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 Post subject: Assassin 306 X
PostPosted: Mon Dec 15, 2014 2:32 pm 
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Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Assassin 306 X

I've got a new simplified way for making assassins:

1. use JSudoku to create a grid; but

2. instead of Ed's way of merging cages; then

3. remove small cages until it has an appropriate score.


SS gives it 1.45 and JS uses a couple of big fish.

Apologies for posting late but given we have missed two weekends I thought that you might be feeling a bit "cold turkey".


Image


JS Code:
3x3:d:k:3585:3585:5378:5378:2563:2563:3076:5125:5125:3078:3585:5378:3591:32:33:3076:5125:5125:3078:3078:3593:3591:3850:34:35:2572:2572:3341:3593:3593:7438:3850:36:37:3343:2576:3341:3345:3345:7438:7438:38:39:3343:2576:40:41:42:7438:7438:7438:3861:3861:43:44:3863:3863:45:46:47:48:49:50:5915:5915:3863:51:52:53:3356:4637:4637:5915:5915:54:55:3871:3871:3356:3356:4637:



Solution:
936728514
128543769
475961328
681392457
749615283
253874691
367159842
892436175
514287936


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 Post subject: Re: Assassin 306 X
PostPosted: Tue Dec 16, 2014 5:08 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for a fun puzzle. :D

I solved it fairly quickly but possibly not the easiest way. I hope one of the other solvers can find something better than my step 12a.

Here is my walkthrough for Assassin 306 X:
Prelims

a) R1C56 = {19/28/37/46}, no 5
b) R12C7 = {39/48/57}, no 1,2,6
c) R23C4 = {59/68}
d) R34C5 = {69/78}
e) R3C89 = {19/28/37/46}, no 5
f) R45C1 = {49/58/67}, no 1,2,3
g) R45C8 = {49/58/67}, no 1,2,3
h) R45C9 = {19/28/37/46}, no 5
i) R5C23 = {49/58/67}, no 1,2,3
j) R6C78 = {69/78}
k) R9C56 = {69/78}
l) 21(3) cage at R1C3 = {489/579/678}, no 1,2,3

1. 45 rule on N3 1 innie R3C7 = 3, placed for D/, clean-up: no 9 in R12C7, no 7 in R3C89

2. R45C8 = {49/58} (cannot be {67} which clashes with R6C78), no 6,7 in R45C8
2a. Killer pair 8,9 in R45C8 and R6C78, locked for N6, clean-up: no 1,2 in R45C9
2b. Killer pair 6,7 in R45C9 and R6C78, locked for N6
2c. 3 in N6 only in R456C9, locked for C9

3. 45 rule on N1 1 outie R1C4 = 1 innie R3C3 + 2, no 1,8,9 in R3C3, no 5 in R1C4

4. 45 rule on N7 2 innies R7C1 + R9C3 = 7 = {16/25/34}, no 7,8,9

5. 45 rule on N1 3 innies R123C3 = 19 = {289/469/478/568}
5a. 5 of {568} must be in R3C3 (R12C3 cannot be {58} because 21(3) cage cannot contain both of 5,8) -> no 5 in R12C3
5b. 21(3) cage at R1C3 = {489/678}, CPE no 8 in R1C12

6. 6 in N6 only in R45C9 = {46} or R6C78 = {69} -> R45C8 = {58} (cannot be {49}, locking-out cages), locked for C8 and N6, clean-up: no 2 in R3C9, no 7 in R6C78
6a. Naked pair {69} in R6C78, locked for R6 and N6, clean-up: no 4 in R45C9
6b. Naked pair {37} in R45C9, locked for C9 and N6
[I missed 45 rule on N6 3 innies R45C7 + R6C9 = 7 = {124}, locked for N6, :oops: which would have simplified this step and given the three combinations directly in step 2.]

