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 Post subject: Assassin 362
PostPosted: Thu Nov 01, 2018 7:08 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 788
Location: Sydney, Australia
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Assassin 362
Got a scare with how many chains JSudoku had to use to solve this even though SS 'only' scores it 1.60 so I went with some big contradiction moves. However, then I had a look at SS solving log and didn't even use any big "45"s like usual. Tried again and found a much more satisfying way through. Still used 3 advanced steps so still no pushover. Presumably there is a simpler way.
code:
3x3::k:1280:3867:3867:3098:5635:5635:5635:3332:3332:1280:6405:3867:3098:8454:8454:8454:3332:5122:6405:6405:6405:3098:8454:8454:2311:2311:5122:2569:2569:2058:2058:8454:2059:2059:2311:5122:1805:2574:4111:4111:4111:6672:6672:6672:6672:1805:2574:6161:6161:1810:1810:3603:6672:2324:4117:4117:5142:6161:6161:3603:3603:5655:2324:3096:4117:5142:5142:1049:1049:5655:5655:3585:3096:2060:2060:5142:4104:4104:4104:3585:3585:
solution:
Code:
+-------+-------+-------+
| 1 6 7 | 4 9 8 | 5 3 2 |
| 4 5 2 | 3 1 6 | 9 8 7 |
| 8 9 3 | 5 7 2 | 1 6 4 |
+-------+-------+-------+
| 6 4 1 | 7 8 5 | 3 2 9 |
| 5 3 8 | 6 2 9 | 7 4 1 |
| 2 7 9 | 1 4 3 | 8 5 6 |
+-------+-------+-------+
| 7 1 5 | 8 6 4 | 2 9 3 |
| 9 8 4 | 2 3 1 | 6 7 5 |
| 3 2 6 | 9 5 7 | 4 1 8 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 362
PostPosted: Wed Nov 07, 2018 8:16 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 788
Location: Sydney, Australia
Here's how I went.
a362 start:
Preliminaries courtesy of SS
Cage 4(2) n8 - cells ={13}
Cage 5(2) n1 - cells only uses 1234
Cage 7(2) n4 - cells do not use 789
Cage 7(2) n5 - cells do not use 789
Cage 8(2) n45 - cells do not use 489
Cage 8(2) n56 - cells do not use 489
Cage 8(2) n7 - cells do not use 489
Cage 12(2) n7 - cells do not use 126
Cage 9(2) n69 - cells do not use 9
Cage 10(2) n4 - cells do not use 5
Cage 10(2) n4 - cells do not use 5
Cage 22(3) n9 - cells do not use 1234
Cage 22(3) n23 - cells do not use 1234
Cage 9(3) n36 - cells do not use 789
Cage 20(3) n36 - cells do not use 12

1. "45" on n23: 3 outies r4c589 = 19 (no 1)
1a. but {379/568} blocked by the two 8(2) cages in r4 need one of 3/7 or one of 5/6
1b. = {289/469/478}(no 3,5)

2. 5 in r4 only in one of 8(2) -> 3 locked for r4 (Locking cages)
2a. 10(2)r4c1 = {19/28/46}(no 7)

3. 7(2)r5c1: {34} blocked by 5(2)n1 = 3/4
3a. 7(2) = {16/25}(no 3,4)

4. 7(2)n4 = {16} -> 10(2)r4c1 = {28}; or 7(2) = {25}
4a. 2 locked for n4 in those two cages (Combined cages)
4b. no 8 in 10(2)r5c2

5. "45" on c1: 3 innies r347c1 = 21 = {489/579/678}(no 1,2,3)
5a. no 8,9 in r4c2

6. "45" on n4: 3 innies r456c3 = 18
6a. must have both {37} or neither for n4 since the only other spot is 10(2)r5c2 -> {369/567} blocked (Locking-out cages)
6b. = {189/378/459/468}
6c. note: either {37} in r56c2 or {378} in r456c3

7. "45" on n7: 2 innies r78c3 = 9 (no 9)
7a. = {18/27/36/45}
7b. note: with {378} in r456c3 -> h9(2) = {45} only

