SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Fri Mar 29, 2024 10:26 am

All times are UTC




Post new topic Reply to topic  [ 5 posts ] 
Author Message
 Post subject: Ix Killer 4X
PostPosted: Sun Apr 19, 2015 4:50 pm 
Offline
Addict
Addict

Joined: Sat Mar 28, 2015 8:36 pm
Posts: 24
For this weeks puzzle I tried my hand at creating an X-Killer. This one has a vanilla X in the solution grid that some might find interesting.

ImageImage
SS Score: 1.50

A comment on SScore, by adding two more cages the score changed from 1.50 to 1.70, and removing a cage dropped the score to 1.40. I have no idea why adding more constraints would cause SSolver to use harder steps, or how taking away a cage could open easier steps up, but apparently it did.

Code: paste into solver:
3x3:d:k:0000:4096:2562:2562:4622:0000:0000:0000:0000:4096:4096:2823:1547:4622:4622:0000:0000:0000:3341:2823:2823:1547:1547:0000:0000:0000:0000:3341:1548:1548:5393:5393:0000:0000:3592:0000:3855:3855:1548:5393:0000:3600:5641:3592:3592:0000:3855:0000:0000:3600:3600:5641:5641:3076:0000:0000:0000:0000:2821:2821:3846:3846:3076:0000:0000:0000:5123:5123:2821:3846:4097:4097:0000:0000:0000:0000:5123:1802:1802:4097:0000:

Solution:
983765214
175284396
624319857
732896145
561437928
849152673
417628539
358941762
296573481

Vanilla XSudoku:
Image

Vanilla X code:
003700004100080000020009800700006100000400020000050003400000009050000700006003080D

You can remove r1c9, r3c7, and r4c6 from the vanilla sudoku and still get a unique solution, but it is extremely difficult so I don't suggest you try it.

And as always, feedback or suggestions for either puzzle is appreciated.


Top
 Profile  
Reply with quote  
 Post subject: Re: Ix Killer 4X
PostPosted: Wed Apr 22, 2015 2:06 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks ixsetf for this interesting puzzle. It starts easily; then I needed to use a short chain to crack it.

Here is my walkthrough for Ix Killer 4X:
Prelims

a) R1C34 = {19/28/37/46}, no 5
b) R34C1 = {49/58/67}, no 1,2,3
c) R67C9 = {39/48/57}, no 1,2,6
d) R9C67 = {16/25/34}, no 7,8,9
e) 11(3) cage at R2C3 = {128/137/146/236/245}, no 9
f) 6(3) cage at R2C4 = {123}
g) 6(3) cage at R4C2 = {123}
h) 21(3) cage at R4C4 = {489/579/678}, no 1,2,3
i) 22(3) cage at R5C7 = {589/679}
j) 11(3) cage at R7C5 = {128/137/146/236/245}, no 9
k) 20(3) cage at R8C4 = {389/479/569/578}, no 1,2

Steps resulting from Prelims
1a. Naked triple {123} in 6(3) cage at R2C4, locked for N2, clean-up: no 7,8,9 in R1C3
1b. Naked triple {123} in 6(3) cage at R4C2, locked for N4
1c. 22(3) cage at R5C7 = {589/679}, 9 locked for N6, clean-up: no 3 in R7C9

2. 15(3) cage at R5C1 = {456} (only remaining combination), locked for N4, clean-up: no 7,8,9 in R3C1

3. 45 rule on N1 3 innies R1C13 + R3C1 = 18 = {369/459/468/567} (cannot be {189/279/378} because 7,8,9 only in R1C1), no 1,2, clean-up: no 8,9 in R1C4
3a. 7,8,9 only in R1C1 -> R1C1 = {789}
3b. Naked triple {789} in R146C1, locked for C1

4. 45 rule on N6 3 innies R4C79 + R6C9 = 9 = {135/234} (cannot be {126} because no 1,2,6 in R6C9), no 6,7,8, 3 locked for N6, clean-up: no 4,5 in R7C9
4a. 3 of 6(3) cage at R4C2 = {123} must be in R4C23 (R4C23 cannot be {12} which clashes with R4C79), no 3 in R5C3
4b. 3 in N4 only in R4C23, locked for R4
4c. R6C9 = 3 (hidden single in N6) -> R7C9 = 9
4d. Killer pair 1,2 in R4C23 and R4C79, locked for R4

5. 45 rule on N9 2 remaining innies R9C79 = 5 = [14/32/41], clean-up: no 1,2,5 in R9C6

6. 22(3) cage at R5C7 = {589/679}
6a. 5,6 must be in R6C78 (R6C78 cannot be {79/89} which clash with R6C13, ALS block) -> no 5,6 in R5C7
6b. Killer triple 7,8,9 in R6C13 and R6C78, locked for R6

7. 14(3) cage at R5C6 = {149/158/167/248/257} (cannot be {239/347} because 3,7,9 only in R5C6, cannot be {356} = 3{56} which clashes with R6C78), no 3
7a. 7,8,9 only in R5C6 -> R5C6 = {789}
7b. Killer triple 7,8,9 in 21(3) cage at R4C4 and R5C6, locked for N5

