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 Post subject: Assassin 344
PostPosted: Fri May 12, 2017 2:08 pm 
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Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 530
Assassin 344
I pulled up JSudoku to do a final check on an assassin and this popped up - Quite pretty

SS gives it 1.8 and JS uses 6 fishes but I managed it with a couple of fishes.

I think that there are a lot of potential interactions here so I'm interested in seeing your solutions.

Coming soon: I've been working on a good new varient recently and have quite a few puzzles. I'll publish a batch of them in a while - probably on a spreadsheet.
It is a combination of SkyScraper Sum (SSS) and Odd Row and Column (ORC) hence SSS ORC.
The SSS clues work quite differently on the even and odd rows/columns and I've come up with some variants on solving techniques.
Solving is quite combinatorial with additional effects.
I've published separate SSS and ORC in the variants section which I suggest you give a try.

Image

JS Code:
3x3::k:4609:3330:3330:6147:6147:6147:1540:1540:4613:4609:4609:4870:4870:6147:4103:4103:4613:4613:2568:2568:2569:4870:6147:4103:4874:1803:1803:6412:2569:2569:4870:10765:4103:4874:4874:4110:6412:6412:10765:10765:10765:10765:10765:4110:4110:6412:3855:3855:4112:10765:5905:4626:4626:4110:2067:2067:3855:4112:6676:5905:4626:2837:2837:3606:3606:4112:4112:6676:5905:5905:3863:3863:3606:2072:2072:6676:6676:6676:2073:2073:3863:

Solution:
649823517
573641829
281975643
736182495
814569732
925437186
358216974
497358261
162794358


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 Post subject: Re: Assassin 344
PostPosted: Sun May 28, 2017 10:06 pm 
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Master
Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 148
Location: California, out of London
Thanks again HATMAN. Here's how I did it. One very inelegant step I'm sorry to say.

Assassin 344 WT:
1. Innies n1 = r23c3 = +4(2) = {13}
6(2) and 7(2) in n3 must be {15},{34} or {24},{16}
-> 10(2)n1 = {28}

2. Innies - Outies n6 -> r3c7 + r7c7 = r5c7 + 8
-> Neither r3c7 nor r7c7 can be 8
Innies n3 -> r23c7 = +14(2)
-> r5c7 cannot be 6 (Would make r37c7 = +14(2))
Innies n9 -> r78c8 = +11(2)
-> r5c7 cannot be 3 (Would make r37c7 = +11(2))

3. 3 in 42(7) in n5
Outies n2 = r2c37 + r4c46 = +14(4)
r2c3 from (13) and 3 not in r4c46 -> r2c7 cannot be 9.
-> Innies n3 -> r23c7 = +14(2) = [86] or [59]

4. (This cracks it but I don't like it).
Can r23c7 be [59]?
Would put remaining innies c789 = r58c7 = +12(2) = {48}
Puts 6(2)n3 = [24]
Puts r4c78 = {37}
Puts Innies r1234 = r4c159 = +20(3) = {569}
Leaves no solution for 10(3)n14
-> r23c7 = [86]

5. -> 7(2)n3 = {34}, 6(2)n3 = {15}, 18(3)n3 = {279}
-> r23c3 = [31]
-> Remaining outies n2 -> r4c46 = {12}
Also r4c78 = {49} or {58}
-> r4c23 = [36]
Also r3c456 = [{79}5]
-> 19(4)r2c3 = [3691], 16(4)r2c6 = [1852], r3c5 = 7

6. Innies n7 -> r78c3 = +15(2) = {78}
Since Min r678c4 = +9(3) -> Max r8c3 = 7
-> r78c3 = [87]
-> r678c4 = [4{23}]
Also remainig Innie c123 -> r5c3 = 4
-> r6c23 = {25}
-> 25(4)n4 = {1789}

7. Remaining Innies n8 -> r78c7 = +14(2) = {68}
-> 23(4)r6c6 = [7{68}2]
-> Remaining Innie c789 -> r5c7 = 7
Also r7c7 = 9

8. All of (149) in n7 only in 14(3)
-> HS 9 in c3 -> 13(2)n1 = [49]
Whichever of (19) is in r89c1 also goes in r5c2
-> (78) in r456c1
-> 10(2)n1 = [28]
Also 18(3)n1 = [657]
-> NS 3 in c1 -> r7c12 = [35]
-> r6c23 = [25]
-> r9c23 = [62]
etc.


