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Ed
 Post subject: Assassin 70 V2 Revisit
PostPosted: Sun Oct 02, 2022 7:56 am 
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Assassin 70v2
Thanks to Andrew for noticing I missed this puzzle as a Revisit. Looks like it has at least one really nice feature to it from the comments in the archive. It gets 1.65. JSudoku has to work so its no gimmee.
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:5888:1793:4866:4866:4356:3845:3845:1287:4872:5888:1793:4866:5132:4356:3598:3845:1287:4872:5888:2579:2579:5132:4356:3598:4888:4888:4872:5888:6684:2579:5132:4383:3598:4888:3618:4872:6684:6684:6684:4383:4383:4383:3618:3618:3618:2349:5166:815:1328:3633:3634:2355:5172:2869:2349:5166:815:1328:3633:3634:2355:5172:2869:2367:5166:4929:4929:3633:2884:2884:5172:3911:2367:2367:4929:5451:5451:5451:2884:3911:3911:
Solution: 
+-------+-------+-------+
| 9 6 4 | 8 7 2 | 5 1 3 |
| 5 1 7 | 6 9 3 | 8 4 2 |
| 8 2 3 | 5 1 4 | 9 7 6 |
+-------+-------+-------+
| 1 4 5 | 9 2 7 | 3 6 8 |
| 7 9 6 | 3 4 8 | 1 2 5 |
| 3 8 2 | 1 6 5 | 7 9 4 |
+-------+-------+-------+
| 6 5 1 | 4 3 9 | 2 8 7 |
| 4 7 8 | 2 5 1 | 6 3 9 |
| 2 3 9 | 7 8 6 | 4 5 1 |
+-------+-------+-------+
Cheers
Ed
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Andrew
PostPosted: Fri Oct 07, 2022 2:59 am 
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Thanks Ed for posting this Revisit. I commented on one interesting point which I didn't use because I found a more useful step at that point.

My solving path was fairly long until I got my first placement, then it was straightforward.

Here's how I solved Assassin 70V2 Revisited:
Prelims

a) R12C2 = {16/25/34}, no 7,8,9
b) R12C8 = {14/23}
c) R67C1 = {18/27/36/45}, no 9
d) R67C3 = {12}
e) R67C4 = {14/23}
f) R67C6 = {59/68}
g) R67C7 = {18/27/36/45}, no 9
h) R67C9 = {29/38/47/56}, no 1
i) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
j) 20(3) cage at R2C4 = {389/479/569/578}, no 1,2
k) 10(3) cage at R3C2 = {127/136/145/235}, no 8,9
l) 19(3) cage at R3C7 = {289/379/469/478/568}, no 1
m) 20(3) cage at R6C2 = {389/479/569/578}, no 1,2
n) 20(3) cage at R6C8 = {389/479/569/578}, no 1,2
o) 9(3) cage at R8C1 = {126/135/234}, no 7,8,9
p) 19(3) cage at R8C3 = {289/379/469/478/568}, no 1
q) 11(3) cage at R8C6 = {128/137/146/236/245}, no 9
r) 21(3) cage at R9C4 = {489/579/678}, no 1,2,3
s) 26(4) cage at R4C2 = {2789/3689/4589/4679/5678}, no 1
t) 14(4) cage at R4C8 = {1238/1247/1256/1346/2345}, no 9