This is the key step I missed 1st time through through since have to see different elements
8. from step 6c and 7b. r56c2 = {37} or r78c3 = {45} -> [35] blocked from r9c23, no 3 in r9c2, no 5 in r9c3

9. "45" on c12: 2 outies r37c3 - 3 = 1 innie r1c2. Since r1c2 and r3c3 are in the same nonet they can't be the same -> no 3 in r9c3 (IOU)
9a. 8(2)n7 = {17/26}(no 5) = 2/7

10. h9(2)r78c3: {27} blocked by 8(2)
10a. = {18/36/45}(no 2,7)

11. 4(2)n8 = {13} both locked for r8 and n8
11a. no 9 in r9c1, no 6,8 in r7c3 (h9(2))

12. "45" on n7: 2 outies r89c4 = 11 ={29/47/56}(no 8)

13. "45" on r9: 3 outies (remembering h11(2)r89c4) r8c149 = 16 = {259/268/457}
13a. -> 4 remaining innies r8c2378 = 25 = {2689/4579/4678}
13b. 2 in {2689} must be in r8c2
13d. {57} in {4579} blocked from r8c78 by can't make cage total -> must have 9 in r8c78
13e. -> no 9 in r8c2

MOre than 4 combinations but really helpful.
14. 16(3)r7c1: {169} blocked by 8(2)n7 = 1/6
14a. {358} blocked by h9(2)r78c3 = 3/5/8
14b. {367} blocked by 8(2) = 6/7
14c. = {178/259/268/349/457}
14d. 2 in n4 in r4c2 or in 7(2)r56c1 = {25} = 2/5
14e. -> r7c1 + r8c2 cannot be [52]
14f. -> {259} in 16(3) can't have 9 in r7c2
14g. and {349} must have 3 in r7c2
14g. -> no 9 in r7c2

15. 9 in n7 only in c1: 9 locked for c1
15a. no 1 in r4c2

16. h21(3)r347c1: {579} blocked by r4c1 = (468)
16a. = {489/678}(no 5)
16b. must have 8, locked for c1
16c. no 4 in 12(2)n7

17. 12(2)n7+8(2)n7 = {39}/{57/26} = 3/6
17a. ->[36] blocked from r78c3 (no 3,6)

Another hard to see
18. 8 in n4 in r4c1 -> 2 in r4c2 or 8 in c3
18a. -> [28] blocked from r8c23 -> {2689} blocked fom h25(4)r8c2378
18b. = {4579/4678}(no 2)
18c. must have 4: 4 locked for r8 and n7
18d. no 5 in r8c3 (h9(2))

19. 2 in r8 must be in h16(3)r8c148: but {268} blocked by no 2,6,8 in r8c1 = {259} only: 5,8 locked for r8

20. 22(3)n9 must have 9 -> r7c8 = 9
21. -> r8c78 = {67} only: both locked for r8 and n9

21. r8c1 = 9 (hsingle c1), r9c1 = 3


cracked
Cheers
Ed


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 Post subject: Re: Assassin 362
PostPosted: Sun Nov 11, 2018 11:52 pm 
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Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 177
Location: California, out of London
Thanks Ed. Finally had some time to write my WT. Did this before looking at yours. You certainly made good use of 45s there! :) . As usual we had quite different approaches.

Cheers, wellbeback

Assassin 362 WT:
1. 5(2) and 7(2) in c1 are from {14}{25} or {23}{16}
At least one of the two 8(2)s in r4 must be from {17} and {35}
-> 10(2)r4 cannot be {37}
-> 10(2)r4 from [91], [82], or {46}

2. Either 5(2)n1 = {14} or 7(2)n4 = {16} and 10(2)n4 = [82]
Either way 12(2)c1 cannot be {48}
-> 8(2)n7 cannot be {35}

3. 4(2)n8 = {13}
(48) in n7 not in 12(2) and not in 8(2) and at most one of them in 16(3)
-> Innies n7 = r78c3 = +9(2) from [18] or {45}

4! Outies n7 = r89c4 = +11(2)
-> Innies r89 = r8c2378 = +25(4)
Since Min r8c78 = +13(2) -> Max r8c23 = +12(2)

Either r78c3 = {45} -> 12(2)n7 = [93] -> r7c8 = 9
Or r78c3 = [18] -> 8(2)n7 = {26} -> r8c2 = 4 (Since max r8c23 = +12(2)) -> r8c78 = +13(2) -> r7c8 = 9
Either way r7c8 = 9!

