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PostPosted: Sat Jul 16, 2016 1:32 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 692
Location: Saudi Arabia
Assassin 337 Based on DKS 12931

This is based on a DKS level 10 killer with score 0.9.

SS gives it 1.65 and JS uses a couple of fishes.



Image

JS Code:
3x3::k:5126:5126:3354:3354:7170:7170:4611:4611:4611:5126:3336:3336:1289:7170:7170:5124:5124:4611:3591:3336:4874:1289:5893:5893:5893:5124:4611:3591:3336:4874:6423:6423:6423:5893:6420:6420:3591:4107:4874:2067:4377:6423:5893:6420:6420:4107:4107:2067:4377:2584:6423:1558:1558:3354:5389:5390:27:2584:5136:5136:5136:3861:3354:5389:5390:5390:3599:3599:3861:3861:3861:5394:5389:5389:5389:3599:2577:2577:2577:5394:5394:

Solution:
581697423
762348951
349215768
216574839
954183276
837926514
173859642
695432187
428761395


This is an easier one SS gives it 0.90 but I think harder than the DKS.



Image

JS Code:
3x3::k:5126:5126:4122:4122:7170:7170:4611:4611:4611:5126:3336:3336:1289:7170:7170:5124:5124:4611:3591:3336:4874:1289:5893:5893:5893:5124:4611:3591:3336:4874:6423:6423:6423:5893:6420:6420:3591:4107:4874:2067:4377:6423:5893:6420:6420:4107:4107:2067:4377:2584:6423:1558:1558:4122:5389:5390:4122:2584:5136:5136:5136:3861:4122:5389:5390:5390:3599:3599:3861:3861:3861:5394:5389:5389:5389:3599:2577:2577:2577:5394:5394:


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PostPosted: Sun Jul 31, 2016 9:26 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Back again! :) I've been busy on other things since returning from our holiday; it's now about two months since I last worked on a puzzle on this site, so I decided to try the easier version first.

It's probably too easy for this site, although if there are any newbies around I can recommend that they try it.

Here is my walkthrough for Assassin 337 Easier version:
Prelims

a) R23C4 = {14/23}
b) 8(2) cage at R5C4 = {17/26/35}, no 4,8,9
c) 17(2) cage at R5C5 = {89}
d) 10(2) cage at R6C5 = {19/28/37/46}, no 5
e) R6C78 = {15/24}
f) 20(3) cage at R1C1 = {389/479/569/578}, no 1,2
g) 20(3) cage at R2C7 = {389/479/569/578}, no 1,2
h) 19(3) cage at R3C3 = {289/379/469/478/568}, no 1
i) 21(3) cage at R7C2 = {489/579/678}, no 1,2,3
j) 20(3) cage at R7C5 = {389/479/569/578}, no 1,2
k) 21(3) cage at R8C9 = {489/579/678}, no 1,2,3
l) 10(3) cage at R9C5 = {127/136/145/235}, no 8,9
m) 28(4) cage at R1C5 = {4789/5689}, no 1,2,3
n) 13(4) cage at R2C2 = {1237/1246/1345}, no 8,9
o) 16(5) disjoint cage at R1C3 = {12346}
p) 18(5) cage at R1C7 = {12348/12357/12456}, no 9

1. 45 rule on N3 1 innie R3C7 = 7

2. 45 rule on N7 1 innie R7C3 = 3
2a. Naked quad {1246} in R1C34 + R67C9, CPE no 1,2,4,6 in R1C9
[Step 2a isn't really necessary but, since I saw it here, I put it in.]