1a. Naked pair {12} in R67C3, locked for C3
1b. 10(3) cage at R3C2 = {136/145/235} (cannot be {127} because 1,2 only in R3C2), no 7
1c. -> R3C2 = {12}
1d. Combined half cage R7C3 + 9(3) cage at R8C1 = 10,11 = {1234/1235}, no 6, 1,2,3 locked for N7, clean-up: no 6,7,8 in R6C1
1e. 45 rule on C12 1 outie R5C3 = 1 innie R3C2 + 4, R3C2 = {12} -> R5C3 = {56}
1f. 45 rule on C12 3 outies R345C3 = 14 = {356} (only remaining combination), locked for C3
1g. 45 rule on C123 2 outies R18C4 = 10 = {28/37/46}, no 5,9
1h. 45 rule on C1234 2 innies R59C4 = 10 = [19/28/37/46/64], no 5 -> R5C4 = {12346}
1i. 5 in C4 only in 20(3) cage at R2C4 = {569/578}, no 3,4
1j. 1 in C4 only in R59C4 = [19] or R67C4 = {14} -> R59C4 = [19/28/37] (cannot be {46}, blocking cages), no 4,6
[That would also have eliminated {479} from 20(3) cage if that hadn’t been eliminated in step 1i.
Before I saw the step this way I was looking at the interactions between 21(3) cage at R9C4 and R5C46; they eliminated R59C4 = [64] but not [46].]
1k. 45 rule on C6789 2 innies R59C6 = 14 = {59/68}
1l. Naked quad {5689} in R5679C6, locked for C6
1m. 14(3) cage at R2C6 = {347} (only remaining combination), locked for C6
1n. Max R1C6 = 2 -> min R12C7 = 13, no 1,2,3 in R12C7
1o. 45 rule on C89 1 innie R3C8 = 1 outie R5C7 + 6 -> R3C8 = {789}, R5C7 = {123}
1p. 26(4) cage at R4C2 = {3689/4589/4679/5678} (cannot be {2789} because R5C3 only contains 5,6), no 2
1q. 45 rule on C1 1 innie R5C1 = 1 outie R9C2 + 4 -> min R5C1 = 5
1r. 3 in N7 only in 9(3) cage at R8C1 = {135/234}
1s. 45 rule on C1 3 innies R589C1 = 13 = {139/157/238/247/346} (cannot be {148/256} which aren’t consistent with 9(3) cage) -> R5C1 = {6789}, clean-up: no 1 in R9C2
1t. 1 in C2 only in R123C2, locked for N1

2a. R18C4 (step 1g) = {28/37/46}
2b. 45 rule on N7 4(3+1) outies R6C123 + R8C4 = 15
2c. R6C123 + R8C4 = 15 cannot be {124}8 because R18C4 = [28] clashes with R67C4 = [32] -> no 8 in R8C4, clean-up: no 2 in R1C4
2d. Hidden killer pair 1,2 in 17(3) cage at R1C5 and R1C6 for N2, R1C6 = {12} -> 17(3) cage must contain one of 1,2 = {179/269/278}, no 3,4,5
2e. 5 in N2 only in R23C4 -> no 5 in R4C4
2f. 14(3) cage at R6C5 = {149/158/248/347/356} (cannot be {167/239/257} which clash with 17(3) cage)
2g. 45 rule on C5 3 innies R459C5 = 14 = {149/158/248/347/356} (cannot be {167/239/257} which clash with 17(3) cage)
2h. 19(3) cage at R8C3 = {289/379/469/478}
2i. 3 of {379} must be in R8C4, {478} cannot be [478/874] which clashes with 21(3) cage at R9C4 -> no 7 in R8C4, clean-up: no 3 in R1C4
2j. 3 in N2 only in R23C6 -> no 3 in R4C6
2k. 20(3) cage at R6C2 = {479/569/578} (cannot be {389} which clashes with 19(3) cage), no 3
2l. {479} cannot be 4{79} which clashes with 19(3) cage -> no 4 in R6C2

3a. 45 rule on C9 1 innie R5C9 = 1 outie R9C8, max R5C9 = 8 -> max R9C8 = 8
3b. 14(4) cage at R4C8 = {1238/1247/1256/1346/2345}
3c. Consider placement for 6 in C8
6 in R459C8 => 6 in R45C8 + R5C9 => 14(4) cage = {1256/1346}
or 6 in 20(3) cage at R6C8 = {569}, locked for C8 => R3C8 = {78} => one of 7,8 in R459C8 => one of 7,8 in R45C8 + R5C9 => 14(4) cage = {1238/1247}
-> 14(4) cage = {1238/1247/1256/1346}, 1 locked for N6, clean-up: no 8 in R7C7
[Alternatively 45 rule on N3 and 45 rule on N9 eliminate 1 from R4C9 and R6C7.]

4a. Consider placement for 6 in N7
R7C1 = 6 => R6C1 = 3
or 20(3) cage at R6C2 = {569}, locked for C2 => R12C2 = {34}, locked for C2
-> no 3 in R45C2
4b. Hidden killer triple 1,2,3 in R12C2, R3C2 and R9C2 for C2, R12C2 contains one of 1,2,3, R3C2 = {12} -> R9C2 = {23}, clean-up: no 8,9 in R5C1 (step 1q)
4c. R67C1 = [18/27/36] (cannot be {45} which clash with 9(3) cage at R8C1), no 4,5
4d. 26(4) cage at R4C2 (step 1p) = {4679/5678} (cannot be {4589} because R6C1 only contains 6,7), 6,7 locked for N4
4e. 45 rule on R1234 3 innies R4C258 = 12 = {129/138/156/237/246} (cannot be {147} which clashes with R4C6, cannot be {345} which clashes with R4C3)
4f. 7,8,9 of {129/138/237} must be in R4C2 -> no 7,8,9 in R4C58
4g. R4C258 = {129/138/156/246} (cannot be {237} = 7{23} which clashes with R4C3 + R5C13 only contain 3,5,6,7) -> no 7 in R4C2
4h. 7 in N4 only in R5C12, locked for R5