5. -> r8c23 = +12(2) = [84], [48], or [75]
-> HS 9 in n7 -> 12(2)n7 = [93]
-> 5(2)c1 = {14}
-> 7(2)c1 = {25}
-> 10(2)n4 = [64]
-> 8 in n4 in r56c3
-> r78c3 = {45}
-> r89c4 = [29]
-> Remaining Innies r9 = r9c89 = +9(2)
-> r8c9 = 5
-> r8c78 = {67}
-> r9c89 = {18}
-> 8(2)n7 = {26}
-> 16(3)r9 = [{57}4]
-> r7c79 = {23}
Also r8c23 = [84]
-> r7c123 = [715]
-> r3c1 = 8

6. Two 8(2)s in r4 = {17} and {35}
-> r4c8 = 2 and r4c59 = {89}

7. Outies n2 = r12c7 + r4c5 = +22(3)
-> Min r12c7 = +13(2)
-> HS 2 in n3 -> r1c9 = 2
-> r7c79 = [23]
-> r6c9 = 6

8. r7c456 = {468}
Given 4 already in c7 -> 14(3)r6c7 = [842]
-> r4c59 = [89]
-> 20(3)c9 = [{47}9]
-> r3c78 = {16}
-> r12c7 = {59}
-> r12c8 = {38}
-> r9c89 = [18]
-> r3c78 = [16]
-> r8c78 = [67]
-> r56c8 = {45}
-> r5c9 = 1
-> r5c67 = [97]
-> r4c67 = [53]
-> 7(2)n5 = [43]
-> 4(3)n8 = [31]
Also r9c56 = [57]
Also r7c45 = [86]
-> r6c34 = [91]
etc.


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 Post subject: Re: Assassin 362
PostPosted: Sun Feb 10, 2019 11:37 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
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Location: Lethbridge, Alberta, Canada
Another Assassin which got left behind because I'd got out of practice with Assassins, as explained in my A361 post. I came back to this one yesterday and really can't explain why I didn't finish it at the time, apart from having been out of practice in November.

Here's my walkthrough for Assassin 362:
Prelims

a) R12C1 = {14/23}
b) R4C12 = {19/28/37/46}, no 5
c) R4C34 = {17/26/35}, no 4,8,9
d) R4C67 = {17/26/35}, no 4,8,9
e) R56C1 = {16/25/34}, no 7,8,9
f) R56C2 = {19/28/37/46}, no 5
g) R6C56 = {16/25/34}, no 7,8,9
h) R67C9 = {18/27/36/45}, no 9
i) R89C1 = {39/48/57}, no 1,2,6
j) R8C56 = {13}
k) R9C23 = {17/26/35}, no 4,8,9
l) 22(3) cage at R1C5 = {589/679}
m) 20(3) cage at R2C9 = {389/479/569/578}, no 1,2
n) 9(3) cage at R3C7 = {126/135/234}, no 7,8,9
o) 22(3) cage at R7C8 = {589/679}

Steps Resulting From Prelims
1a. Naked pair {13} in R8C56, locked for R8 and N8, clean-up: no 9 in R9C1
1b. 22(3) cage at R1C5 = {589/679}, 9 locked for R1
1c. 22(3) cage at R7C8 = {589/679}, 9 locked for N9

2a. R56C1 = {16/25} (cannot be {34} which clashes with R12C1), no 3,4
2b. Killer pair 1,2 in R12C1 and R56C1, locked for C1, clean-up: no 8,9 in R4C2

3a. 45 rule on N7 2 innies R78C3 = 9 = [18/36]/{27/45}, no 9, no 6,8 in R7C3
3b. 45 rule on N7 2 outies R89C4 = 11 = {29/47/56}, no 8