3. Naked pair {89} in 17(2) cage at R5C5, locked for N5
3a. 45 rule on N5 2 innies R5C4 + R6C5 = 3 = {12}, locked for N5
3b. 8(2) cage at R5C4 = [17/26]
3c. 10(2) cage at R6C5 = [19/28]
3d. Naked pair {89} in R67C4, locked for C4
3e. Killer pair 1,2 in R23C4 and R5C4, locked for C4
3f. Killer pair 4,6 in R1C4 and 28(4) cage at R1C5, locked for N2, clean-up: no 1 in R23C4
3g. Naked pair {23} in R23C4, locked for C4 and N2 -> 8(2) cage at R5C4 = [17], 10(2) cage at R6C5 = [28], 17(2) cage at R5C5 = [89], clean-up: no 4 in R6C78
3h. Naked pair {15} in R6C78, locked for R6 and N6

4. 45 rule on N14 1 innie R1C3 = 1
4a. 16(5) disjoint cage at R1C3 = {12346} -> R7C9 = 2
4b. 13(4) cage at R2C2 = {1237/1246/1345} -> R4C2 = 1

5. 28(4) cage at R1C5 = {4789/5689}, 8,9 locked for N2
5a. Naked pair {15} in R3C56, locked for R3 and N2
5b. R3C567 = {15}7 = 13 -> R45C7 = 10 = [82] (cannot be {46} which clashes with R6C9)
5a. 28(4) cage = {4789} (only remaining combination), locked for N2 -> R1C4 = 6, R6C9 = 4

6. 8 in R6 only in R6C12 -> 16(3) cage at R5C2 = {358} (only possible combination) -> R5C2 = 5, R6C12 = {38}, 3 locked for R6 and N4 -> R6C6 = 6

7. 14(3) cage at R8C4 = {347} (only possible combination) -> R8C5 = 3, R89C4 = {47}, locked for C4 and N8, R4C4 = 5
7a. 20(3) cage at R7C5 = {569} (only possible combination), locked for R7

8. 20(3) cage at R2C7 = {389/569}, no 4
8a. R1C78 + R2C9 = [421] (hidden triple in N3)
8b. 28(4) cage at R1C5 = {4789}, 4 locked for R2

9. R9C7 = 3 (hidden single in N9) -> R9C56 = 7 = [52/61]
9a. Naked triple {569} in R7C56 + R9C5, locked for N8
9b. Naked pair {12} in R89C6, locked for C6 -> R3C56 = [15], R7C6 = 9

10. 14(3) cage at R3C1 = {239/248}, 2 locked for C1
10a. 2 in N7 only in R9C23, locked for R9 -> R9C6 = 1, R9C5 = 6 (cage total), R7C57 = [56], R8C6 = 2

11. 45 rule on N1 2 remaining innies R3C13 = 12 = [39/48/84]
11a. R4C1 = 2 (hidden single in C1)
11b. 19(3) cage at R3C3 = {469} (only remaining combination), locked for C3, 6 also locked for N4, clean-up: no 4 in R3C1
11c. 13(4) cage at R2C2 = {1237/1246} (cannot be {1345} which clashes with R3C13) -> R2C3 = 2, R23C2 = [73/64], R34C4 = [32]
11d. Killer pair 3,4 in R3C13 and R3C2, locked for R3 and N1
11e. R1C9 = 3 (hidden single in R1) -> R3C9 = 8 (cage sum), R3C1 = 3, R5C1 = 9 (cage sum), R3C2 = 4, R2C2 = 6 (cage sum)

12. R7C2 = 7 -> R8C23 = 14 = [95]

and the rest is naked singles.

Rating Comment:
Based on Mike's original definitions, I'll rate this at 0.75. It's about the same level as the first dozen of Ruud's Assassins.
SudokuSolver tends to rate easier puzzles a bit too high; that's because it's optimised for puzzles in the 1.0 to 1.5 range.


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PostPosted: Wed Aug 03, 2016 2:17 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
And then I tried the Assassin level version.

