The New Sudoku Players' Forum

[djwillard]

I need help with this one:
Original:
96- --8 2--
2-- 94- --1
-3- --- --6

-8- --- ---
--9 6-5 1--
--- --- -7-

8-- --- -6-
4-- -37 --9
--1 2-- -83

I got this far:
96- 318 2-7
2-- 946 --1
13- --2 --6

-8- --- --4
-49 6-5 1-8
-12 48- -75

8-3 --- -62
426 837 519
--1 26- -83

This is the 2nd time I have cried wolf and asked for help via this forum. Thank you all for your kind and patient advice!
DJ

[QBasicMac]

I presume these are your pencilmarks:

Code: Select all

+----------------+--------------+-------------+
| 9     6    45  | 3   1    8   | 2    45   7 |
| 2     57   578 | 9   4    6   | 38   35   1 |
| 1     3    48  | 57  57   2   | 89   49   6 |
+----------------+--------------+-------------+
| 3567  8    57  | 17  279  139 | 369  239  4 |
| 37    4    9   | 6   27   5   | 1    23   8 |
| 36    1    2   | 4   8    39  | 369  7    5 |
+----------------+--------------+-------------+
| 8     79   3   | 15  59   149 | 47   6    2 |
| 4     2    6   | 8   3    7   | 5    1    9 |
| 57    579  1   | 2   6    49  | 47   8    3 |
+----------------+--------------+-------------+


(Just asking - no idea how to proceed)

Mac

[djwillard]

Pencil marks are as I have them except R7C2 I have 579

[liteman]

*-----------*
|96.|..8|2..|
|2..|94.|..1|
|.3.|...|..6|
|---+---+---|
|.8.|...|...|
|..9|6.5|1..|
|...|...|.7.|
|---+---+---|
|8..|...|.6.|
|4..|.37|..9|
|..1|2..|.83|
*-----------*

Here is the solution to your puzzle
*-----------*
|964|318|257|
|257|946|831|
|138|752|946|
|---+---+---|
|785|123|694|
|349|675|128|
|612|489|375|
|---+---+---|
|873|591|462|
|426|837|519|
|591|264|783|
*-----------*

After solving for singles -- the biggest part of opeing up this puzzle was finding the triple in C2 -- r2 r7 and r9

[Ruud]

liteman, The solution may be correct,

but there is NO way to find it with only a triple.

this sudoku requires at least one Tabling step.

Testing candidate 5 in R9C2 will help.

Ruud.

[QBasicMac]

Pencil marks are as I have them except R7C2 I have 579

Well, even though it doesn't help us much, here is what happened to the 5 in r7c2: Box 8 has only two 5's and they are in row 7. That means no other 5's can be on row 7.

Now what is next? I used T&E and found the puzzle indeed has one solution. I then got out my Beginner's Sudoku Puzzle book and started working on something that was more fun (no pencilmarks).

Mac

P.S. My T&E solution:

Code: Select all

Trying pencilmark 4 in cell r9c7
r7c7 = 7
r9c6 = 9
r6c6 = 3
r7c5 = 5
r3c5 = 7
r4c6 = 1
r5c5 = 2
r5c8 = 3
r6c1 = 6
r6c7 = 9
r7c2 = 9
r7c4 = 1
r7c6 = 4
r2c8 = 5
r3c4 = 5
r3c7 = 8
r4c4 = 7
r4c5 = 9
r4c7 = 6
r4c8 = 2
r5c1 = 7
r9c1 = 5
But now both r2c2 and r9c2 are single 7's.
Not possible, so r9c2 = 7
Puzzle solves easily.


[ronk]

[edit: post deleted]

[Hud]

I presume these are your pencilmarks:

Code: Select all

+----------------+--------------+-------------+
| 9     6    45  | 3   1    8   | 2    45   7 |
| 2     [b]57[/b]   578 | 9   4    6   | 38   35   1 |
| 1     3    48  | 57  57   2   | 89   49   6 |
+----------------+--------------+-------------+
| 3567  8    57  | 17  279  139 | 369  239  4 |
| 37    4    9   | 6   27   5   | 1    23   8 |
| 36    1    2   | 4   8    39  | 369  7    5 |
+----------------+--------------+-------------+
| 8     [b]79[/b]   3   | 15  [b]59[/b]   149 | 47   6    2 |
| 4     2    6   | 8   3    7   | 5    1    9 |
| 57    579  1   | 2   6    49  | 47   8    3 |
+----------------+--------------+-------------+


(Just asking - no idea how to proceed)

Mac

I tried it twice on paper and both times I found the x-y wing in bold type. I eliminated the 5 in r3c5, but still came up with an invalid solution to the puzzle. I'm too tired to try it again tonight (sans tabling).

[Hud]

Oops, I messed up the x-y wing, sorry.

[Myth Jellies]

We can salvage that starred potential xy-wing or xz-almost locked set pattern using POM.

