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Børge

Post subject: Assassin 199

Posted: Fri Sep 10, 2010 4:53 pm

Grand Master

Joined: Mon Apr 21, 2008 10:32 am
Posts: 868

Assassin 199 SS score v3.3.A2: 1.72 ◄ Select to see the SS score

Assuming that the regular Assassins (Afmob. Andrew, Ed, Elaine, Frank, goooders, HATMAN, Joe Casey, manu, mhparker, Ronnie G, etc.) and the other big guns (djape, gary w, h3lix, Jean-Christophe, Nasenbaer, Para, rcbroughton, tarek, udosuk, wellbeback, etc.) all want to be the one posting A200, and all have an Assassin ready to post, I hereby puncture the abscessus by posting A199. Since my "Blind Dates" were not a total disaster, I again take the change of making a complete fool of myself.

The SS score might seem a bit high, but from SudokuSolver's pretty short Step Analysis without any T&E, chains or other really advanced techniques, but containing several of the interesting techniques required according to Ed's Asassin guide, I assume that the SS score is too high.
But I let the Assassin experts be the judges.

I only plan on posting a v1, but the cage structure easily produces puzzles with an SS score ranging from 0.73 through unsolvable by logic only.

This as an X Killer without the need for diagonal lines.
If you cannot figure out the value of r5c5 within 3 seconds after seeing the coloured image, this puzzle is not for you. :rambo:

(Moderator) HTML programming failed, so has been deleted.

Code strings.

Without diagonal lines:
3x3::k:11520:3329:3329:4867:5380:3845:3329:3329:11016:3849:11520:4867:4867:5380:3845:3845:11016:5905:3849:1555:11520:3861:5380:3861:11016:3097:5905:1555:1555:3869:11520:3861:11016:3105:3097:3097:4388:4388:4388:3869:11520:3105:4906:4906:4906:4397:4397:3869:11016:5681:11520:3105:3636:3636:3849:4397:11016:5681:2106:5681:11520:3636:5905:3849:11016:3905:3905:2106:4164:4164:11520:5905:11016:5961:5961:3905:2106:4164:5961:5961:11520:

With diagonal lines:
3x3:d:k:11520:3329:3329:4867:5380:3845:3329:3329:11016:3849:11520:4867:4867:5380:3845:3845:11016:5905:3849:1555:11520:3861:5380:3861:11016:3097:5905:1555:1555:3869:11520:3861:11016:3105:3097:3097:4388:4388:4388:3869:11520:3105:4906:4906:4906:4397:4397:3869:11016:5681:11520:3105:3636:3636:3849:4397:11016:5681:2106:5681:11520:3636:5905:3849:11016:3905:3905:2106:4164:4164:11520:5905:11016:5961:5961:3905:2106:4164:5961:5961:11520:

As Zero Killer:
3x3::k:11008:3329:3329:4867:5380:3845:3329:3329:11016:3849:11008:4867:4867:5380:3845:3845:11016:5905:3849:1555:11008:3861:5380:3861:11016:3097:5905:1555:1555:3869:11008:3861:11016:3105:3097:3097:4388:4388:4388:3869:40:3105:4906:4906:4906:4397:4397:3869:11016:5681:11008:3105:3636:3636:3849:4397:11016:5681:2106:5681:11008:3636:5905:3849:11016:3905:3905:2106:4164:4164:11008:5905:11016:5961:5961:3905:2106:4164:5961:5961:11008:

Solution

+-------+-------+-------+
| 8 6 2 | 9 7 5 | 1 4 3 |
| 5 4 7 | 3 8 1 | 9 6 2 |
| 3 1 9 | 2 6 4 | 5 7 8 |
+-------+-------+-------+
| 2 3 5 | 6 9 8 | 7 1 4 |
| 9 7 1 | 4 2 3 | 6 8 5 |
| 4 8 6 | 1 5 7 | 2 3 9 |
+-------+-------+-------+
| 6 5 4 | 8 1 9 | 3 2 7 |
| 1 9 3 | 7 4 2 | 8 5 6 |
| 7 2 8 | 5 3 6 | 4 9 1 |
+-------+-------+-------+

EDIT:
Although the cage structure/layout does not guarantee it: This as an X Killer.
it has the same single unique solution both as non-X Killer and as X Killer.
The nine cells in the 45 cage on the downward diagonal must of course contain all the values 1 through 9, i.e. no repeats allowed.
The value in r5c5 could however be repeated in the eight cell 43 cage on the upward diagonal, but this is not the case.
Knowing that it is an X Killer does not make it easier to solve.

Last edited by Børge on Tue Sep 14, 2010 7:36 pm, edited 2 times in total.