Here is my walkthrough for Assassin 337:
Prelims

a) R23C4 = {14/23}
b) 8(2) cage at R5C4 = {17/26/35}, no 4,8,9
c) 17(2) cage at R5C5 = {89}
d) 10(2) cage at R6C5 = {19/28/37/46}, no 5
e) R6C78 = {15/24}
f) 20(3) cage at R1C1 = {389/479/569/578}, no 1,2
g) 20(3) cage at R2C7 = {389/479/569/578}, no 1,2
h) 19(3) cage at R3C3 = {289/379/469/478/568}, no 1
i) 21(3) cage at R7C2 = {489/579/678}, no 1,2,3
j) 20(3) cage at R7C5 = {389/479/569/578}, no 1,2
k) 21(3) cage at R8C9 = {489/579/678}, no 1,2,3
l) 10(3) cage at R9C5 = {127/136/145/235}, no 8,9
m) 28(4) cage at R1C5 = {4789/5689}, no 1,2,3
n) 13(4) disjoint cage at R1C3 = {1237/1246/1345}, no 8,9
o) 13(4) cage at R2C2 = {1237/1246/1345}, no 8,9
p) 18(5) cage at R1C7 = {12348/12357/12456}, no 9

1. 45 rule on N3 1 innie R3C7 = 7
1a. 20(3) cage at R2C7 = {389/569}, no 4

2. 45 rule on N7 1 innie R7C3 = 3

3. Naked pair {89} in 17(2) cage at R5C5, locked for N5
3a. 45 rule on N5 2 innies R5C4 + R6C5 = 3 = {12}, locked for N5
3b. 8(2) cage at R5C4 = [17/26]
3c. 10(2) cage at R6C5 = [19/28]
3d. Naked pair {89} in R67C4, locked for C4
3e. Killer pair 1,2 in R23C4 and R5C4, locked for C4
3f. Killer pair 1,2 in R6C5 and R6C78, locked for R6
3g. Killer pair 8,9 in R7C4 and 20(3) cage at R7C5, locked for R7
3h. Min R89C4 = 8 (cannot be {34} which clashes with R23C4) -> max R8C5 = 6

4. 28(4) cage at R1C5 = {4789/5689}, 8,9 locked for N2

5. 45 rule on N14 2 innies R16C3 = 8 = [17/26]
5a. 45 rule on N89 2 innies R7C49 = 10 = [82/91]
5b. R1C3 + R7C9 = {12} -> 13(4) disjoint cage at R1C3 = {1237/1246}, no 5
5c. R1C3 + R7C9 = {12}, CPE no 1,2 in R1C9

6. Hidden killer pair 1,2 in R1C3 and R1C78 for R1, R1C3 = {12} -> R1C78 must contain one of 1,2 -> R23C9 must contain one of 1,2
6a. Killer pair 1,2 in R23C9 and R7C9, locked for C9

7. 45 rule on N2 3 innies R1C4 + R3C56 = 12 = {147/156/237} (cannot be {246/345} which clash with R23C4) -> R1C4 = {67}, R3C56 = {14/15/23}, no 6
7a. 13(4) disjoint cage at R1C3 (step 5b) = {1237/1246} -> R6C9 = {34}
7b. Max R89C4 = 12 (cannot be {67} which clashes with R1C4) -> min R8C5 = 2

8. 45 rule on N6 3 innies R45C7 + R6C9 = 14 = {239/248/356} (cannot be {149} which clashes with R6C78, cannot be {158} because R6C9 only contains 3,4), no 1
8a. R6C9 = {34} -> no 3,4 in R45C7
8b. Killer pair 2,5 in R45C7 and R6C78, locked for N6

9. 15(4) cage at R7C8 = {1239/1248/1257/1347/1356/2346}
9a. 8,9 of {1239/1248} must be in N9 (R7C8 + R8C78 cannot be {124/125} which clash with R7C9) -> no 8,9 in R8C6
9b. Hidden killer pair 8,9 in R7C4 and R7C56 for N8, R7C4 = {89} -> R7C56 must contain one of 8,9
9c. Killer pair 8,9 in R7C4 and R7C56, locked for R7
9d. 20(3) cage at R7C5 = {479/569/578}
9e. 4 of {479} must be in R7C7 -> no 4 in R7C56

10. 13(4) cage at R2C2 = {1237/1246/1345}
10a. 6,7 of {1237/1246} must be in N1 (R2C23 + R3C2 cannot be {123/124} which clash with R1C3) -> no 6,7 in R4C2

