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 Post subject: Assassin 356
PostPosted: Wed Aug 15, 2018 7:59 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
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Assassin 356

Couldn't find a way to stiffen up the middle but the start is (hopefully) enough of a challenge to keep it as an Assassin. SSscore, 1.35
code:
3x3::k:4352:4865:2306:2306:4867:8964:8964:3589:3589:4352:4865:4865:2306:4867:4867:8964:3334:3334:4352:4865:5127:5127:6920:4867:8964:8964:8964:4352:1801:1801:5127:6920:3594:8964:4363:4363:4620:5901:5901:5901:6920:3594:3594:3594:4363:4620:4620:7950:5901:6920:3343:1552:1552:4369:7950:7950:7950:5906:6920:3343:3343:4627:4369:3092:3092:7950:5906:5906:5141:4627:4627:4369:3350:3350:7950:7950:5906:5141:5141:4627:4369:
solution:
Code:
+-------+-------+-------+
| 7 1 5 | 3 4 9 | 2 6 8 |
| 3 6 8 | 1 2 7 | 5 4 9 |
| 2 4 9 | 5 8 6 | 1 7 3 |
+-------+-------+-------+
| 5 3 4 | 6 1 2 | 8 9 7 |
| 8 2 6 | 7 9 4 | 3 5 1 |
| 1 9 7 | 8 3 5 | 4 2 6 |
+-------+-------+-------+
| 9 5 3 | 2 6 1 | 7 8 4 |
| 4 8 2 | 9 7 3 | 6 1 5 |
| 6 7 1 | 4 5 8 | 9 3 2 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 356
PostPosted: Sun Aug 19, 2018 3:27 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
Thanks Ed for your latest Assassin. Quite a lot of steps in my solving path and I was a bit slow in spotting my key breakthrough.

Here is my walkthrough for Assassin 356:
Prelims

a) R1C89 = {59/68}
b) R2C89 = {49/58/67}, no 1,2,3
c) R4C23 = {16/25/34}, no 7,8,9
d) R6C78 = {15/24}
e) R8C12 = {39/48/57}, no 1,2,6
f) R9C12 = {49/58/67}, no 1,2,3
g) 9(3) cage at R1C3 = {126/135/234}, no 7,8,9
h) 20(3) cage at R3C3 = {389/479/569/578}, no 1,2
h) 20(3) cage at R8C6 = {389/479/569/578}, no 1,2
i) 14(4) cage at R4C6 = {1238/1247/1256/1346/2345}, no 9

1. 45 rule on N3 2 outies R1C6 + R4C7 = 17 = {89}, locked for 35(7) cage at R1C6, CPE no 8 in R4C6
1a. 35(7) cage must contain 5, locked for N3, clean-up: no 9 in R1C89, no 8 in R2C89
1b. Naked pair {68} in R1C89, locked for R1 and N3 -> R1C6 = 9, R4C7 = 8, clean-up: no 7 in R2C89
1c. Naked pair {49} in R2C89, locked for R2 and N3
1d. 9 in C7 only in R789C7, locked for N9

2. 1,2 in N7 only in R7C123 + R8C23, locked for 31(7) cage at R6C3, no 1,2 in R6C3 + R9C4
2a. 45 rule on N7 2 outies R6C3 + R9C4 = 11 = {38/47/56}, no 9

3. 45 rule on C1234 2 outies R89C5 = 12 = {39/48/57}, no 1,2,6
3a. R89C5 = 12 -> R78C4 = 11 = {29/38/47/56}, no 1
3b. 1 in N8 only in R7C56, locked for R7
3c. 1 in N7 only in R89C3, locked for C3, clean-up: no 6 in R4C2

4. 45 rule on C6789 2 outies R12C5 = 6 = [15/42/51]
4a. R12C5 = 6 -> R23C6 = 13 = {58/67}
4b. 20(3) cage at R8C6 = {389/479/578} (cannot be {56}9 which clashes with R23C6), no 6
4c. 9 of {389/479} must be in R9C7 -> no 3,4 in R9C7
4d. 7 of {578} must be in R9C7 (cannot be {78}5 which clashes with R23C6) -> no 5 in R9C7
4e. So 20(3) cage = {38}9/{47}9/{58}7
4f. Killer pair 7,8 in R23C6 and R89C6, locked for C6
4g. R89C5 (step 3) = {39/57} (cannot be {48} which clashes with R89C6), no 4,8

