## Help needed!

Post the puzzle or solving technique that's causing you trouble and someone will help

### Help needed!

I've reduced the problem puzzle to the following:

819324765
763195000
020876193
058060401
201500006
607000050
082650000
000008600
076902508

I _know_ what the answer is by using brute force, and I know that if I force R7C7 = 3 then everything else just falls into place. (If I set R7C7 to its only other possible candidate, the puzzle becomes unsolvable.)

What I can't seem to find is a solution rule (other than brute force / guessing) that leads me to the correct solution.

Any clues
pgoyette

Posts: 2
Joined: 22 March 2008

Code: Select all
*-----------*
|819|324|765|
|763|195|...|
|.2.|876|193|
|---+---+---|
|.58|.6.|4.1|
|2.1|5..|..6|
|6.7|...|.5.|
|---+---+---|
|.82|65.|...|
|...|..8|6..|
|.76|9.2|5.8|
*-----------*

Code: Select all
# Assuming you found 2x Locked Candidate (1)
# A Unique Rectangle Type 1 elimination exists for 45 in [r8c1]
*--------------------------------------------------------------------*
| 8      1      9      | 3      2      4      | 7      6      5      |
| 7      6      3      | 1      9      5      | 28     248    24     |
|*45     2     *45     | 8      7      6      | 1      9      3      |
|----------------------+----------------------+----------------------|
| 39     5      8      | 27     6      379    | 4      237    1      |
| 2      349    1      | 5      348    379    | 389    378    6      |
| 6      349    7      | 24     1348   139    | 2389   5      29     |
|----------------------+----------------------+----------------------|
| 1349   8      2      | 6      5      137    | 39     134    479    |
|*139-45 39    *45     | 47     134    8      | 6      1234   2479   |
| 134    7      6      | 9      134    2      | 5      134    8      |
*--------------------------------------------------------------------*

Code: Select all
# After 3x Singles, you are left with ...
# There's probably an elegant elimination here, but all I have is a loop
*-----------------------------------------------------------*
| 8     1     9     | 3     2     4     | 7     6     5     |
| 7     6     3     | 1     9     5     | 28    248   24    |
| 5     2     4     | 8     7     6     | 1     9     3     |
|-------------------+-------------------+-------------------|
| 39    5     8     |e27    6     379   | 4    d237   1     |
| 2     349   1     | 5     348   379   | 389   378   6     |
| 6     349   7     |f24    1348  139   | 2389  5     29    |
|-------------------+-------------------+-------------------|
| 1349  8     2     | 6     5     137   | 39    134   479   |
| 139   39    5     |a7-4   134   8     | 6    c1234 b2479  |
| 134   7     6     | 9     134   2     | 5     134   8     |
*-----------------------------------------------------------*

Code: Select all
4=[r8c4]=7=[r8c9]=2=[r8c8]-2-[r4c7]=2=[r4c4]-2-[r6c4]-4-[r8c4]; => [r8c4]<>4

SSTS completes the puzzle.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Yep, I had found the UR.

I had also found an elimination based on r7c7 = 9. In this case none of the remaining candidates for r4c8 result in a solution. (I have no idea of the notation that would be used to represent this!)

I guess my real question is, how does finding an elimination chain differ from guessing? It seems that both require you to pick some arbitrary cell and try all the possible remaining candidates to see if (all but) one result in a contradiction?

Is there some algorithmic way (rather than arbitrarily or randomly) selecting the cell to try?
pgoyette

Posts: 2
Joined: 22 March 2008

pgoyette wrote:I guess my real question is, how does finding an elimination chain differ from guessing? It seems that both require you to pick some arbitrary cell and try all the possible remaining candidates to see if (all but) one result in a contradiction?

The question of guessing vs. technique has been discussed numerous times. I'm not going to reopen that Pandora's Box.

I'm a terrible manual Sudoku player. However, there are many talented manual players who could easily find my chain -- and others. All but one link in my chain conforms to a b/b plot, and that's considered a technique -- not guessing.

http://forum.enjoysudoku.com/viewtopic.php?t=2143
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006