11. 45 rule on N9 3 innies R7C79 + R9C7 = 1 outie R8C6 + 9
11a. Min R7C79 + R9C7 = 10 cannot be [622] -> min R9C7 = 3
11b. Max R7C79 + R9C7 = 13 -> max R8C6 = 4
11c. 10(3) cage at R9C5 = {136/145/235} (cannot be {127} because 1,2,7 only in R9C56), no 7

[I’m a bit out of practice with Assassins, so maybe it’s a bit early to try a forcing chain …]
12. 20(3) cage at R7C5 = {479/569/578}, 10(3) cage at R9C5 (step 11c) = {136/145/235}
12a. Consider combinations for 14(3) cage at R8C4 = {257/347/356}
14(3) cage = {257/347}, 7 locked for N8 => 20(3) cage = {569}
or 14(3) cage = {356}, locked for N8 -> 10(3) cage = {14}5 => 20(3) cage = {479} (cannot be {78}5)
-> 20(3) cage = {479/569}, 9 locked for R7
12b. R7C4 = 8 -> R6C5 = 2, R5C4 = 1 -> R6C3 = 7, 17(2) cage at R5C5 = [89], clean-up: no 4 in R23C4, no 4 in R6C78
12c. Naked pair {23} in R23C4, locked for C4 and N2
12d. Naked pair {15} in R6C78, locked for R6 and N6
12e. 14(3) cage at R8C4 = {347/356} -> R8C5 = 3
12f. Killer pair 6,7 in R1C4 and R89C4, locked for C4
12g. R6C3 = 7 -> R1C3 = 1 (step 5) -> R7C9 = 2
12h. 10(3) cage at R9C5 (step 11c) = {136/145/235}
12i. 3 of {136} must be in R9C7 -> no 6 in R9C7

13. 13(4) cage at R2C2 = {1237/1246/1345} -> R4C2 = 1
13a. 45 rule on N1 2 remaining innies R3C13 = 12 = [39/48/84]
13b. 2 in N1 only in 13(4) cage = {1237/1246}, no 5
13c. Killer pair 3,4 in 13(4) cage and R3C13, locked for N1

14. 15(4) cage at R7C8 = {1248/1257}, no 6,9 -> R8C6 = 2
14a. 9 in N9 only in 21(3) cage at R8C9 = {489/579}, no 6
14b. R7C7 = 6 (hidden single in N9) -> R7C56 = 14 = {59}, locked for R7 and N8
14c. 14(3) cage at R8C4 = {347} (only remaining combination), 4,7 locked for C4 and N8 -> R1C4 = 6, R6C9 = 4 (cage sum), R4C4 = 5
14d. Naked pair {16} in R9C56, locked for R9, R9C7 = 3 (cage sum)

15. 45 rule on N2 2 remaining innies R3C56 = 6 = {15}, locked for R3 and N2, R3C7 = 7 -> R45C7 = 10 = [82]

16. 8 in R6 only in 16(3) cage at R5C2 = {358} (only possible combination) -> R5C2 = 5, R6C12 = {38}, locked for R6 and N4 -> R6C6 = 6, R9C56 = [61], R3C56 = [15], R7C56 = [59]

17. R1C78 + R2C9 = [421] (hidden triple in N3)
17a. 28(4) cage at R1C5 = {4789}, 4 locked for R2
17b. R2C7 = 9 (hidden single in C7) -> R1C5 = 9 (hidden single in N2)
17c. 20(3) cage at R1C1 = {578} (only remaining combination), locked for N1, 5 also locked for C1 -> R3C13 (step 13a) = [39]
17d. R3C3 = 9 -> R45C3 = 10 = {46}, locked for C3 and N4, R2C23 = [62], R3C3 = 4
17e. R7C2 = 7 -> R8C23 = 14 = [95]
17f. R1C9 = 3 (hidden single in R1) -> R3C9 = 8 (cage sum)

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough at Easy 1.5. I used one short forcing chain.

Now to look at some of the Assassins and other puzzles which were posted while I wasn't active on this site; wellbeback has already solved some of them.