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Børge

Post subject: Assassin 199 v0.25, V0.50 and v0.75

Posted: Sun Sep 12, 2010 12:14 pm

Grand Master

Joined: Mon Apr 21, 2008 10:32 am
Posts: 868

I got a nice email (thank you very much) from GuestKiller (nice nickname

) referring to the following sentence in my A199 post "I only plan on posting a v1, but the cage structure easily produces puzzles with an SS score ranging from 0.73 through unsolvable by logic only." asking if I could post an easier version more suitable for pen & paper solving.

Going through the to be deleted scratch files for A199, I seem to only have saved the PS-code for one easier puzzle than the posted one, which from SudokuSolver's Step Analysis does not seem especially fun, but taste varies. I have posted it below as v0.50.

I originally played around with a somewhat different cage layout, which yielded only "too easy" puzzles (SS score v3.3.A2 < 1.00) or far too difficult ones (SS score > 4.50). Below a v0.25 and v0.75 with this cage layout.

I now definitely have broken my intention of only posting a single version, but since so few new Killers are posted here nowadays, I hopefully will be forgiven by the regular Assassins.

A199 v0.25 SS score v3.3.A2: 0.68 ◄ Select to see the SS score

Images:

normalized PS-code:

Solution:

+-------+-------+-------+
| 6 1 3 | 2 9 7 | 8 5 4 |
| 4 2 8 | 1 6 5 | 3 7 9 |
| 7 5 9 | 3 8 4 | 1 6 2 |
+-------+-------+-------+
| 3 9 5 | 4 1 2 | 6 8 7 |
| 1 4 2 | 6 7 8 | 9 3 5 |
| 8 6 7 | 9 5 3 | 2 4 1 |
+-------+-------+-------+
| 9 7 6 | 8 4 1 | 5 2 3 |
| 2 8 4 | 5 3 9 | 7 1 6 |
| 5 3 1 | 7 2 6 | 4 9 8 |
+-------+-------+-------+

A199 v0.50 SS score v3.3.A2: 0.82 ◄ Select to see the SS score

Images:

normalized PS-code:

Solution:

+-------+-------+-------+
| 8 7 4 | 6 1 5 | 3 9 2 |
| 5 1 3 | 9 7 2 | 8 4 6 |
| 2 9 6 | 3 8 4 | 7 5 1 |
+-------+-------+-------+
| 7 3 9 | 5 2 6 | 4 1 8 |
| 6 8 2 | 4 3 1 | 5 7 9 |
| 1 4 5 | 8 9 7 | 2 6 3 |
+-------+-------+-------+
| 4 2 1 | 7 6 3 | 9 8 5 |
| 3 5 8 | 1 4 9 | 6 2 7 |
| 9 6 7 | 2 5 8 | 1 3 4 |
+-------+-------+-------+

A199 v0.75 SS score v3.3.A2: 0.87 ◄ Select to see the SS score

Images:

normalized PS-code:

Solution:

+-------+-------+-------+
| 9 6 8 | 5 4 1 | 3 2 7 |
| 4 3 7 | 8 2 9 | 6 1 5 |
| 5 1 2 | 6 3 7 | 9 8 4 |
+-------+-------+-------+
| 2 4 1 | 7 9 6 | 8 5 3 |
| 7 9 5 | 1 8 3 | 2 4 6 |
| 3 8 6 | 2 5 4 | 1 7 9 |
+-------+-------+-------+
| 6 7 3 | 4 1 2 | 5 9 8 |
| 1 5 9 | 3 7 8 | 4 6 2 |
| 8 2 4 | 9 6 5 | 7 3 1 |
+-------+-------+-------+

Top

Post subject: Re: Assassin 199

Posted: Thu Sep 16, 2010 12:33 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

What a fantastic puzzle is A199!!! I got hooked on the interesting cage structure very quickly. Those two big cages play havoc with lots of "45"s. Thanks Børge!

r5c5 comes on step 5, so as Børge says, it's not a big disadvantage that this is not an X killer. Used a couple of nice tricks to cut down the combo work (steps 8b and 13), then lots of placements but it still isn't cracked. Steps 28 and 29 took the longest to find, though perhaps the technically hardest step is step 30. As always, I've tried to keep the combo analysis to a minimum.

BTW, the ALT 4 scoring that Richard has put in the next release of SudokuSolver gives A199 a score of 1.57 ◄ Select

Assassin 199 walk-through

33 steps:

Cheers
Ed

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Andrew

Post subject: Re: Assassin 199

Posted: Thu Sep 16, 2010 5:04 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Thanks Børge for a challenging Assassin! I agree with Ed that it's an interesting cage pattern. I don't remember seeing two cages occupying both diagonals before. As Ed said, it breaks things up a lot and limits the number of 45s.

I also liked:

Ed wrote:

As always, I've tried to keep the combo analysis to a minimum.

My solving path was the opposite, I used a lot of combination and permutation analysis.

However I didn't use:

Even though our solving paths were very different:

I liked Ed's steps 8b and 13 which considerably shortened his solving path. Step 8b would have reduced the amount of my combination and permutation analysis if I'd spotted that step.