4. 45 rule on N9 3 innies R7C79 + R9C7 = 9 = {126/135/234}, no 7,8,9, clean-up: no 1,2 in R6C9

5. 45 rule on R4 3 innies R4C589 = 19 = {289/379/469/478/568}, no 1
5a. 2,3 of {289/379} must be in R4C8 -> no 2,3 in R4C5, no 3 in R4C9
5b. 4 in R4 only in R4C12 = {46} or in R4C589 -> R4C589 = {289/379/469/478} (cannot be {568}, locking-out cages, or maybe it’s blocking cages), no 5
[Alternatively variable hidden killer triple 5,6,7 in R4C34, R4C67 and R4C589 for R4, R4C34 and R4C67 each contain one of 5,6,7 -> R4C589 cannot contain more than one of 5,6,7 -> R4C589 = {289/379/469/478} (cannot be {568} which contains 5 and 6), no 5
5c. 5 in R4 only in R4C34 = {35} or R4C78 = {35} (locking cages), 3 locked for R4, clean-up: no 7 in R4C12
5d. 9(3) cage at R3C7 = {126/234}, (cannot be {135} because R4C8 only contains 2,4,6), no 5
5e. 9(3) cage = {126/234}, CPE no 2 in R12C8

6. 45 rule on N4 3 innies R456C3 = 18 = {189/279/369/378/459/468/567}
6a. Hidden killer pair 3,7 in R56C2 and R456C3 for N4, R56C2 contains both or neither of 3,7 -> R456C3 must contain both of neither of 3,7 -> R456C3 = {189/378/459/468} (cannot be {279/369/567} which only contain one of 3,7), no 2, clean-up: no 6 in R4C4
6b. 1,5,6 of {189/459/468} must be in R4C3 -> no 1,5,6 in R56C3
6c. Consider combinations for R456C3 = {189/378/459/468}
R456C3 = {189/378/468}, 8 locked for N4
or R456C3 = {459} => R56C2 = {37} (hidden pair in N4)
-> no 8 in R56C2, clean-up: no 2 in R56C2

7. 45 rule on C1 3 innies R347C1 = 21 = {489/579/678}, no 3

8. 45 rule on N2 3(2+1) outies R12C7 + R4C5 = 22
8a. Max R12C7 = 17 -> no 4 in R4C5
8b. Max R1C7 + R4C5 = 18 -> min R2C7 = 4

9. 45 rule on C12 2 outies R39C3 = 1 innie R1C2 + 3, IOU no 3 in R9C3, clean-up: no 5 in R9C2

10. 45 rule on C1234 2 outies R57C5 = 8 = [17/26/35/62]

11. 45 rule on R89 2 outies R7C38 = 1 innies R8C2 + 6, IOU no 6 in R7C8

[After slow going, this step achieved much more than I expected.]
12. Consider combinations for R12C1 = {14/23}
R12C1 = {14} => R56C1 = {25} => R89C1 = [93] => R4C12 = [64]
or R12C1 = {23}, R56C1 = {16} => R4C12 = [82]
-> R4C12 = [64/82]
12a. R4C589 (step 5b) = {289/469} (cannot be {478} which clashes with R4C12), no 7
12b. Hidden quad 1,3,5,7 in R4C3467 -> R4C34 = {17/35}, R4C67 = {17/35}
12c. R347C1 (step 7) = {489/678} (cannot be {579} because R4C1 only contains 6,8), no 5, 8 locked for C1, clean-up: no 4 in R89C1
12d. Killer pair 2,6 in R4C12 and R56C1, locked for N4, clean-up: no 4 in R56C2
12e. 6 in N4 only in R456C1, locked for C1
12f. R9C23 = {17/26} (cannot be [35] which clashes with R89C1), no 3,5
12g. R78C3 (step 3a) = [18/36]/{45} (cannot be {27} which clashes with R9C23), no 2,7
12h. R89C1 = {57}/[93], R9C23 = {17/26} -> combined cage R89C1 + R9C23 = {57}{26}/[93]{17}/[93]{26}
12i. R78C3 = [18]/{45} (cannot be [36] which clashes with combined cage R89C1 + R9C23), no 3,6
12j. R456C3 (step 6c) = {189/378/459}, R78C3 = [18]/{45} -> combined cage R45678C3 = {189}{45}/{378}{45}/{459}[18], 4,5,8 locked for C3