8. R5C5 = 3 (hidden single in N5), placed for both diagonals
8a. 45 rule on N5 2 remaining innies R4C6 + R6C4 = 7 = [52/61]
8b. Naked triple {123} in R236C4, locked for C4

9. 45 rule on N8 3 innies R7C4 + R9C46 = 14 = {347/356} -> R9C6 = 3, R9C7 = 4, R9C9 = 1 (step 5), placed for D\
9a. R79C4 = [47/56/65]

10. 1,2 in N8 only in 11(3) cage at R7C5 = {128}, 8 locked for N8

11. 3 in N9 only in 15(3) cage at R7C7 = {357}, locked for N9

12. 8 in C4 only in R45C4, locked for N5
12a. 21(3) cage at R4C4 contains 8 = {489/678}, no 5
12b. 5 in C4 only in R789C4, locked for N8

13. 11(3) cage at R2C3 = {128/137/236/245} (cannot be {146} which clashes with R1C13 + R3C1)
13a. 7 of {137} must be in R3C3 -> no 7 in R2C3 + R3C2
13b. 8 of {128} must be in R3C23 (R3C23 cannot be {12} which clashes with R3C5) -> no 8 in R2C3
13c. 6 of {236} must be in R3C23 (R3C23 cannot be {23} which clashes with R3C45, ALS block) -> no 6 in R2C3

14. 16(3) cage at R1C2 = {178/259/268/349/367/457} (cannot be {169/358} which clash with R1C13 + R3C1)
14a. 1 of {178} must be in R2C1 -> no 1 in R1C2

15. R1C4 = {467}, R79C4 (step 9a) = [47/56/65] -> combined half cage R179C4 = 4{56}/6{47}/7{56}, 6 locked for C4

16. 45 rule on N2 3 innies R1C46 + R3C6 = 21 = {489/579/678}
16a. 4 of {489} must be in R1C4 -> no 4 in R13C6
16b. Consider combinations for 21(3) cage at R4C4 (step 12a) = {489/678}
21(3) cage = {489}, locked for N5 => R2C6 = 4 (hidden single in C6)
or 21(3) cage = {678}, locked for N5 => R5C6 = 9 => R1C46 + R3C6 = {678}
-> no 4 in R1C4, clean-up: no 6 in R1C3
16c. R1C46 + R3C6 = {579/678}, 7 locked for N2

17. Killer pair 6,7 in R1C4 and R79C4, locked for C4
17a. 21(3) cage at R4C4 (step 12a) = {489} (only remaining combination, cannot be {678} because 6,7 only in R4C5), locked for N5 -> R5C6 = 7

18. R1C4 = 7 (hidden single in N2) -> R1C3 = 3
18a. R1C13 + R3C1 (step 3) contains 3 = {369} -> R3C1 = 6, R4C1 = 7, R1C1 = 9, placed for D\, R6C1 = 8, R6C3 = 9

19. R5C7 = 9 (hidden single in N6) -> R6C78 = 13 = {67}, locked for R6 and N6
19a. R5C6 = 7 -> R6C56 = 7 = {25}, locked for R6 -> R4C6 = 6, R6C4 = 1, both placed for D/, R6C2 = 4

20. 11(3) cage at R2C3 (step 11) = {128/245}, no 7, 2 locked for N1
20a. R2C2 = 7 (hidden single in N1), placed for D\ -> R7C7 = 5, placed for D\, R6C6 = 2, placed for D\
20b. R8C8 = 6 (hidden single on D\) -> R6C78 = [67], R7C8 = 3, R8C7 = 7
20c. R9C5 = 7 (hidden single in N8) -> R8C45 = 13 = {49}, locked for R8 and N8

21. Naked pair {18} in R78C6, locked for C6 and N8 -> R13C6 = [59], R1C2 = 8 -> R2C1 = 1 (cage sum), R3C3 = 4, placed for D\

22. Naked pair {12} in R45C3, locked for C3 and N4 -> R4C2 = 3

23. Naked pair {12} in R14C7, locked for C7 -> R3C7 = 8, placed for D/
23a. Naked pair {25} in R8C2 + R9C1, locked for N7 and D/

24. R8C3 = 8, R8C9 = 2, R1C9 = 4, R4C9 = 5, R5C9 = 8, R4C8 = 4, R5C8 = 2 (cage sum)

and the rest is naked singles, without using the diagonals.

Rating Comment:
I'll rate my walkthrough for Ix Killer 4X at Easy 1.5. I used a short forcing chain.

ixsetf wrote:
A comment on SScore, by adding two more cages the score changed from 1.50 to 1.70, and removing a cage dropped the score to 1.40. I have no idea why adding more constraints would cause SSolver to use harder steps, or how taking away a cage could open easier steps up, but apparently it did.
Ed has told me that SSscores aren't just for the hardest step it uses. SS uses some form of weighting which takes account of the number of steps used and how easy or difficult they are. I'll guess that adding two more cages required SS to use more steps, while removing one cage may have reduced the number of steps needed. If you need more information on scoring, please ask Ed; or maybe he'll comment anyway - he's been solving these puzzles.