Børge wrote:

I assume that the SS score is too high. But I let the Assassin experts be the judges.

I'm not so sure about that. I've rated my walkthrough at about the level of the original SS score, Ed's updated one looks maybe a little low to me. I've no idea what rating to give to Ed's step 30 which is, as he said, his technically most difficult step.

Rating Comment:

I thought that I'd managed to solve A199 a couple of days ago but on checking I found that I'd had an "aberration" thinking that a particular candidate in R2 was only in R2C13, locked for N1, when it was also still in R2C5. I therefore had to re-work from that stage and found that, instead of the final steps being fairly routine, A199 got harder again at the end; one might say it had "a sting in the tail".

Here is my walkthrough for A199:

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Andrew

Post subject: Re: Assassin 199

Posted: Tue Sep 21, 2010 6:17 pm

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

I hope that GuestKiller, and others, enjoyed Børge's easier variants.

V0.25 and V0.75 were both easy Killers, compared with most puzzles on this forum. They are probably both "paper solvable" although I didn't solve them that way; my walkthroughs used elimination solving.

V0.5 was harder than I'd expected; maybe I missed something.

I'm posting my walkthroughs because I feel that all posted puzzles on this forum should have, wherever possible, at least one posted walkthrough. Please feel free to post your own walkthroughs if you found a better or different way to solve them, for example "paper solvable" walkthroughs for V0.25 and V0.75.

Rating Comment:

Here is my walkthrough for A199 V0.25:

Here is my walkthrough for A199 V0.5:

Here is my walkthrough for A199 V0.75:

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Børge

Post subject: Assassin 199 v1.75 and v3

Posted: Fri Oct 01, 2010 4:22 pm

Grand Master

Joined: Mon Apr 21, 2008 10:32 am
Posts: 868

To those who posted a WT I sent a PM with the three other versions I have of A199.

In a PM to me Andrew wrote:

A challenging and interesting puzzle which I enjoyed. Please go ahead and post it as A199 V1.75.

A199 v1.75 SS score v3.3.A2: 1.75 ◄ Select to see the SS score Only solvable as an X Killer

Images:

normalized PS-code:

Solution:

+-------+-------+-------+
| 7 5 3 | 6 4 9 | 8 2 1 |
| 6 8 1 | 7 2 3 | 4 9 5 |
| 9 2 4 | 8 1 5 | 7 3 6 |
+-------+-------+-------+
| 8 1 5 | 9 3 6 | 2 4 7 |
| 2 3 9 | 4 5 7 | 6 1 8 |
| 4 6 7 | 2 8 1 | 9 5 3 |
+-------+-------+-------+
| 5 9 8 | 1 6 2 | 3 7 4 |
| 1 4 2 | 3 7 8 | 5 6 9 |
| 3 7 6 | 5 9 4 | 1 8 2 |
+-------+-------+-------+

Of the two remaining versions, I only think the following one is solvable by logic only. For the third Killer SS uses 1 Bowmans Bingo Complex 19, and JS cannot solve it.
This is probably a very difficult puzzle. You are hereby warned.

A199 v3 SS score v3.3.A2: 2.35 ◄ Select to see the SS score

Images:

normalized PS-code:

Solution:

+-------+-------+-------+
| 7 5 3 | 8 9 2 | 1 4 6 |
| 1 4 9 | 5 6 7 | 3 8 2 |
| 6 8 2 | 3 4 1 | 9 7 5 |
+-------+-------+-------+
| 9 7 6 | 1 2 3 | 4 5 8 |
| 8 3 4 | 7 5 9 | 6 2 1 |
| 2 1 5 | 4 8 6 | 7 3 9 |
+-------+-------+-------+
| 3 9 7 | 2 1 5 | 8 6 4 |
| 4 2 1 | 6 3 8 | 5 9 7 |
| 5 6 8 | 9 7 4 | 2 1 3 |
+-------+-------+-------+

Top

Andrew

Post subject: Re: Assassin 199

Posted: Sat Oct 02, 2010 7:20 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

As I commented in my PM to Børge, I found A199 V1.75 a challenging and interesting puzzle so thanks for posting it. While the key area was the same as for A199 the solving techniques used were different.

Rating Comment:

Here is my walkthrough for A199 V1.75. I've had another look at step 20b and found that my original eliminations were correct but I hadn't explained one clearly; I hope it's better now. I've also corrected a few typos.

40(8) cage at R1C9, 18(4) cage at R1C2, 21(4) cage at R2C1, 24(4) cage at R2C9 and 22(4) cage at R9C2 are disjoint cages. I hope that people won’t be confused by my use of the term “disjoint cages”; they are more commonly called “remote cages” but I find that “disjoint” is a better description.

