6     1     9     | 2     3     5     |
 | 1     5     9     | 238   28    23    | 6     7     4     |
 | 3     6     2     | 5     4     7     | 1     9     8     |
 *-----------------------------------------------------------*

ALS-xz rule:
A: r1c139={1246}
B: r3c8={16}
Restricted common: x=1
Common: z=6

Therefore r3c3<>6, and the rest are all singles.

[re'born]

After a few more basic moves (including a triple on r6), we reach this position:

Code: Select all

 *-----------------------------------------------------------*
 |@24    7    @46    | 9     3     126   | 8     5    @12    |
 | 9     123   5     | 28    278   126   | 47    146   1237  |
 | 8     123  -36    | 4     257   1256  | 9    #16    1237  |
 |-------------------+-------------------+-------------------|
 | 24    239   1     | 7     259   235   | 34    8     6     |
 | 5     8     37    | 1     6     4     | 37    2     9     |
 | 6     239   47    | 23    29    8     | 5     14    17    |
 |-------------------+-------------------+-------------------|
 | 7     4     8     | 6     1     9     | 2     3     5     |
 | 1     5     9     | 238   28    23    | 6     7     4     |
 | 3     6     2     | 5     4     7     | 1     9     8     |
 *-----------------------------------------------------------*

ALS-xz rule:
A: r1c139={1246}
B: r3c8={16}
Restricted common: x=1
Common: z=6

Therefore r3c3<>6, and the rest are all singles.

Of course this move is also an xy-chain:

[r3c3]-6-[r1c3]-4-[r1c1]-2-[r1c9]-1-[r2c8]-6-[r3c3]

and hence r3c3<>6.

[daj95376]

So far, a Skyscraper followed by either an XY-Chain or ALS-xz.

Instead of any of the above techniques, UR in [r28c45] => [r2c5]=7 or [r8c4]=3.

Code: Select all

[r2c5]=7 => [r5c7]=7 => [r5c3]=3 => [r3c3]=6 => [r1c3]=4 => ...
...         [r1c1]=2 => [r1c9]=1 => [r3c8]=3 => [r2c7]=4 => [b6]=Invalid


Therefore, [r8c4]=3 ... and the puzzle solves with singles.

Note: This is not a valid deduction based on the UR, but I used the UR to indicate that my initial selection of [r2c5]=7 was not completely arbitrary.

{Edit: Thanks udosuk for catching the typo!]

[re'born]

So far, a Skyscraper followed by either an XY-Chain or ALS-xz.

I was hoping that someone would find a way to take advantage of the UR in [r28c45]. That darn <7> doesn't want to be eliminated easily. Too bad because the <3> cracks the puzzle without the need for any of the above techniques!

I tried that, but the best I can say is that the x-wing on the 8's implies that r2c4=8 and r8c5=8. This doesn't seem to advance the puzzle.

[udosuk]

Code: Select all

[r2c5]=7 => [r5c7]=7 => [r5c3]=3 => [r3c3]=6 => [r1c3]=4 => ...
...         [r1c1]=2 => [r1c9]=1 => [r2c8]=3 => [r1c7]=4 => [b6]=Invalid


Shouldn't it be:

[r2c5]=7 => [r5c7]=7 => [r5c3]=3 => [r3c3]=6 => [r1c3]=4 => ...
... [r1c1]=2 => [r1c9]=1 => [r3c8]=3 => [r2c7]=4 => [b6]=Invalid