7. R5C23 = {49/67} (cannot be {58} which clashes with R5C8), no 5,8 in R5C23

8. 45 rule on N14 3 innies R6C123 = 1 outie R1C4 + 3
8a. R6C123 cannot be {124} = 7 which clashes with R6C9 -> no 4 in R1C4, clean-up: no 2 in R3C3 (step 3)

9. Hidden killer quad 1,2,3,4 in R1C56 + R2C56 + R3C6 for N2, R1C56 contains one of 1,2,3,4 -> R2C56 = {1234}, R3C6 = {124}

10. 5 in N2 only in R23C4 = {59}, locked for C4 and N2, clean-up: no 1 in R1C56, no 7 in R3C3 (step 3), no 6 in R4C5

11. 45 rule on N5 3 innies R4C56 + R5C6 = 16
11a. Min R4C5 = 7 -> max R45C6 = 9, no 9 in R45C6
11b. 9 in N5 only in R45C5, locked for C5, clean-up: no 6 in R9C6
11c. R34C5 = [69]{78}, R9C56 = [69]/{78} -> combined half cage R349C5 = [69]{78}/{78}6, 6 locked for C5, clean-up: no 4 in R1C6

12. R123C3 (step 5) = {469/478/568} = {49}6/{68}5/{78}4 (cannot be {69}4 because 21(3) cage at R1C3 cannot contain both of 6,9)
12a. 12(3) cage at R2C1 cannot be {138} = 3{18} which clashes with R123C3 = {478/568} and with R3C389 = 6{19/28} -> no 8 in 12(3) cage

13. Consider placement for 9 in C5
R4C5 = 9
or R5C5 = 9 => R5C23 = {67}, locked for R5 => R45C9 = [73] => R4C5 = 8
-> R4C5 = {89}, clean-up: no 8 in R3C5

14. R3C9 = 8 (hidden single in R3) -> R3C8 = 2, clean-up: no 4 in R12C7
14a. Naked pair {57} in R12C7, locked for C7 and N3
14b. 8 in N2 only in R1C456, locked for R1
14c. Min R3C12 = {15} = 6 (R3C12 cannot be {14} which clashes with R3C6) -> max R2C1 = 6

15. 12(3) cage at R2C1 = {129/147/156} (cannot be {237} because 2,3 only in R2C1, cannot be {246/345} which clashes with R123C3), no 3, 1 locked for N1
15a. 1 in R1 only in R1C89, locked for N3

16. 3 in N1 only in 14(3) cage at R1C1 = {239/347/356}, no 8
16a. R2C3 = 8 (hidden single in N1) -> R1C34 = 13 = {67}, locked for R1 -> R12C7 = [57]
16b. 8 in N2 only in R1C56 = {28}, locked for R1 and N1
16c. 14(3) cage = {239} (only remaining combination, cannot be {356} because 5,6 only in R2C2) -> R1C12 = {39}, locked for R1 and N1, R2C2 = 2, placed for D\
16d. R2C89 = {69} (hidden pair in N3), locked for R2 -> R23C4 = [59]
16e. Naked pair {69} in R26C8, locked for C8

17. R1C4 = R3C3 + 2 (step 3)
17a. R1C4 = {67} -> R3C3 = {45}

18. R6C123 = R1C4 + 3 (step 8)
18a. Max R1C4 = 7 -> max R6C123 = 10, no 8 in R6C12

19. 8 in R6 only in R6C456, locked for N5 -> R4C5 = 9, R3C5 = 6, R1C34 = [67], clean-up: no 4 in R5C1, no 7 in R5C2, no 1 in R7C1 (step 4), no 9 in R9C6
19a. R1C4 = R3C3 + 2 (step 3)
19b. R1C4 = 7 -> R3C3 = 5, placed for D\, clean-up: no 2 in R7C1 (step 4)
19c. Naked pair {78} in R9C56, locked for R9 and N8
19d. R6C4 = 8 (hidden single in C4), placed for D/

20. R7C7 = 8 (hidden single on D\)
20a. 45 rule on N9 2 remaining innies R7C89 = 6 = [15/42]

21. 9 in N4 only in R45C1 = [49] or R5C23 = {49} -> 4 in R4C1 + R5C23, locked for N4 (locking cages)

22. R6C123 = R1C4 + 3 (step 8)
22a. R1C4 = 7 -> R6C123 = 10 = {127/235}, 2 locked for R6 and N4
22b. Naked pair {14} in R16C9, locked for C9
22c. R78C9 = {25} (hidden pair in C9), locked for N9
22d. R3C3 = 5 -> R4C23 = 9 = [63/81]

23. 18(3) cage at R8C8 = {279/459/567} (cannot be {369} because R8C9 only contains 2,5), no 1,3

24. 1 on D\ only in R4C4 + R5C5 + R6C6, locked for N5
24a. R4C56 + R5C6 = 16 (step 11)
24b. R4C5 = 9 -> R45C6 = 7 = {25} (cannot be {34} which clashes with R23C6, ALS block), locked for C6 and N5 -> R1C56 = [28], R9C56 = [87]
24c. R78C6 = {69} (hidden pair in C6), locked for N8