Prelims

a) 7(3) cage at R1C5 = {124}
b) 11(3) cage at R3C2 = {128/137/146/236/245}, no 9
c) 19(3) cage at R6C1 = {289/379/469/478/568}, no 1
d) 11(3) cage at R6C5 = {128/137/146/236/245}, no 9
e) 22(3) cage at R7C5 = {589/679}
f) 10(3) cage at R8C3 = {127/136/145/235}, no 8,9
g) 40(8) disjoint cage at R1C9 = {12346789}, no 5

Steps resulting from Prelims
1a. Naked triple {124} in 7(3) cage at R1C5, locked for C5 and N2
1b. 22(3) cage at R7C5 = {589/679}, 9 locked for C5 and N8

[Now for the obvious move seen in less than 3 seconds.]
2. R5C5 = 5 (hidden single on D/), clean-up: no 8 in 22(3) cage at R7C5 (step 1b)
[Alternatively 45 rule on D/ 1 innie R5C5 = 5, ...
I’ve omitted my usual “placed on diagonal” statements because they are placements within the 40(8) and 45(9) cages.]

3. Naked triple {679} in 22(3) cage at R7C5, locked for C5 and N8
3a. Naked pair {38} in R46C5, locked for N5

4. 11(3) cage at R6C5 = {128} (cannot be {245} because R6C5 only contains 3,8) -> R6C5 = 8, R7C46 = {12}, locked for R7 and N8

5. R4C5 = 3 (naked single), R3C46 = 13 = {58/67}, no 9

6. 45 rule on N8 2 remaining outies R8C37 = 7 = {16/25/34}, no 7,8,9

7. 10(3) cage at R8C3 = {145/235} (cannot be {136} because 1,6 only in R8C3) -> R8C3 = {12}, 5 locked for C4 and N8, clean-up: R8C7 = {56} (step 6), no 8 in R3C6 (step 5)

8. 8 in N8 only in R89C6, locked for C6

9. 45 rule on N2 2 remaining outies R2C37 = 5 = {14/23}

10. 45 rule on R5 2 remaining innies R5C46 = 11 = {29/47}, no 1,6

11. 14(3) cage at R1C4 = {167/239/347} (cannot be {149/248} because 1,2,4 only in R1C4), no 8
11a. 2,4 of {239/347} must be in R2C3 -> no 3 in R2C3, clean-up: no 2 in R2C7 (step 9)

12. R3C4 = 8 (hidden single in C4), R3C6 = 5 (step 5)

13. 14(3) cage at R5C1 = {167/239/347} (cannot be {149/248} which clash with R5C46), no 8

14. 8 in R5 only in 15(3) cage at R5C7, locked for N6
14a. 15(3) cage = {168/348}, no 2,7,9

15. 18(3) cage at R4C7 = {279/459} (cannot be {369} which clashes with 15(3) cage at R5C7, cannot be {567} which clashes with R8C7), no 1,3,6

16. 3,5 in C4 only in R1289C4 -> R1289C4 = {37}{45}/{39}{45}/{67}{35} (only combinations for R12C4 consistent with 14(3) cage at R1C4 ) = 19,21
16a. Combined cage 14(3) cage at R1C4 + 10(3) cage at R8C3 = 24, R1289C4 = 19,21 -> R28C3 = 3,5 = {12/14}, 1 locked for C3

17. 11(3) cage at R3C2 = {128/137/146/236/245}
17a. 3 of {137} must be in R3C2 -> no 7 in R3C2

18. 19(3) cage at R6C1 = {289/379/469/478/568}
18a. 3 of {379} must be in R6C12 (R6C12 cannot be {79} which clashes with 14(3) cage at R5C1) -> no 3 in R7C2

19. 16(3) cage at R4C3 = {259/268/349/457} (cannot be {358} because no 3,5,8 in R5C4, cannot be {367} which clashes with 14(3) cage at R5C1)
19a. 8 of {268} must be in R4C3 -> no 6 in R4C3

20. 45 rule on N4 3(2+1) outies R37C2 + R5C4 = 15
20a. 8 in R4 only in 11(3) cage at R3C2 or 16(3) cage at R4C3 -> 11(3) cage at R3C2 = {128} or 16(3) cage at R4C3 = {268} = [826]
20b. 11(3) cage at R3C2 (step 17) = {128/146/245} (cannot be {236} which clashes with 16(3) cage = [826], cannot be {137} because R3C2 = 3, R5C4 = 2 from 14(3) cage = [826] so R37C2 + R5C4 cannot total 15), no 3,7
20c. 6 of {146} must be in R3C2 (R4C12 cannot be {16/46} which clash with 16(3) cage = [826]), no 6 in R4C12
20d. 11(3) cage at R3C2 = {128} or 16(3) cage at R4C3 = {268}, CPE no 2 in R5C2
[When I checked my walkthrough, I thought that I’d made an error in step 20b. However on more careful examination I found that it was correct but I hadn’t explained it clearly.]