Top
 Profile  
Reply with quote  
 Post subject: Re: Ix Killer 4X
PostPosted: Wed Apr 22, 2015 2:46 am 
Offline
Addict
Addict

Joined: Sat Mar 28, 2015 8:36 pm
Posts: 24
Thanks Andrew for the walkthrough! It is always interesting to see how you solve the puzzles. Hopefully this one was not too hard to be enjoyable, I will try to make one that's a bit simpler next week.

Andrew wrote:
Ed has told me that SSscores aren't just for the hardest step it uses. SS uses some form of weighting which takes account of the number of steps used and how easy or difficult they are. I'll guess that adding two more cages required SS to use more steps, while removing one cage may have reduced the number of steps needed. If you need more information on scoring, please ask Ed; or maybe he'll comment anyway - he's been solving these puzzles.


Indeed, that would explain scoring changes like this most of the time. I did look over its path though, and it seemed that adding cages increased the difficulty of the hardest step, but I may have just misread the solver order somewhere. Hopefully Ed will be able to comment.


Top
 Profile  
Reply with quote  
 Post subject: Re: Ix Killer 4X
PostPosted: Wed Apr 22, 2015 8:04 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
ixsetf wrote:
Hopefully Ed will be able to comment.
Andrew summarised what I was going to say. Can you post the codes for the two alternative puzzles? Going up to 1.70 from 1.50 is a fair bit so will be interesting to see if SS misses something.


Top
 Profile  
Reply with quote  
 Post subject: Re: Ix Killer 4X
PostPosted: Wed Apr 22, 2015 1:37 pm 
Offline
Addict
Addict

Joined: Sat Mar 28, 2015 8:36 pm
Posts: 24
Ed wrote:
Andrew summarised what I was going to say. Can you post the codes for the two alternative puzzles? Going up to 1.70 from 1.50 is a fair bit so will be interesting to see if SS misses something.


For some reason it seems to be 1.65 rather than 1.70 now, but still a fairly large jump from 1.40.

with two extra cages:
3x3:d:k:0000:4096:2562:2562:4622:0000:0000:0000:0000:4096:4096:2823:1547:4622:4622:4371:4371:0000:3341:2823:2823:1547:1547:0000:0000:4371:0000:3341:1548:1548:5393:5393:0000:0000:3592:0000:3855:3855:1548:5393:0000:3600:5641:3592:3592:0000:3855:0000:0000:3600:3600:5641:5641:3076:0000:3602:0000:0000:2821:2821:3846:3846:3076:0000:3602:3602:5123:5123:2821:3846:4097:4097:0000:0000:0000:0000:5123:1802:1802:4097:0000:

SS: 1.65

with a cage removed:
3x3:d:k:0000:4096:2562:2562:4622:0000:0000:0000:0000:4096:4096:2823:1547:4622:4622:0000:0000:0000:3341:2823:2823:1547:1547:0000:0000:0000:0000:3341:1548:1548:5386:5386:0000:0000:3592:0000:3855:3855:1548:5386:0000:3588:5641:3592:3592:0000:3855:0000:0000:3588:3588:5641:5641:3088:0000:0000:0000:0000:2821:2821:3846:3846:3088:0000:0000:0000:5123:5123:2821:3846:4097:4097:0000:0000:0000:0000:5123:0000:0000:4097:0000:

SS: 1.40

There is an even larger jump with an earlier version.

earlier version:
3x3:d:k:0000:4096:2306:2306:4622:0000:0000:0000:0000:4096:4096:3079:1547:4622:4622:4115:4115:0000:3341:3079:3079:1547:1547:0000:0000:4115:0000:3341:1548:1548:5393:5393:0000:0000:3592:0000:3855:3855:1548:5393:0000:3600:5641:3592:3592:0000:3855:0000:0000:3600:3600:5641:5641:3076:0000:3602:0000:0000:2821:2821:3846:3846:3076:0000:3602:3602:5123:5123:2821:3846:4097:4097:0000:0000:0000:0000:5123:1802:1802:4097:0000:

SS: 1.90

with three cages removed:
3x3:d:k:0000:4096:2306:2306:4622:0000:0000:0000:0000:4096:4096:3079:1547:4622:4622:0000:0000:0000:3341:3079:3079:1547:1547:0000:0000:0000:0000:3341:1548:1548:5386:5386:0000:0000:3592:0000:3855:3855:1548:5386:0000:3600:5641:3592:3592:0000:3855:0000:0000:3600:3600:5641:5641:3076:0000:0000:0000:0000:2821:2821:3846:3846:3076:0000:0000:0000:5123:5123:2821:3846:4097:4097:0000:0000:0000:0000:5123:0000:0000:4097:0000:

SS: 1.45


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 5 posts ] 

All times are UTC


Who is online

Users browsing this forum: No registered users and 7 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB® Forum Software © phpBB Group