13. 45 rule on R5 3 outies R6C128 = 14 = {158/167/239/257/356} (cannot be {248} because 4,8 only in R6C8, cannot be {347} because no 3,4,7 in R6C1, cannot be {149} because [149] clashes with R56C2 = [19], CCC), no 4 in R6C8

14. R456C3 (step 6c) = {189/378/459}
14a. Consider combinations for R78C3 (step 12i) = [18]/{45}
R78C3 = [18] => R456C3 = {459} => R56C2 = {37} (hidden pair in N4), locked for C2
or R78C3 = {45}, locked for N7 => R89C1 = [93]
-> no 3 in R7C2
14b. R9C1 = 3 (hidden single in N7) -> R8C1 = 9, clean-up: no 2 in R12C1
14c. Naked pair {14} in R12C1, locked for C1 and N1, clean-up: no 6 in R56C1
14d. Naked pair {25} in R56C1, locked for N4, R4C2 = 4 -> R4C1 = 6, R4C8 = 2
14e. 4 in C3 only in R78C3 = {45}, locked for N7 and 20(4) cage at R7C3, clean-up: no 3 in R4C4, no 6,7 in R89C4 (step 3b)
14f. R89C4 = [29], clean-up: no 6 in R5C5 (step 10)
14g. R7C8 = 9 (hidden single in N9)
14h. 16(3) cage at R9C5 = {178/268/457}
14i. 2 of {268} must be in R9C7 -> no 6 in R9C7
14j. Killer pair 2,7 in R9C23 and 16(3) cage, locked for R9
14k. 2 in N9 only in R7C79 + R9C7 (step 4) = {126/234}, no 5
14l. 16(3) cage at R9C5 = {178/268/457}
14m. 4 of {457} must be in R9C7 -> no 4 in R9C56
14n. 4 in N8 only in R7C46, locked for R7 -> R78C3 = [54], clean-up: no 3 in R5C5 (step 10)
14o. R6C56 = {16/34} (cannot be {25} which clashes with R6C1), no 2,5
14p. 15(3) cage at R1C2 = {267/357} (cannot be {258} because 5,8 only in R1C2), no 8,9, 7 locked for N1
14q. R37C1 = [87], R7C5 = 6, R5C5 = 2 (step 10), R56C1 = [52], clean-up: no 1 in R6C6, no 1 in R9C23
14r. Naked pair {26} in R9C23, locked for R9 and N7 -> R78C2 = [18], clean-up: no 9 in R56C2
14s. Naked pair {37} in R56C2, locked for C2 and N4 -> R4C3 = 1, R4C4 = 7
14t. R9C56 = {57} (hidden pair in N8), 5 locked for R9, R9C7 = 4 (cage sum)
14u. R9C89 = {18}, locked for N9, R8C9 = 5 (cage sum)
14v. R5C5 = 2 -> R5C34 = 14 = [86], R6C3 = 9, clean-up: no 1 in R6C5
14w. Naked pair {34} in R6C56, locked for R6 and N5 -> R4C67 = [53], R56C2 = [37], R7C7 = 2, R7C9 = 3 -> R6C9 = 6, R9C56 = [57]
14x. 20(3) cage at R2C9 = {479} (only remaining combination) -> R4C9 = 9, R23C9 = {47}, locked for C9 and N3 -> R5C6789 = [9741], R9C89 = [18], R8C78 = [67], R3C7 = 1, R3C8 = 6 (cage sum), R4C5 = 8
14y. R1C9 = 2 -> R12C8 = 11 = {38}, locked for C8 and N3 -> R6C78 = [85], R7C6 = 4, R6C45 = [43], R67C4 = [18], R8C56 = [31]
14z. R123C6 = [862] -> R1C57 = 14 = [95]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A362 at Easy 1.5. I used a few short forcing chains, plus some combined cages.


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