21. R37C2 + R5C4 = 15 (step 20)
21a. R3C2 + R5C4 cannot total 7 -> no 8 in R7C2

22. 19(3) cage at R6C1 = {379/469}, no 2,5
22a. 19(3) cage = {379/469}, CPE no 9 in R5C2
22b. 7 of {379} must be in R7C2 (R6C12 cannot be {37} which clashes with 14(3) cage at R5C1), no 7 in R6C12

Re-work step 23 deleted.

24. 7 in N4 only in 14(3) cage at R5C1 (step 13) = {167/347} or 16(3) cage at R4C3 (step 19) = {457} with 7 in R46C3, CPE no 7 in R5C4, clean-up: no 4 in R5C6 (step 10)
24a. 16(3) cage at R4C3 (step 19) = {259/268/349/457}
24b. 3 of {349} must be in R6C3, 4 of {457} must be in R5C4 -> no 4 in R6C3

25. R37C2 + R5C4 = 15 (step 20)
25a. R5C4 + R7C2 cannot total 14 -> no 1 in R3C2
25b. R3C2 + R5C4 cannot total 9 -> no 6 in R7C2

26. 11(3) cage at R3C2 (step 20b) = {128/146/245}
26a. 11(3) cage at R3C2 = {128} or 16(3) cage at R4C3 = {268} (step 20d) = [826], 6 locked for N4 => 14(3) cage at R5C1 (step 13) = {239/347} => 1 in N4 only in R4C12
-> 1 in N4 only in R4C12, locked for R4 and N4
26b. 11(3) cage at R3C2 = {128/146}, no 5
26c. 2 of {128} must be in R3C2 -> no 2 in R4C12
26d. 2,6 only in R3C2 -> R3C2 = {26}

27. 1 in R5 only in 15(3) cage at R5C7, locked for N6
27a. 15(3) cage (step 14a) = {168} (only remaining combination), 6 locked for R5 and N6

28. 3 in R5 only in 14(3) cage at R5C1, locked for N4
28a. 19(3) cage at R6C1 (step 22a) = {469} (only remaining combination), no 7, 6 locked for R6, CPE no 4 in R5C2

29. R37C2 + R5C4 = 15 (step 20) = [249/294] (only remaining permutations) -> R3C2 = 2, R5C4 = {49}, clean-up: no 3 in R2C7 (step 9), no 9 in R5C6 (step 10)

30. R3C2 = 2 -> 11(3) cage at R3C2 (step 23b) = {128} (only remaining combination), 8 locked for N4

31. Naked pair {14} in R2C37, locked for R2 -> R2C5 = 2

32. 14(3) cage at R1C4 (step 11) = {167/347}, no 9, 7 locked for C4 and N2
32a. 16(3) cage at R1C6 = {169/349}, 9 locked for C6

33. 5 in N4 only in R46C3, locked for C3
33a. 16(3) cage at R4C3 (step 19) = {259/457}
33b. R5C4 = {49} -> no 4,9 in R46C3

34. 18(3) cage at R4C7 (step 15) = {279} (only remaining combination, cannot be {459} because R5C6 only contains 2,7), 9 locked for C7 and N6

35. 14(3) cage at R3C8 = {257/347} (cannot be {149/167/239/356} because 1,3,6,9 only in R3C8), no 1,6,9
35a. 14(3) cage = {257/347}, CPE no 7 in R6C8
35b. 3 of {347} must be in R3C8 -> no 4 in R3C8

36. 3 in N6 only in R6C89, locked for 15(3) cage at R6C8, no 3 in R7C8
36a. 15(3) cage = {348/357}, no 2,6,9
36b. 8 of {348} must be in R7C8 -> no 4 in R7C8

37. 45 rule on N6 3(2+1) outies R3C8 + R5C6 + R7C8 = 17 = [377/728], no 5, 7 locked for C8
37a. 15(3) cage at R6C8 (step 36a) = {348/357}
37b. R7C8 = {78} -> no 7 in R6C9

38. 14(3) cage at R3C8 (step 35) = {257/347}, CPE no 7 in R123C9
38a. 4 of {347} must be in R4C8 -> no 4 in R4C9

39. 7 in C8 only in R37C8, 7 in 14(3) cage at R3C8 only in R3C8 + R4C9
R7C8 = 7 or R3C8 = 7 => no 7 in R4C9 => 7 in N6 only in R46C7
-> R7C8 = 7 or R46C7 must contain 7, CPE no 7 in R79C7

40. 18(3) cage at R4C7 = {279} (step 34)
40a. Consider placement for 7 in C6
R4C6 = 7
or R5C6 = 7 => R4C9 = 7 (hidden single in N6)
or R6C6 = 7 => R4C7 = 7 (hidden single in 18(3) cage at R4C7)
-> 7 locked in R4C679, locked for R4