25. Naked pair {14} in R17C8, locked for C8 -> R8C8 = 7, placed for D\, R9C8 = 3, clean-up: no 4 in R7C1 (step 4)

26. 5 in R9 only in R9C12, locked for N7, clean-up: no 2 in R9C3 (step 4)

27. R7C3 = 7 (hidden single on D/) -> R7C2 + R8C3 = 8 = [62], R7C1 = 3, R9C3 = 4 (step 4), R1C1 = 9, placed for D\, R9C9 = 6, placed for D\

28. R8C9 = 5, R7C9 = 2 -> R7C8 = 4 (step 20a), R1C8 = 1, R1C9 = 4, placed for D/, R5C5 = 1, placed for D/

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

Rating Comment:
I'll rate my walkthrough for A306 X at 1.5 because for step 12a. Before that I'd been thinking Easy 1.5 for locking-out cages and the short forcing chain in step 13, which I'd already seen.


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 Post subject:
PostPosted: Tue Dec 16, 2014 6:12 am 
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Grand Master
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
This Killer looks more like a Human Solvable than like an Assassin. :shock: Is this the first Assassin with missing cages or am I just remembering things wrong?

This code also works for SumoCue:
SumoCue code:
3x3:d:k:3584:3584:5378:5378:2564:2564:3078:5127:5127:3081:3584:5378:3596:13:14:3078:5127:5127:3081:3081:3604:3596:3862:23:24:2585:2585:3355:3604:3604:7454:3862:32:33:3362:2595:3355:3365:3365:7454:7454:41:42:3362:2595:45:46:47:7454:7454:7454:3891:3891:53:54:3895:3895:57:58:59:60:61:62:5951:5951:3895:66:67:68:3397:4678:4678:5951:5951:74:75:3916:3916:3397:3397:4678:


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 Post subject: Re:
PostPosted: Tue Dec 16, 2014 9:02 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
Afmob wrote:
Is this the first Assassin with missing cages or am I just remembering things wrong?
Been lots of them though only one since Afmob has been posting WTs again. Had a quick look through the last 100 and 12 have missing cages, some of them, many missing.

Andrew hasn't done the archives for the last 80 yet so won't give the url for each. From the reactions, we loved them!! Keep them coming HATMAN!

A294, 274, 259, 249, 247, 245, 238, 237, 232, 231, 228, 225.

Cheers
Ed


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 Post subject:
PostPosted: Tue Dec 16, 2014 5:44 pm 
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Grand Master
Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the reminder, Ed! I didn't need any chains, so this Killer is definitely not a Human Solvable. :D

A306X Walkthrough:
1. C789
a) Innie N3 = R3C7 = 3
b) Innies N6 = 7(3) = {124} locked for N6
c) 10(2) @ N6 = {37} locked for C9+N6
d) 15(2) = {69} locked for R6+N6
e) 13(2) = {58} locked for C8

2. R123+N4
a) Innies R12 = 13(4) = 14{26/35} since R2C4 = (5689) -> 1,4 locked for R2; R2C156 <> 5,6
b) 14(2) = [59/68]
c) Innies+Outies N1: 2 = R1C4 - R3C3 -> R3C3 <> 1,8,9; R1C4 <> 5
d) ! Innies+Outies N14: -3 = R1C4 - R6C123: R1C4 <> 4 since R6C123 = {124} blocked by R6C9 = (124)
e) ! Killer quad (6789) locked in R13C4 + R3C5 + 10(2) for N2
f) R2C4 = 5 -> R3C4 = 9

3. R123
a) 10(2) @ R3 = [28]/{46}
b) 12(2) = [57] since (48) is a Killer pair of 10(2) @ N3 -> R2C7 = 7, R1C7 = 5
c) 1 locked in 20(4) @ N3 = 19{28/46} for R1
d) 8 locked in R123C9 @ N3 for C9
e) Innies+Outies N1: 2 = R1C4 - R3C3: R3C3 = (456)
f) 1 locked in 12(3) @ N1 = 1{38/47/56} <> 2
g) 2 locked in 14(3) @ N1 = 2{39/48}
h) Killer pair (89) locked in 14(3) + Innies N1 = 19(3) for N1
i) 12(3) <> 3
j) Innies R12 = 8(3) = {134} locked for R2; 3 also locked for N2
k) 3 locked in 14(3) @ N1 = {239} locked for N1