5. 45 rule on N6 2 outies R45C6 = 1 innie R6C9
5a. Min R45C6 = 3 -> min R6C9 = 3
5b. Hidden killer pair 1,2 in R45C6 and R67C6 for C6, min R67C6 = 4 cannot contain both of 1,2 -> R45C6 must contain one or both of 1,2
5c. Max R45C6 = 8 -> no 9 in R6C9
5d. 9 in N6 only in 17(3) cage at R4C8 = {179/269/359}, no 4
5e. 45 rule on N9 2 innies R79C7 = 1 outie R6C9 + 10
5f. Max R79C7 = 16 -> max R6C9 = 6
5g. Min R6C9 = 3 -> min R79C7 = 13, no 2,3 in R7C7

6. 45 rule on N2 2 innies R3C45 = 1 outie R1C3 + 8
6a. Min R1C3 = 2 -> min R3C45 = 10, no 9 in R3C4 -> no 1 in R3C5

7. 45 rule on N1 2 innies R13C3 = 1 outie R4C1 + 9
7a. Max R13C3 = 14 -> max R4C1 = 5
7b. Min R13C3 = 10, max R1C3 = 5 -> min R3C3 = 6 (since cannot be [55])

8. 45 rule on N8 3 innies R7C56 + R9C4 = 1 outie R9C7 + 2 -> max R7C56 + R9C4 = 11, no 9 in R7C5
8a. 9 in N8 only in 23(4) cage at R7C4 = {2579/3479/3569} (cannot be {2489} because 2,4,8 only in R78C4), no 8, clean-up: no 3 in R78C4 (step 3a)
8b. 20(3) cage in R8C6 (step 4e) = {38}9/{47}9/{58}7
8c. Combined 23(4) cage + R89C6 = {2579}{38}/{3479}{58}/{3569}{47}, 3,5,7 locked for N8, clean-up: no 4,6,8 in R6C3 (step 2a)
8d. R9C7 = 7,9 -> R7C56 + R9C4 = 9,11 and must contain 1 in R7C56 = {126/128/146}
8e. 8 of {128} must be in R9C4 -> no 8 in R7C5

9. 14(4) cage at R4C6 = {1247/1256/1346/2345}
9a. 45 rule on N6 3 innies R5C78 + R6C9 = 14 = {167/347/356} (cannot be {257} which clashes with R6C78), no 2
9b. 3 of {347} must be in R6C9 (cannot be {37}4 because 14(4) cage cannot contain both of 3,7), no 4 in R6C9
9c. R79C7 = R6C9 + 10 (step 5e)
9d. R6C9 = {356} -> R79C7 = 13,15,16 = [49/67/69/79], no 5 in R7C7