41. 14(3) cage at R3C8 (step 35) = {347} (only remaining combination, cannot be {257} which clashes with R4C3) -> R3C8 = 3, R4C89 = [47], R6C89 = [53], R7C8 = 7 (step 36a)

42. Naked pair {29} in R46C7, locked for C7 and 18(3) cage at R4C7 -> R5C6 = 7, R5C4 = 4 (step 10)

43. R5C2 = 3, R5C13 = {29}, locked for N4 -> R46C3 = [57]

44. Naked pair {46} in R6C12, locked 19(3) cage at R6C1 -> R7C2 = 9, R7C5 = 6

45. Naked pair {35} in R89C4, locked for C4 and N8, R8C3 = 2 (step 7), R8C7 = 5 (step 6), R5C13 = [29], R89C4 = [35]

46. R2C3 = 1 (hidden single in C3), R2C7 = 4

47. Naked pair {67} in R12C4, locked for C4 and N2

48. R4C6 = 6 (hidden single in C6)

49. R7C1 = 5 (hidden single in R7)
49a. 21(4) disjoint cage at R2C1 = {1569/3459/3567} (cannot be {1578} which clashes with R4C1), no 8
49b. 3 of {3567} must be in R2C1 -> no 7 in R2C1
49c. 4 of {3459} must be in R8C1 -> no 4 in R3C1
49d. Killer pair 4,6 in 21(4) disjoint cage and R6C1, locked for C1

50. 3 on D/ only in R7C3 + R9C1, locked for N7

51. R2C9 = 5 (hidden single in R2)
51a. 24(4) disjoint cage at R2C9 = {4569} (only remaining combination) -> R7C9 = 4, R38C9 = {69}, locked for C9

52. R1C2 = 5 (hidden single in R1)
52a. 18(4) disjoint cage at R1C2 = {2358/2457} (cannot be {1359} which clashes with R1C6, cannot be {1458} which clashes with R1C5, cannot be {3456} because 3,4 only in R1C3) -> R1C8 = 2, R1C3 = {34}, R1C7 = {78}

53. R3C9 = 6 (hidden single in N3)

and the rest is naked singles.

Last edited by Andrew on Thu Nov 11, 2010 2:34 am, edited 2 times in total.

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Andrew

Post subject: Re: Assassin 199

Posted: Sat Oct 02, 2010 7:28 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Thanks Børge for also posting A199 V3. When I saw your introductory comments I wondered whether to try it but I'm glad that I did. I found it easier than either of A199 or A199 V1.75.

Rating Comment:

Here is my walkthrough for A199 V3.

44(8) cage at R1C9, 13(4) cage at R1C2, 14(4) cage at R2C1, 18(4) cage at R2C9 and 17(4) cage at R9C2 are disjoint cages. I hope that people won’t be confused by my use of the term “disjoint cages”; they are more commonly called “remote cages” but I find that “disjoint” is a better description.

I’ve omitted my usual “placed on diagonal” statements because they are placements within the 44(8) and 45(9) cages.

Prelims

a) 22(3) cage at R1C4 = {589/679}
b) 19(3) cage at R1C5 = {289/379/469/478/568}, no 1
c) 24(3) cage at R3C2 = {789}
d) 6(3) cage at R3C4 = {123}
e) 20(3) cage at R3C8 = {389/479/569/578}, no 1,2
f) 20(3) cage at R4C7 = {389/479/569/578}, no 1,2
g) 9(3) cage at R5C7 = {126/135/234}, no 7,8,9
h) 11(3) cage at R7C5 = {128/137/146/236/245}, no 9
i) 13(4) disjoint cage at R1C2 = {1237/1246/1345}, no 8,9
j) 14(4) disjoint cage at R2C1 = {1238/1247/1256/1346/2345}, no 9
k) 44(8) disjoint cage at R1C9 = {23456789}, no 1

Steps resulting from Prelims
1a. 22(3) cage at R1C4 = {589/679}, CPE no 9 in R2C56
1b. Naked triple {789} in 24(3) cage at R3C2, CPE no 7,8,9 in R56C2
1c. Naked triple {123} in 6(3) cage at R3C4, CPE no 2,3 in R123C5
1d. 13(4) disjoint cage at R1C2 = {1237/1246/1345}, 1 locked for R1

2. 45 rule on R5 3 innies R5C456 = 21 = {489/579/678}, no 1,2,3
[This step shows that this puzzle cannot be a Killer-X, which would require R5C5 = 1.]