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 Post subject: Re: Assassin 344
PostPosted: Fri Jun 02, 2017 4:06 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1559
Location: Lethbridge, Alberta, Canada
Quite a long time since I've posted a walkthrough. I was so busy with other things in April and the first half of May that I didn't have time to work on Assassin level puzzles. Then when I 'came back' this one was harder than most V1 Assassins.

wellbeback wrote:
Here's how I did it. One very inelegant step I'm sorry to say.
But it was a very powerful step.


My solving path was a long one with very hard combination/permutation analysis.

Here is my walkthrough for Assassin 344:
Prelims

a) R1C23 = {49/58/67}, no 1,2,3
b) R1C78 = {15/24}
c) R3C12 = {19/28/37/46}, no 5
d) R3C89 = {16/25/34}, no 7,8,9
e) R7C12 = {17/26/35}, no 4,8,9
f) R7C89 = {29/38/47/56}, no 1
g) R9C23 = {17/26/35}, no 4,8,9
h) R9C78 = {17/26/35}, no 4,8,9
i) 10(3) cage at R3C3 = {127/136/145/235}, no 8,9
j) 19(3) cage at R3C7 = {289/379/469/478/568}, no 1
k) 42(7) cage at R4C5 = {3456789}

1. R3C89 = {16/34} (cannot be {25} which clashes with R1C78), no 2,5
1a. Killer pair 1,4 in R1C78 and R3C89, locked for N3
1b. 45 rule on N3 2 innies R23C7 = 14 = {59/68}
1c. R23C7 = 14 -> R34C7 cannot be 14 (CCC) -> no 5 in R4C8
1d. 7 in N3 only in 18(3) cage at R1C9 = {279/378} (cannot be {567} which clashes with R23C7), no 5,6
1e. R3C12 = {19/28/37} (cannot be {46} which clashes with R3C89), no 4,6
1f. Min R2C7 = 5 -> max R234C6 = 11, no 9 in R234C6

2. 45 rule on N1 2 innies R23C3 = 4 = {13}, locked for C3 and N1, clean-up: no 7,9 in R3C12, no 5,7 in R9C2
2a. Naked pair {28} in R3C12, locked for R3 and N1, clean-up: no 5 in R1C23, no 6 in R2C7 (step 1b)
2b. Killer pair 1,3 in R3C3 and R3C89, locked for R3
2c. 7 in R3 only in R3C456, locked for N2
2d. 6 in N3 only in R3C789, locked for R3
2e. Min R2C7 + R3C6 = 9 -> max R24C6 = 7, no 7,8 in R24C6
2f. R34C3 cannot total 4 -> no 6 in R4C2

3. 45 rule on N7 2 innies R78C3 = 15 = {69/78}
3a. Killer triple 5,6,7 in R7C12, R78C3 and R9C23, locked for N7
3b. Min R7C3 = 6 -> max R6C23 = 9, no 8,9 in R6C2, no 9 in R6C3
3c. Min R8C3 = 6 -> max R678C4 = 10, no 8,9 in R678C4

4. 45 rule on N9 2 innies R78C7 = 11 = {29/38/47} (cannot be {56} which clashes with R23C7), no 1,5,6
4a. R78C7 = 11 -> R67C7 cannot be 11 (CCC) -> no 7 in R6C8

5. 45 rule on R1234 3 innies R4C159 = 20 = {389/479/569/578}, no 1,2

6. 45 rule on N6 2 outies R37C7 = 1 innie R5C7 + 8, IOU no 8 in R7C7, clean-up: no 3 in R8C7 (step 4)
6a. Max R37C7 = 16 -> max R5C7 = 8