[I ought to have seen the first part of this step sooner. Step 10 has been available immediately after doing Prelims, but the key step 10a depended on R9C4 being reduced to 4,8 in steps 8c and 10]
10. 6 in N7 only in R7C123 + R8C3 + R9C123, CPE no 6 in R9C4, clean-up: no 5 in R6C3 (step 2a)
10a. R9C4 ‘sees’ all cells in N7 except for R8C12, R9C4 = {48} -> R8C12 must contain at least one of 4,8 = {48}, locked for R8 and N7, clean-up: no 5,9 in R9C12
10b. Naked pair {67} in R9C12, locked for R9 and N7 -> R9C7 = 9, R89C6 = 11 = [38/74]
10c. Naked pair {48} in R9C46, locked for R9 and N8
10d. 45 rule on N9 1 remaining innie R7C7 = 1 outie R6C9 + 1 -> R6C9 + R7C7 = [34/56/67]
10f. 13(3) cage at R6C6 = {157/247/256} (cannot be {346} = [364] which clashes with R6C9 + R7C7 = [34], IOD clash), no 3
10g. 7 of {247} must be in R7C7 -> no 4 in R7C7, clean-up: no 3 in R6C9
10h. R7C7 = {67} -> no 6 in R67C6
10i. 4,5 of {157/247/256} only in R6C6 -> R6C6 = {45}
10j. Killer pair 4,5 in R6C6 and R6C78, locked for R6 -> R6C9 = 6, R1C89 = [68]
10k. R6C9 = 6 -˃ R79C7 = 16 (step 5e) = [79]
10l. R7C8 + R8C7 = [86] (hidden pair in N9) = 14 -˃ R89C8 = 4 = {13}, locked for C8 and N9, clean-up: no 5 in R6C7
10m. Naked pair {25} in R89C9, locked for C9 -> R7C9 = 4, R2C89 = [49], clean-up: no 2 in R6C7
10n. R4C8 = 9 (hidden single in N6) -> R45C9 = 8 = {17}, locked for C9 and N6
10o. R5C8 = 5, R6C78 = [42], R5C7 = [35] = 8 -> R45C6 = 6 = {24}, locked for C6 and N6, R67C6 = [51], R9C46 = [48], R8C6 = 3 (hidden single in C6), R89C8 = [13], R9C359 = [152], R8C9 = 5, R3C89 = [73], R23C6 = [76], R6C3 = 7 (step 2a), clean-up: no 1 in R12C5 (step 4)
10p. R12C5 = [42], R37C5 = [86]
10q. R3C34 = [95] -> R4C4 = 6 (cage sum), clean-up: no 1 in R4C2
10r. Naked pair {13} in R12C4, locked for C4, R1C3 = 5 (cage sum), R78C3 = [32], R4C3 = 4 -> R4C2 = 3
10s. R37C5 = [86] = 14 -> R456C5 = 13 = [193] (only remaining permutation)
10t. R5C34 + R6C4 = [678] = 21 -> R5C2 = 2
10u. R2C3 = 8 -> R123C2 = 11 = [164] (only remaining permutation)

and the rest is naked singles.

Rating Comment:
I'll rate my WT for A356 at Easy 1.5. I used a 'sees all except' step and an IOD clash.


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 Post subject: Re: Assassin 356
PostPosted: Mon Aug 27, 2018 7:54 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Love 10a Andrew! I found a different way to work in that area. Looks like my step 3 made a big difference too.

A356 WT
start:
Preliminaries
Cage 6(2) n6 - cells only uses 1245
Cage 14(2) n3 - cells only uses 5689
Cage 7(2) n4 - cells do not use 789
Cage 12(2) n7 - cells do not use 126
Cage 13(2) n7 - cells do not use 123
Cage 13(2) n3 - cells do not use 123
Cage 9(3) n12 - cells do not use 789
Cage 20(3) n89 - cells do not use 12
Cage 20(3) n125 - cells do not use 12
Cage 14(4) n56 - cells do not use 9

No clean-up done unless stated.
1. 1,2,3 in n3 only in 35(7) = {1235789}(no 4,6)

2. 4 in n3 only in 13(2) = {49} only: both locked for r2, 9 for n3
2a. -> 14(2)n3 = {68} only: both locked for r1, 8 for n3
2b. -> 8 which must be in 35(7) only in r4c7 -> r4c7 = 8
2c. and same logic for 9 -> r1c6 = 9

3. 31(7)r6c3 = {1234579/1234678} (note: can't have both 5 & 6)
3a. must have 1,2 for n7 -> no 1,2 in r6c3 + r9c4
3b. "45" on n7: 2 outies r6c3 + r9c4 = 11
3c. but can't be {56} in a 31(7) cage
3d. = {38/47}(no 5,6,9)

4. "45" on c6789: 2 innies r23c6 = 13 = {58/67}(no 1,2,3,4) = 5/6
4a. r23c6 = 13 -> r12c5 = 6 = {15}/[24](no 3,6,7,8; no 2 in r1c5)

5. 20(3)r8c6, {569} as {56}[9] only blocked by h13(2) (step 4.)
5a. = {389/479/578}(no 6)

6. "45" on c1234: 2 outies r89c5 = 12 = {39/48/57}(no 1,2,6)
6a. -> r78c4 = 11 (no 1)

7. hidden killer triple 1,2,6 in n8 -> r7c56 from {126} only
7a. & h11(2)r78c4 = {29/56}(no 3,4,7,8)
7b. 1 in n8 only in r7: locked for r7

8. 23(4)r7c4 must have {29/56} for r78c4 = {2489/2579/3569/4568} = 5/8 (no eliminations yet)