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PostPosted: Mon Dec 25, 2017 9:11 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1039
Location: Sydney, Australia
The key step for this straightforward solution is available from step 2 but have done the more routine stuff first. Some really interesting interactions with this cage set-up but unfortunately, are not required to solve this puzzle. Like it a lot. Thanks HATMAN!

Assassin 337
start:
Preliminaries courtesy of SudokuSolver
Cage 17(2) n5 - cells = {89}
Cage 5(2) n2 - cells only uses 1234
Cage 6(2) n6 - cells only uses 1245
Cage 8(2) n45 - cells do not use 489
Cage 10(2) n58 - cells do not use 5
Cage 21(3) n9 - cells do not use 123
Cage 21(3) n7 - cells do not use 123
Cage 10(3) n89 - cells do not use 89
Cage 20(3) n1 - cells do not use 12
Cage 20(3) n89 - cells do not use 12
Cage 20(3) n3 - cells do not use 12
Cage 19(3) n14 - cells do not use 1
Cage 28(4) n2 - cells do not use 123
Cage 13(4) n14 - cells do not use 89
Cage 13(4) n1269 - cells do not use 89
Cage 18(5) n3 - cells do not use 9

1. "45" on n3: 1 innie r3c7 = 7
1a. "45" on n7: 1 innie r7c3 = 3

2. "45" on n236: 2 outies r1c3 + r7c9 = 3 = {12} only
2a. r1c9, r1c4 and r6c9 see both these cells -> no 1,2 in r1c9, r1c4 and r6c9

3. r1c3 + r7c9 = 3 -> r1c4 + r6c9 = 10 (cage sum) (no 5)

4. 28(4)n2 = {4789/5689}: must have both 8,9; both locked for n2

5. "45" on n2: 3 innies r1c4 + r3c56 = 12
5a. but {246} and {345} are blocked by 5(2)n2 = [2/4, 3/4]
5b. = {147/156/237}
5c. 7 in {147/237} must be in r1c4 and 6 in {156} must be in r1c4 -> r1c4 = (67)
5d. -> r6c9 = (34) (h10(2))

6. "45" on n89: 2 innies r7c49 = 10 = [91/82]
6a. r6c5 = (12)

7. "45" on n14: 2 innies r16c3 = 8 = [17/26]
7a. ->r5c4 = (12)

The crack step now which works after step 2
8. 7 in n1 in 13(4)r2c2 = {1237} with 1/2 in r4c2 to avoid clashing with r1c3 = (12) ie, must have the 3 in n1
8a. or 7 in n1 in 20(3) -> 3 in 20(3) must also have 7 or there would be no 7 available for n1 (Locking-out cages)
8b. can't have both 3 & 7 in a 20(3) -> no 3 in 20(3)

9. 3 in r1 only in n3 in 18(5) = {12348} only: all locked for n3

10. naked quint {12348} in r12367c9: all locked for c9

11. 7 in n6 only in 25(4)
11a. but {4579} blocked by 6(2)n6 = [4/5..]
11b. = {1789/3679/4678}(no 2,5)

12. 5 in c9 only in 21(3)r8c9 = {579} only: all locked for n9
12a. no 5 in r9c8

13. 6 in c9 only in 25(4)n6 = {3679/4678}(no 1), 6 locked for n6 (and no 6 in r45c8)

14. "45" on n6: 3 innies r45c7 + r6c9 = 14 and must have 3/4 for r6c9
14a. but {149} blocked by 6(2)n6 = [1/4..]
14b. = {239/248}(no 1,5)
14c. must have 2 which is only in r45c7: locked for n6, c7 and no 2 in r3c56

15. 6(2)n6 = {15} only: both locked for r6

16. r6c5 = 2, r7c4 = 8 (cage sum), r7c9 = 2 (h10(2)), r1c3 = 1 (h3(2)), r6c3 = 7 (h8(2))

17. 8 in n9 only in r8c78 in 15(4) = {1248} only -> r8c6 = 2; 1,4 locked for n9; 8 locked for r8

on from there. Much easier now.
(edit: thanks Andrew for that correction)
Cheers
Ed


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