4. N1245
a) 8 locked in 21(3) @ N1 for 21(3)
b) Innies+Outies N14: -3 = R1C4 - R6C123: R6C123 <> 8 since R1C4 <= 7
c) 8 locked in 29(6) @ R6 for N5
d) 15(2) = [69/87]
e) 10(2) = {28/46}
f) Killer pair (68) locked in 10(2) + R3C5 for N2
g) Innies+Outies N1: 2 = R1C4 - R3C3 -> R1C4 = 7, R3C3 = 5
h) 21(3) = {678} -> 6,8 locked for C3+N1

5. R456
a) Hidden Killer pair (13) in 14(3) @ N4 since Innies N4 = 10(3) <> 6 -> 14(3) = 5[63/81]
b) 2 locked in Innies N4 = 10(3) @ N4 = 2{17/35} for R6
c) 2 locked in R45C7 @ N6 for C7
d) Killer pair (79) locked in 29(6) + R4C5 for N5

6. R789
a) 5 locked in 23(4) @ R9 for N7
b) Innies N7 = 7(2) = {34}/[61]
c) Killer pair (46) locked in 15(3) + Innies N7 for N7
d) 6 locked in R7C12 @ N7 for R7
e) Hidden Killer pair (69) in R789C7 @ C7
f) 18(3) = {279/459/567} <> 1,3 since {369} blocked by Killer pair (69) of R789C7
g) Killer pair (69) locked in 18(3) + R789C7 for N9
h) Innies N9 = 14(3) = {149/158/239/248} <> 7 since 7{25/34} blocked by Killer pairs (47,57) of 18(3); R7C7 = (89)
i) 13(3) <> 7 since R89C7 <> 2,7
j) 7 locked in 18(3) @ N9 = 7{29}/[56] -> R8C2 = 7

7. R789+N5
a) 1,4 locked in 29(6) @ D\ for N5
b) R6C4 = 8
c) Hidden single: R7C7 = 8 @ D\
d) 15(3) = 2{49/67} -> 2 locked for N7
e) 23(4) = {1589} locked for N7 since R8C2 = (19)
f) 15(3) = {267} -> R8C3 = 2, R7C3 = 7, R7C2 = 6
g) Hidden Single: R9C6 = 7 @ C6 -> R9C5 = 8, R5C3 = 9 @ C3 -> R5C2 = 4
h) R3C5 = 6 -> R4C5 = 9

8. N129
a) 10(2) = [28] -> R1C5 = 2, R1C6 = 8
b) 14(3) = {239} -> R2C2 = 2; 9 locked for R1
c) 18(3) = {567} -> R8C9 = 5, R9C9 = 6
d) R5C5 = 1

9. Rest is singles without considering diagonals.

Rating:
1.25. I used a Killer quad.


Last edited by Afmob on Tue Dec 23, 2014 6:35 am, edited 4 times in total.

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 Post subject: Re: Assassin 306 X
PostPosted: Tue Dec 16, 2014 7:17 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Assassins have gradually evolved since Ruud first introduced them in 2006. They were originally harder versions of the standard killers which appeared in newspapers, etc.

Different features were first introduced either as puzzles with different names or sometimes as harder variants of Assassins.

The first different feature was Killer-X, followed by cages with diagonally-connected cells, disjoint/remote cages and missing cages (zero killers).

Ed's PANIV X in January 2007 was notable in having several of these features:- Killer-X, diagonally-connected cells and a large missing area.

The first V1 Assassin with different features, unless I've missed any earlier ones, was the first Assassin posted on this forum, Nasenbaer's Assassin 101 which was a Killer-X with a diagonally-connected cage.

All these different features have become accepted over time and used in V1 Assassins. The only ones I don't particularly like are disjoint/remote cages which are split in two dimensions, therefore reducing applications of the 45 rule; disjoint/remote cages in one dimension are more acceptable, even though they also remove some 45s.

While most/all of HATMAN's Human Solvables do have missing cages, their intention is that they can be solved by creative steps which won't be programmed into software solvers.

And thanks Ed for reminding me that the last 80 Assassins haven't yet been archived. They will get done. A204-A225, plus accompanying variants and puzzles, were done in October; after that I concentrated on finishing the TJK Archive.


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