3. 45 rule on C5 3 innies R456C5 = 15
3a. 15(3) cannot contain more than one of 1,2,3, which must be in R4C5 -> no 1,2,3 in R6C5

4. 45 rule on N4 3(2+1) outies R37C2 + R5C4 = 24
4a. Max R37C2 = 17 -> min R5C4 = 7
4b. Min R37C2 = 15 -> min R7C2 = 6
4c. Min R7C2 = 6 -> max R6C12 = 6, no 6,7,8,9 in R6C12

5. 45 rule on N6 3(2+1) outies R37C8 + R5C4 = 22
5a. Max R37C8 = 17 -> min R5C6 = 5
5b. Min R37C8 = 13, no 1,2,3 in R37C8

6. Hidden killer triple 1,2,3 in 12(3) cage at R1C6 and 6(3) cage at R3C4 for N2, 6(3) cage must have two of 1,2,3 in N2 -> 12(3) cage at R1C6 must contain one of 1,2,3 in N2
6a. Min R12C6 = {14} = 5 -> max R2C7 = 7

7. 19(3) cage at R1C5 = {469/478/568}
7a. R456C5 = 15 (step 3) = {159/249/258/357} (cannot be {168/267/348/456} which clash with 19(3) cage at R1C5), no 6
7b. 11(3) cage at R7C5 = {128/137/236} (cannot be {146/245} which clash with 19(3) cage at R1C5), no 4,5

8. R5C456 (step 2) = {579/678} (cannot be {489} which clashes with R456C5, CCC because 4 of {489} only in R5C5), no 4, 7 locked for R5 and N5
8a. 6 of {678} must be in R5C6 -> no 8 in R5C6

9. R456C5 (step 7a) = {249/258/357} (cannot be {159} which clashes with R5C456, CCC for either 5 or 9 in R5C5), no 1
9a. 4 of {249} must be in R6C5 -> no 9 in R6C5
9b. 1 in N5 only in R4C4 + R6C6, locked for D\

10. 1 in C5 only in 11(3) cage at R7C5, locked for N8
10a. 11(3) cage = {128/137}, no 6

11. 6 in C5 only in 19(3) cage at R1C5, locked for N2
11a. 19(3) cage (step 7) = {469/568}, no 7
11b. 22(3) cage at R1C4 = {589/679}
11c. 5,8 of {589} must be in R12C4 (R12C4 cannot be {59/89} which clash with 19(3) cage) -> no 5,8 in R2C3
11d. 6 of {679} must be in R2C3 -> no 7 in R2C3

12. 6(3) cage at R3C4 = {123}, 1 locked for R3 and N2

13. 45 rule on N2 3(2+1) outies R2C37 + R4C5 = 14 = [653/932/923], no 1,4,6,7 in R2C7

14. 12(3) cage at R1C6 = {237/345}, no 8,9
14a. 5 of {345} must be in R2C7 (R12C6 cannot {45} which clashes with 19(3) cage at R1C5) -> no 5 in R12C6

15. Hidden killer pair 8,9 in 15(3) cage at R5C1 and R5C456 for R5, R5C456 contains one of 8,9 -> 15(3) cage at R5C1 must contain one of 8,9
15a. Killer triple 7,8,9 in R4C12 and 15(3) cage at R5C1, locked for N4
15b. 7 in N4 only in R4C12, locked for R4 and 24(3) cage at R3C2, no 7 in R3C2

16. 20(3) cage at R3C8 = {389/479/569/578}
16a. 7 of {479} only in R3C8 -> no 4 in R3C8

17. 15(3) cage at R5C1 = {159/168/249/348} (cannot be {258} which clashes with R5C456)
17a. 18(3) cage at R4C3 = {459/468/567} (cannot be {189/279/378} because 7,8,9 only in R5C4, cannot be {369} which clashes with 15(3) cage at R5C1), no 1,2,3
17b. Killer triple 4,5,6 in 18(3) cage at R4C3 and 15(3) cage at R5C1, locked for N6
17c. Max R6C12 = {23} = 5 -> min R7C2 = 7

18. Naked triple {789} in R347C2, locked for C2

19. R4C3 = 1 (hidden single in R4), R3C4 = 1 (hidden single in R3)

20. 22(3) cage at R1C4 = {589} (only remaining combination, cannot be {679} which clashes with 18(3) cage at R4C3) -> R2C3 = 9, R12C4 = {58}, locked for C4 and N2

21. R3C2 = 8 (naked single), R4C12 = {79}, 9 locked for R4 and N4

22. R2C37 + R4C5 (step 13) = [932/923], no 5, CPE no 3 in R4C7

23. Naked triple {469} in 19(3) cage at R1C5, locked for C5 and N2

24. 7,9 in R5 only in R5C456 (step 8) = {579} (only remaining combination), 5,9 locked for R5 and N5 -> R6C5 = 8, R5C5 = 5 (hidden single in C5), R4C5 = 2 (step 9), R3C4 = 3, R2C7 = 3 (step 22)

