| View previous topic :: View next topic |
| Author |
Message |
Pat
Joined: 23 Feb 2010
Posts: 207
|
 Posted: Tue Dec 13, 2022 1:58 pm Post subject: a 10.1 from coloin |
 |
|
45 givens
2.8..51.3...3.18.21.384256..3218....8.753.21..1..27.38...21.38.32...8..1.81.5372.
[ play ]
| Code: |
2 . 8 | . . 5 | 1 . 3
. . . | 3 . 1 | 8 . 2
1 . 3 | 8 4 2 | 5 6 .
-------+-------+------
. 3 2 | 1 8 . | . . .
8 . 7 | 5 3 . | 2 1 .
. 1 . | . 2 7 | . 3 8
-------+-------+------
. . . | 2 1 . | 3 8 .
3 2 . | . . 8 | . . 1
. 8 1 | . 5 3 | 7 2 .
|
|
|
| Back to top |
|
 |
Pat
Joined: 23 Feb 2010
Posts: 207
|
| Posted: Sat Dec 17, 2022 9:01 am Post subject: |
|
|
| i posted this puzzle because a comment by eleven shows it can be solved by humans... |
|
| Back to top |
|
|
dongrave
Joined: 06 Mar 2014
Posts: 568
|
| Posted: Sat Dec 17, 2022 7:34 pm Post subject: |
|
|
| Do you mean that it can be solved by humans using the 3 dozen or so techniques that human Sudoku experts use? Or do you mean that it can be solved AT ALL by humans - including trial and error? |
|
| Back to top |
|
|
Pat
Joined: 23 Feb 2010
Posts: 207
|
| Posted: Sun Dec 18, 2022 1:31 pm Post subject: |
|
|
| eleven wrote: |
Can be easily solved with variable replacement
|
| totuan wrote: |
can easily solve by "impossible pattern"
|
|
|
| Back to top |
|
|
dongrave
Joined: 06 Mar 2014
Posts: 568
|
| Posted: Sun Dec 18, 2022 7:07 pm Post subject: |
|
|
| Wow! Eleven's Variable Replacement is ingenious! I did a google search on 'sudoku eleven variable replacement' and read a long detailed explanation of it today! Then I used it to solve this puzzle! What an amazing idea! If you want, I'll take the time to post the grid after basics followed by the solution using variable replacement! That was so interesting! Thanks for posting it! |
|
| Back to top |
|
|
Pat
Joined: 23 Feb 2010
Posts: 207
|
| Posted: Sun Dec 18, 2022 8:30 pm Post subject: |
|
|
perhaps with your recommendation,
others will look at it too... |
|
| Back to top |
|
|
dongrave
Joined: 06 Mar 2014
Posts: 568
|
| Posted: Sun Dec 18, 2022 9:28 pm Post subject: |
|
|
For anyone that's interested in eleven's 'variable replacement' method, this is how I used it today to solve this puzzle.
This was the grid that I ended up with after basics:
| Code: | +------------------+---------------+--------------+
| 2 4679 8 | 679 679 5 | 1 479 3 |
| 45679 45679 4569 | 3 679 1 | 8 479 2 |
| 1 79 3 | 8 4 2 | 5 6 79 |
+------------------+---------------+--------------+
| 469 3 2 | 1 8 469 | 469 57 57 |
| 8 469 7 | 5 3 469 | 2 1 469 |
| 4569 1 4569 | 469 2 7 | 469 3 8 |
+------------------+---------------+--------------+
| 45679 45679 4569 | 2 1 469 | 3 8 4569 |
| 3 2 4569 | 4679 679 8 | 469 59 1 |
| 469 8 1 | 469 5 3 | 7 2 469 |
+------------------+---------------+--------------+ |
I originally got nowhere with this one but then after reading about eleven's 'variable replacement', I returned to it.
The idea of 'variable replacement' is that when you see the same repeated candidates in many cells, you can assign variables to those candidates and then replace the candidates in the cells with the variables!
I noticed that the values 4, 6, and 9 were the only candidates in the unsolved cells in rows 4, 5, and 9 - and also in columns 6 and 7 - and since column 6 had 2 of the cells in the same box, I decided to assign A to r4c6, B to r5c6, and C to r7c6.