7. 45 rule on N4 2 outies R37C3 = 1 innie R5C3 + 5, max R37C3 = 12 -> max R5C3 = 7
7a. 42(7) cage at R4C5 = {3456789}, 9 locked for N5

8. 45 rule on C789 3 innies R258C7 = 17
8a. R23C7 = 14 (step 1c) -> R28C7 cannot be 14 (CCC) -> no 3 in R5C7
8b. R78C7 = 11 (step 4) -> R28C7 cannot be 11 (CCC) -> no 6 in R5C7
8b. R258C7 = {278/458}, no 9, 8 locked for C7, clean-up: no 5 in R3C7 (step 1b), no 2 in R7C7 (step 4)
8c. 2 of {278} must be in R8C7 -> no 7 in R8C7, clean-up: no 4 in R7C7 (step 4)
8d. 5 in R3 only in R3C456, locked for N2
8e. 42(7) cage at R4C5 = {3456789}, 3 locked for N5
8f. Max R34C7 = 16 -> min R4C8 = 3

9. 16(4) cage at R2C6 = {1258/1348/1357/1456} (cannot be {1267/2347} because R2C7 only contains 5,8, cannot be {2356} because 2,3,6 only in R24C6), 1 locked for C6
9a. 5 of {1258} must be in R3C6, 5 of {1357/1456} must be in R2C7 -> no 5 in R4C6

10. 45 rule on N2 4(2+2) outies R2C37 + R4C46 = 14, min R2C37 = 6 -> max R4C46 = 8, no 8 in R4C4
10a. R2C3 = {13}, R2C7 = {58}, R23C7 (step 1b) = [59/86], 16(4) cage at R2C6 (step 9) = {1258/1348/1357/1456}
10b. R2C37 + R4C46 = [1571/1841] (both because 16(4) cage must contain 1)/[3551/3812/3821] (cannot be [3524/3542] because no valid combinations for 16(4) cage with R3C6 = {457}) -> R4C4 = {12457}, R4C6 = {12}, 1 in R4C46, locked for R4 and N5
10c. 3,6 of 16(3) cage = {1348/1456} must be in R2C6 -> no 4 in R2C6
[Now analysing further which permutations of 19(4) cage at R2C3 and 16(4) cage at R2C6 fit with the possible permutations for R2C37 + R4C46]
10d. R2C37 + R4C46 = [1571/1841/3812] (cannot be [3551] because 19(4) cage = [3295] clashes with R23C7 = [59] and 19(4) cage = [3475] clashes with 16(4) cage = [6541], cannot be [3821] because 19(4) cage = [3952] clashes with 16(4) cage = [2851]), no 2,5 in R4C4
10e. R2C37 + R2C46 + R3C46 + R4C46 = [15635771/18935441/38619512] (cannot be other permutations which clash with R23C7 or the 19(4) cage and 16(4) cage clash with each other) -> R2C4 = {69}, R2C6 = {13}, R3C4 = {59}
10f. R2C37 + R2C46 + R3C46 + R4C46 = [15635771/38619512] (cannot be [18935441] because R23C7 = [86] and then R3C67 = [46] clashes with R3C89) -> R2C4 = 6, R3C6 = {57}, R4C4 = {17}, 5 in R3C46, locked for R3
10g. Naked pair {13} in R2C36, locked for R2
10h. 18(3) cage at R1C9 (step 1d) = {279/378}
10i. 3 of {378} must be in R1C9 -> no 8 in R1C9
10j. 8 in R1 only in R1C456, locked for N2
10k. 10(3) cage at R3C3 = {136/145/235} (cannot be {127} which clashes with R4C46, ALS block), no 7