25. Naked triple {137} in 11(3) cage at R7C5, 3,7 locked for N8

26. Naked pair {27} in R12C6, locked for C6 -> R5C6 = 9, R5C4 = 7

27. R5C4 = 7 -> 18(3) cage at R4C3 (step 17a) = {567} (only remaining combination), 5,6 locked for C3 and N4

28. 6 in R5 only in 9(3) cage at R5C7 = {126} (only remaining combination), locked for R5 and N6

29. R5C6 = 9 -> R46C7 = 11 = [47]

30. R6C12 = {12} (hidden pair in N4), R7C2 = 9 (cage sum), R4C12 = [97]

31. 8 in R4 only in R4C89 -> 20(3) cage at R3C8 = {389/578}
31a. 7,9 only in R3C8 -> R3C8 = {79}

32. 9 in R6 only in R6C89 -> 18(3) cage at R6C8 = {369/459}
32a. 4,6 only in R7C8 -> R7C8 = {46}

33. R6C5 = 8 -> R7C46 = 7 = [25]

34. 9 in N8 only in R89C4 -> 16(3) cage at R8C3 = {169/349}
34a. 1,3 only in R8C3 -> R8C3 = {13}

35. 8 in N8 only in R89C6 -> 17(3) cage at R8C6 = {458} (only remaining combination) -> R8C7 = 5, R89C6 = {48}, 4 locked for C6 and N8

36. 16(3) cage at R8C3 (step 34) = {169} (only remaining combination) -> R8C3 = 1

37. R6C4 = 4 (hidden single in C4)

38. 8,9 in 45(9) cage at R1C1 only in R7C7 + R8C8 + R9C9, locked for N9

39. 9 on D/ only in R1C9 + R3C7, locked for N3 -> R3C8 = 7

40. R3C8 = 7 -> 20(3) cage at R3C8 (step 31) = {578} (only remaining combination), 5 locked for R4 and N6 -> R46C3 = [65], R46C6 = [36], R7C7 = 8, R7C3 = 7

41. 18(3) cage at R6C8 (step 32) = {369} (only remaining combination) -> R7C8 = 6

42. Naked pair {24} in R2C2 + R3C3, locked for N1 and 45(9) cage at R1C1 -> R1C3 = 3, R1C1 = 7, R12C6 = [27]

43. 13(4) disjoint cage at R1C2 = {1345} (only remaining combination) -> R1C7 = 1, R1C2 = 5, R1C8 = 4

44. 3,9 in 45(9) cage at R1C1 only in R8C8 + R9C9, locked for N9

45. R9C89 = [21] = 3 -> R9C23 = 14 = [68]

and the rest is naked singles.

Last edited by Andrew on Thu Nov 11, 2010 2:39 am, edited 2 times in total.

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Børge

Post subject: Re: Assassin 199

Posted: Sat Oct 02, 2010 10:11 am

Grand Master

Joined: Mon Apr 21, 2008 10:32 am
Posts: 868

Andrew wrote:

Thanks Børge for also posting A199 V3. When I saw your introductory comments I wondered whether to try it but I'm glad that I did. I found it easier than either of A199 or A199 V1.75.

That you found v3 easier than v1 and v1.75 again proves the superiority of the human brain.

For completeness, here the supposedly unsolvable v2

A199 v2 SS score v3.3.A2: 1.88 ◄ Select to see the SS score

Images:

normalized PS-code:

Solution:

+-------+-------+-------+
| 6 2 7 | 9 4 1 | 5 3 8 |
| 3 9 4 | 5 2 8 | 6 1 7 |
| 1 5 8 | 3 6 7 | 9 4 2 |
+-------+-------+-------+
| 8 4 2 | 7 9 6 | 3 5 1 |
| 7 3 5 | 8 1 4 | 2 6 9 |
| 9 6 1 | 2 3 5 | 7 8 4 |
+-------+-------+-------+
| 2 8 3 | 1 5 9 | 4 7 6 |
| 4 7 9 | 6 8 3 | 1 2 5 |
| 5 1 6 | 4 7 2 | 8 9 3 |
+-------+-------+-------+

Here the SS scores for all 7 versions using the latest alternative solveroptions aka ALT5

SS ALT5 scores for all 7 versions":

v0.25   0.68
v0.50   0.85
v0.75   0.71
v1      1.83 (1.79 as an X Killer)
v1.75   1.80
v2      1.96
v3      2.44

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Andrew

Post subject: Re: Assassin 199

Posted: Sat Nov 13, 2010 7:24 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Børge wrote:

For completeness, here the supposedly unsolvable v2

While "putting to bed" my files for A199 and the other variants a couple of days ago, I found that I'd only done Prelims and five steps for this V2 so decided to have another try at it "because it's there".

A199 V2 was a very hard puzzle, definitely the hardest of the A199 series, but not unsolvable. I'll describe my solving method as "chainy" permutation analysis which started as early as step 6. However there were also a few interesting steps.

Rating Comment:

Here is my walkthrough for A199 V2; it's very long so I've put it into hidden text:

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