Here is a complete POM merge grid, although we only really needed to work out the labels for the 5's and 7's

Code: Select all

+-----------------------+--------------------+-----------------+
| 9      6      4ab     | 3       1     8    | 2      4cd    7 |
|               5ab     |                    |        5cdef    |
|                       |                    |                 |
| 2      5cd    5ef     | 9       4     6    | 3abc   3de    1 |
|        7a     7bcdefg |                    | 8b     5ab      |
|               8a      |                    |                 |
|                       |                    |                 |
| 1      3      4cd     | 5ace    5bdf  2    | 8a     4ab    6 |
|               8b      | 7abcde  7fg        | 9a     9bcde    |
+-----------------------+--------------------+-----------------+
| 3b     8      5cd     | 1a      2a    1b   | 3d     2b     4 |
| 5abef         7a      | 7fg     7de   3ce  | 6b     3a       |
| 6a                    |         9bc   9d   | 9e     9a       |
| 7bc                   |                    |                 |
|                       |                    |                 |
| 3ade   4      9       | 6       2b    5    | 1      2a     8 |
| 7defg                 |         7abc       |        3bc      |
|                       |                    |                 |
| 3c     1      2       | 4       8     3abd | 3e     7      5 |
| 6b                    |               9ae  | 6a              |
|                       |                    | 9bcd            |
+-----------------------+--------------------+-----------------+
| 8     *7bdf   3       | 1b     *5ace  1a   | 4bd    6      2 |
|       *9b             | 5bdf   *9ade  4ac  | 7aceg           |
|                       |               9c   |                 |
|                       |                    |                 |
| 4      2      6       | 8       3     7    | 5      1      9 |
|                       |                    |                 |
|*5cd    5abef  1       | 2       6     4bd  | 4ac    8      3 |
|*7a     7ceg           |               9b   | 7bdf            |
|        9acde          |                    |                 |
+-----------------------+--------------------+-----------------+


Cells r2c2, r4c3, and r9c1 give you the equations

5cd = 7bcdefg; and 5abef = 7a;

while cells r3c4 and r3c5 give you the equations

5ace = 7fg; and 5bdf = 7abcde;

These 4 equations can only be true if
5c = 7fg;
5d = 7bcde;
5bf = 7a;
and 5a & 5e are invalid.

Now we bring in the starred almost locked sets xz-pattern
A = {r7c2, r7c5}; B = {r9c1}; z=7; x=5 (or maybe vice-versa).
Because of the xz-pattern, we know that the only valid patterns for 5's must either be in A, or B. Thus 5b and 5f are also invalid, leaving 5cd as the only valid labels for 5's. This kills a whole bunch of 5 candidates and basically solves the puzzle.

Edit - actually, since there is another xz-pattern using cells r4c3, r4c4, and r7c4, that also invalidate labels 5ae, we don't need the labels for 7's after all.

[rubylips]

Here's a chain that cracks it:

Code: Select all

     9    6   45 |   3    1    8 |    2   45  7
     2   57  578 |   9    4    6 |   38   35  1
     1    3   48 |  57   57    2 |   89   49  6
-----------------+---------------+-------------
  3567    8   57 |  17  279  139 |  369  239  4
    37    4    9 |   6   27    5 |    1   23  8
    36    1    2 |   4    8   39 |  369    7  5
-----------------+---------------+-------------
     8   79    3 |  15   59  149 |   47    6  2
     4    2    6 |   8    3    7 |    5    1  9
    57  579    1 |   2    6   49 |   47    8  3

Consider the chain r2c2=5=r4c3-<5|1>-r4c4-1-r7c4-<1|7>-r7c2.
When the cell r2c2 contains the value 7, so does the cell r7c2 - a contradiction.
Therefore, the cell r2c2 cannot contain the value 7.
- The move r2c2:=7 has been eliminated.
The value 5 is the only candidate for the cell r2c2.


Some notes on the more subtle links:
i. r2c2=5=r4c3
Since r2c2 doesn't contain a 5, one of r1c3 and r2c3 must, which means that r4c3 can't.
ii. r7c4-<1|7>-r7c2.
r7c4<>1 => r7c4=5 => r7c5=9 => r7c2=7

[Carcul]

Here is a longer chain that also craks the puzzle:

[r2c3]=7=[r2c2]-7-[r7c2]-9-[r7c5]-5-[r7c4]-1-[r4c4]-7-[r4c3]-5-[r1c3]
-4-[r3c3]-8-[r2c3] => r2c3<>8.

Carcul

[Jeff]

Here is a longer chain that also craks the puzzle:

[r2c3]=7=[r2c2]-7-[r7c2]-9-[r7c5]-5-[r7c4]-1-[r4c4]-7-[r4c3]-5-[r1c3]-4-[r3c3]-8-[r2c3] => r2c3<>8.

Nice chain. In fact, this is the first double implication chain identified for this grid.

[ronk]

Here is a longer chain that also craks the puzzle:

[r2c3]=7=[r2c2]-7-[r7c2]-9-[r7c5]-5-[r7c4]-1-[r4c4]-7-[r4c3]-5-[r1c3]
-4-[r3c3]-8-[r2c3] => r2c3<>8.

Carcul

If I'm reading the above correctly, one starts on the left with r2c3<>7 ... and following the chain ends on the right with r2c3<>8 ... but how does the conclusion r2c3<>8 follow from that?

[QBasicMac]

Supposedly "Medium", but I'm stuck

Convinced it is not "Medium"?



Mac