So now that means that even though I don't currently know which value each variable is equal to, I know that those 3 variables can only exist once in any house (i.e. row, column, or box).
After assigning the variables to the cells mentioned above, I was able to perform some more basics until I reached the following grid:
| Code: | +------------------+-------------+---------------+
| 2 ABC7 8 | AB7 ABC 5 | 1 ABC7 3 |
| ABC57 ABC57 ABC5 | 3 ABC 1 | 8 ABC7 2 |
| 1 ABC7 3 | 8 4 2 | 5 6 ABC7 |
+------------------+-------------+---------------+
| BC 3 2 | 1 8 A | BC 57 57 |
| 8 AC 7 | 5 3 B | 2 1 AC |
| AB5 1 AB5 | C 2 7 | AB 3 8 |
+------------------+-------------+---------------+
| AB57 AB57 AB5 | 2 1 C | 3 8 AB5 |
| 3 2 ABC5 | AB7 AB7 8 | AC ABC5 1 |
| ABC 8 1 | AB 5 3 | 7 2 ABC |
+------------------+-------------+---------------+
|
Then at this point I began looking for the same sort of chains that I look for when I don't have variables assigned and I noticed that if r9c9 is not C, then r9c1 must be C, so r4c1 cannot be C, so r4c7 would have to be C. Therefore r5c9 cannot be C!
After removing the candidate C from r5c9 and performing more basics, I ended up with the following grid:
| Code: | +-------------+-------------+-------------+
| 2 B 8 | 7 C 5 | 1 A 3 |
| A 5 C | 3 B 1 | 8 7 2 |
| 1 7 3 | 8 4 2 | 5 6 C |
+-------------+-------------+-------------+
| B 3 2 | 1 8 A | C 5 7 |
| 8 C 7 | 5 3 B | 2 1 A |
| 5 1 A | C 2 7 | B 3 8 |
+-------------+-------------+-------------+
| 7 A B | 2 1 C | 3 8 5 |
| 3 2 5 | B 7 8 | A C 1 |
| C 8 1 | A 5 3 | 7 2 B |
+-------------+-------------+-------------+
|
Then at this point I could see that the C in r3c9 had to be 9 which meant that the A in r1c8 had to be 4 which meant that B had to be 6!
So now just replace the variables with their values and you get the solution to the puzzle:
| Code: | +-------------+-------------+-------------+
| 2 6 8 | 7 9 5 | 1 4 3 |
| 4 5 9 | 3 6 1 | 8 7 2 |
| 1 7 3 | 8 4 2 | 5 6 9 |
+-------------+-------------+-------------+
| 6 3 2 | 1 8 4 | 9 5 7 |
| 8 9 7 | 5 3 6 | 2 1 4 |
| 5 1 4 | 9 2 7 | 6 3 8 |
+-------------+-------------+-------------+
| 7 4 6 | 2 1 9 | 3 8 5 |
| 3 2 5 | 6 7 8 | 4 9 1 |
| 9 8 1 | 4 5 3 | 7 2 6 |
+-------------+-------------+-------------+
|
|
|
| Back to top |
|
|
immpy
Joined: 06 May 2017
Posts: 571
|
| Posted: Mon Dec 19, 2022 6:47 pm Post subject: |
|
|
| Wow! That's pretty neat dongrave. And eleven. Might have to explore this a little. |
|
| Back to top |
|
|
immpy
Joined: 06 May 2017
Posts: 571
|
| Posted: Mon Dec 19, 2022 7:27 pm Post subject: |
|
|
| Just got done reading about this. The method is perfect for a puzzle of this nature with what is left after basics. I have learned something new today, and that's always a good thing. Thanks dongrave. |
|
| Back to top |
|
|
storm_norm22
Joined: 24 Oct 2020
Posts: 15
|
| Posted: Wed Dec 21, 2022 4:19 pm Post subject: |
|
|
| this is the kind of interesting "stuff" that needs to be posted more often. and pinned to the top of some forums for more interesting conversations |
|
| Back to top |
|
|
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