9. 20(3)r8c6: {578} as {58}[7] blocked by 23(4)n8 (step 8)
9a. {578} as {78}[5] blocked by h13(2)r23c6 = 7/8
9b. -> 20(3) = {389/479}(no 5)
9c. must have 9 -> r9c7 = 9

10. "45" on n8: 3 innies r7c56 + r9c4 = 11 and must have 1 for n8 = {12}[8]/{16}[4], r9c4 = (48)
10a. -> r6c3 = (37)(h11(2)r6c3+r9c4)

11. 13(2)n7 = {58/67}(no 4) = 5/7

12. 12(2)n7: {57} blocked by 13(2)n7; 12(2) = {39/48}(no 5,7)

13. 31(7)r6c3 = {1234579/1234678}: note, can't have both 5 and 8
13a. 5 in n7 only in 13(2) = {58} or in 31(7) -> 8 in 31(7) (note: all those 8's see 13(2)) must also have 5 or there would be no 5 for n7
13b. -> {1234678} blocked (since no 5) (Locking-out cages)
13c. = {1234579}(no 8)
13d. r9c4 = 4, r6c3 = 7 (outies n7 = 11)

cracked
Cheers
Ed


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 Post subject: Re: Assassin 356
PostPosted: Fri Aug 31, 2018 4:57 pm 
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Grand Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Just in time before the next one (I hope :) )

Thanks Ed - not too difficult this time. Cheers.

Assassin 356 WT:
1. Outies n3 = +17(2) = {89}
-> Both (89) in the 14(2) and 13(2) in n3
Since 35(7) must contain a 5 -> 14(2)n3 = {68} and 13(2)n3 = {49}
-> r1c6 = 9 and r4c7 = 8

2. Innies c6789 = r23c6 = +13(2)
-> r23c6 from {58} or {67}
Also r12c5 = +6(2)
-> r89c5 = +12(2)

3. Min r1234567c6 = +32(7)
-> Max r89c6 = +13(2)
-> Min r9c7 = 7
-> r9c7 from (79)

4. Outies n7 = +11(2)
31(7)r6c3 = {12347(68|59)}

Trying 13(2)n7 = {49} puts r6c3 = 4 and r9c4 = 7
Contradicts r9c7 from (79)

-> 13(2)n7 from {67} or {58}
Both of them prevent 20(3)r8c6 from being [{58}7]
-> r9c7 = 9
-> 20(3)r8c6 from [{38}9] or [{47}9]

5! -> Either 13(2)n7 = {58}, 12(2)n7 = {39}, r6c3 = 8, r9c4 = 3
-> or 13(2)n7 = {67}, r6c3 = 7, r9c4 = 4, 12(2)n7 = {48}

-> r9c4 from (34)
-> (34) in n8 locked in r9c4 and r89c6
-> H+12(2)r89c5 = {57}

6. Continuing
-> 20(3)r8c6 = [{38}9]
-> 23(4)n8 = [{29}{57}]
Also r9c4 = 4
-> r6c3 = 7
Also 12(2)n7 = {48}
-> r89c6 = [38]
Also -> 13(2)n7 = {67}
-> r89c5 = [75]
Also 19(4)n2 = [{24}{67}]
-> r7c56 = [61]
-> 13(3)r6c6 = [517]
-> r45c6 = {24}
Also 6(2)n6 = {24}
Also r6c9 = 6
-> 14(2)n3 = [68]
-> HS 8 in n9 -> r7c8 = 8
-> 18(4)n9 = [8613]
-> 17(4)r6c9 = [6452]
Also r9c3 = 1

7! Remaining cells in n2 = r123c4 and r3c5 = {1358}
-> 9(3)r1c3 = {135} with 1 in r12c4 (since 1 already in c3)
Also 8 in r3c34

Innies - Outies n1 -> r13c3 = r4c1 + 9
-> Min r13c3 = +10(2)

Since r1c3 from (35)
-> Min r3c3 = 6

-> Only solution for 20(3)r3c3 = [956]
-> 9(3)r1c3 = [5{13}]
Also r3c5 = 8
-> r56c4 = [78]

8. Continuing again
Remaining Outies n1 -> r4c1 = 5
-> 7(2)n4 = {34}
Also r7c2 = 5
-> 31(7)r6c3 = [7953214]
-> r5c23 = [26]
-> 18(3)n4 = [819]
etc.


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