11. 45 rule on N4 5 innies R46C2 + R456C3 = 20 = {12458/23456} (cannot be {12368} because 15(3) cage at R6C2 = [186] clashes with 6 in R45C3, cannot be {12467} because 15(3) cage cannot be [177] and 15(3) cage = [168], R78C3 = [87] clashes with 7 in R5C3, cannot be {13457} because R46C2 = [31] doesn’t provide any combinations for 10(3) cage at R3C3), no 7, 2,4,5 locked for N4
11a. R3C3 = {13} and 15(3) cage at R6C2 -> {12458/23456} can only be {25}[418]/{25}[634]/[364]{25} (cannot be [365]{24} because R78C3 = [96] clashes with R4C3 = 6, other combinations aren’t compatible with 10(3) cage at R3C3 or 15(3) cage at R6C2) -> 4 in R56C3, locked for C3 and N4, R5C3 = {46}, clean-up: no 9 in R1C2
11b. R6C23 = [18/25/34/52] -> R7C3 = {68}, clean-up: no 6,8 in R8C3 (step 3)
11c. R1C3 = {679}, R78C3 = [69/78] -> combined half cage R178C3 must contain 7, locked for C3, clean-up: no 1 in R9C2
[Cracked. The rest is fairly straightforward. No clean-ups in the remaining steps.]

12. 19(4) cage at R2C3 = [1657/3691]
12a. R8C3 = {79} -> 16(4) cage at R6C4 = {234}7/{124}9 (cannot be {135}7 which clashes with 19(4) cage) -> R678C4 = {124/234}, 2,4 locked for C4
12b. 45 rule on N8 4(2+2) outies R6C46 + R8C37 = 20
12c. R8C3 is odd, R6C4 and R8C7 are both even -> R6C6 must be odd = {57}
12d. Naked pair {57} in R36C6, locked for C6
12e. 6,8 in N5 only in 42(7) cage at R4C5 -> no 6 in R5C3, no 8 in R5C7
12f. R5C3 = 4, R6C4 = 4 (hidden single in N5), clean-up: no 3 in R6C2 (step 11b)
12g. R6C46 + R8C37 = 20, min R6C46 + R8C4 = 16 -> max R8C7 = 4

13. R2C7 = 8 (hidden single in C7) -> R234C6 = 8 = [152], R6C6 = 7, R4C4 = 1, R23C3 = [31], R3C47 = [96]
13a. Naked pair {23} in R78C4, locked for C4 and N8, R159C4 = [857], R5C7 = 7
13b. R678C4 = 4{23} = 9 -> R8C3 = 7 (cage sum), R7C3 = 8 (step 3)
13c. R3C3 = 1 -> R4C23 = 9 = [36]
13d. R7C3 = 8 -> R6C23 = 7 = {25}, locked for R6
13e. R1C3 = 9 -> R1C2 = 4, R1C56 = [23], R23C5 = [47], R1C9 = 7
13f. R4C1 = 7 (hidden single in N4)
13g. R7C8 = 7 (hidden single in N9) -> R7C9 = 4, R8C7 = 2 -> R7C7 = 9 (step 4)
13h. R67C6 = [76], R8C7 = 2 -> R8C6 = 8 (cage sum)
13i. R3C7 = 6, R4C7 = 4 (hidden single in C7) -> R4C8 = 9 (cage sum)
13j. R9C78 = {35} (only remaining combination), locked for R9 and N9
13k. R78C4 = [23], R7C1 = 3 (hidden single in R7) -> R7C2 = 5
13l. R5C6 = 9, naked pair {18} in R5C12, locked for R5 and N4
13m. R9C9 = 8 (hidden single in R9)
13n. R6C8 = 8 (hidden single in N6), R7C7 = 9 -> R6C7 = 1 (cage sum)

and the rest is naked singles.

Rating Comment:
It's hard to know what rating to give my WT for A344. At least Hard 1.5 and probably in the 1.75 range.

HATMAN wrote:
JS uses 6 fishes but I managed it with a couple of fishes.
I hope you'll show us how you did it.


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