View previous topic :: View next topic |
Author |
Message |
| renne
| Joined: 28 Dec 2005 | Posts: 2 | : | | Items |
|
Posted: Sun Jan 01, 2006 8:34 pm Post subject: New Solution Rule for Illogical at sudokusolver.co.uk |
|
|
Logical Solver Stops here:
Code: |
1 2 3 4 5 6 7 8 9
---+--------------------------------------------------------------------------------------------
A | 13 2 6 349 35 7 149 59 8
B | 8 9 5 6 2 14 14 7 3
C | 13 7 4 39 8 15 1269 259 169
D | 4 5 7 1 9 3 8 6 2
E | 9 8 3 2 4 6 5 1 7
F | 6 1 2 5 7 8 39 39 4
G | 2 36 9 34 1 45 7 8 56
H | 5 4 8 7 36 9 1236 23 16
I | 7 36 1 8 356 2 369 4 569
|
Principals of the new Rule
Split the Sudoku into 9 3x3 Blocks an mark rows form A to C, columns for 1 to 3 ->
Code: |
| 1 2 3
---+------------------------
A | 13 2 6
B | 8 9 5
C | 13 7 4
| 1 2 3
---+------------------------
A | 349 35 7
B | 6 2 14
C | 39 8 15
| 1 2 3
---+------------------------
A | 149 59 8
B | 14 7 3
C | 1269 259 169
| 1 2 3
---+------------------------
A | 4 5 7
B | 9 8 3
C | 6 1 2
| 1 2 3
---+------------------------
A | 1 9 3
B | 2 4 6
C | 5 7 8
| 1 2 3
---+------------------------
A | 8 6 2
B | 5 1 7
C | 39 39 4
| 1 2 3
---+------------------------
A | 2 36 9
B | 5 4 8
C | 7 36 1
| 1 2 3
---+------------------------
A | 34 1 45
B | 7 36 9
C | 8 356 2
| 1 2 3
---+------------------------
A | 7 8 56
B | 1236 23 16
C | 369 4 569
|
Now over all 9 blocks every number has to 3 times in every row and 3 times in every column !!!
Now I count how often 4 is in the position A1 over all 9 blocks -> 1 to 3 times .. so i don't know exaktly
now for A2 -> zero times for sure
A3 -> 0 – 1 times
B1 -> 0 – 1 times
B2 -> 2 times
B3 -> 0 – 1 times
C1 -> 0
C2 -> 1
C3 -> 2
write the the table
Code: |
| 1 2 3
---+------------------------
A | 1 - 3 0 0 - 1
B | 0 - 1 2 0 - 1
C | 0 1 1
|
now i look a the main sudoku an can see that i have to recalibrate A1 because 4 can either be in A4 or A7 so ->
for A1 1 to 2 times ->
Code: |
| 1 2 3
---+------------------------
A | 1 - 2 0 0 - 1
B | 0 - 1 2 0 - 1
C | 0 1 1
|
now every sum of each row and column has to be 3
the only solution left is:
Code: |
| 1 2 3
---+------------------------
A | 2 0 1
B | 0 2 1
C | 0 1 1
|
now i have to map it back to the sudoku
for example there has to be one "4" on B3 – block-position -> that is G6 in the sudoku
and so on
now it is solveable with normal logic |
|
Back to top |
|
|
| Ruud Site Admin
| Joined: 17 Sep 2005 | Posts: 708 | : | Location: Netherlands | Items |
|
Posted: Sun Jan 01, 2006 9:02 pm Post subject: |
|
|
Hi renne,
A tip: To reach the intended audience, you should post topics like this in the Solving Sudoku forum.
I checked the candidate grid you posted.
Not all logical solvers would not stop at that point. My solver encounters an XY-Wing in the following cells:
x=3, y=5, z=1
xy=R1C5, xz=R1C1, yz=R3C6. Candidate 1 excluded from R3C1, leaving 3 as the remaining candidate.
Your technique looks interesting. Have you written a program for this?
Ruud. _________________ Meet me at sudocue.net |
|
Back to top |
|
|
| Nick70
| Joined: 08 Jun 2005 | Posts: 160 | : | | Items |
|
Posted: Mon Jan 02, 2006 8:55 am Post subject: Re: New Solution Rule for Illogical at sudokusolver.co.uk |
|
|
Very interesting observation, requiring further thought.
One nitpick.
renne wrote: | Code: | | 1 2 3
---+------------------------
A | 1 - 2 0 0 - 1
B | 0 - 1 2 0 - 1
C | 0 1 1
|
|
You said that C3=2, so the table would actually be
Code: | | 1 2 3
---+------------------------
A | 1 - 2 0 0 - 1
B | 0 - 1 2 0 - 1
C | 0 1 2
|
giving
Code: | | 1 2 3
---+------------------------
A | 2 0 1
B | 1 2 0
C | 0 1 2
|
|
|
Back to top |
|
|
| Nick70
| Joined: 08 Jun 2005 | Posts: 160 | : | | Items |
|
Posted: Mon Jan 02, 2006 9:35 am Post subject: Re: New Solution Rule for Illogical at sudokusolver.co.uk |
|
|
renne wrote: | Now I count how often 4 is in the position A1 over all 9 blocks -> 1 to 3 times .. so i don't know exactly |
Unfortunately this is not correct. 4 can be in A1 1 to 4 times, not 3.
I'm afraid this fatally invalidates the reasoning. |
|
Back to top |
|
|
| renne
| Joined: 28 Dec 2005 | Posts: 2 | : | | Items |
|
Posted: Mon Jan 02, 2006 9:55 pm Post subject: |
|
|
You are right
The reasoning is incorrect |
|
Back to top |
|
|
|