5a. 19(3) cage at R8C3 (step 2h) = {289/379/469/478} -> R89C3 + R8C4 = {49}6/{78}4/{79}3/{89}2, 20(3) cage at R6C2 (step 2k) = {479/569/578}
5b. Consider placements for R7C1 = {678}
R7C1 = 6 => 20(3) cage at R6C2 = {479/578}, 7 locked for N7 => R89C3 + R8C4 = {49}6/{89}2
or R7C2 = 7 => R89C3 + R8C4 = {49}6/{89}2
or R7C1 = 8 => R6C1 = 1, R67C3 = [21] => R67C4 = [32] => R89C3 + R8C4 = {49}6
-> R89C3 + R8C4 = {49}6/{89}2, no 7 in R89C3, no 3,4 in R8C4, 9 locked for C3 and N7, clean-up: no 6,7 in R1C4 (step 1g)
5c. 21(3) cage at R9C4 = {579/678} (cannot be {489} which clashes with R9C3), no 4, 7 locked for R9 and N8
5d. Killer pair 2,4 in R18C4 and R67C4, locked for C4, clean-up: no 8 in R9C4 (step 1h)

6a. 45 rule on N1 3(2+1) outies R1C4 + R4C13 = 14, R4C13 cannot total 10 -> R1C4 = 8, R4C13 = 6 = [15], R5C13 = [76], naked pair {47} in R12C3, 4 locked for C3 and N1, R6C13 = [32], R3C3 = 3, R3C2 = 2 (cage sum), R9C2 = 3, 20(3) cage at R2C4 = {569} (only remaining combination), 6,9 locked for C4 -> R89C4 = [27], R18C6 = [21]
[Cracked. Fairly straightforward from here; clean-ups omitted]
6b. R4C1 = 1 -> R123C1 = 22 = {589}, 5,8 locked for C1, 5 locked for N1 -> R7C1 = 6
6c. R4C258 (step 4g) = {246} (only remaining combination) -> R4C2 = 4, R4C58 = {26}, locked for R4
6d. R5C13 = [76] = 13 -> R45C2 = 13 = [49], R6C2 = 8, R4C46 = [97], R23C6 = [34]
6e. R67C4 = [14] (only remaining permutation) -> R5C3 = 3
6f. 45 rule on N5 2 remaining innies R6C56 = 11 = {56}, locked for R6 and N5 -> 17(4) cage at R4C5 = [2348]
6g. R67C6 = [59] (only remaining permutation), R9C6 = 6 -> R9C5 = 8 (cage sum)
6h. 45 rule on R89 3 innies R8C258 = 15 = {357} (only possible combination with 3,5,7 in R8C25), locked for R8
6i. R89C1 = [42], R89C3 = [89], R8C67 = [16] -> R9C7 = 4 (cage sum), R6C7 = 7 -> R7C7 = 2
6j. R1C6 = 2 -> R12C7 = 13 = [58], 19(3) cage at R3C7 = [973]
6k. Naked pair {15} in R9C89, 5 locked for N9, R78C8 = [83] -> R6C8 = 9 (cage sum)
6l. R12C8 = {14} (only remaining combination), locked for N3, 1 locked for C8

and the rest is naked singles.
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wellbeback
PostPosted: Wed Oct 12, 2022 6:17 pm 
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Again it took me a long time looking at promising but ultimately futile approaches before I found a relatively simple path here. And again - the key steps are similar to those Andrew used. Thanks Ed!
Assassin 70 V2 WT:
1. 3(2)r6c3 = {12}
-> 9(3)n7 either {135} or {234} (3 locked in 9(3)n7).

2. 10(3)r3c2 must have a 1 or 2 in r3c2
-> (IOD c12) r5c3 from (56)
-> Innies c123 = r1289c3 = +28(4) = {4789}
-> r345c3 = {356} with 3 in r34c3

3. Innies c1 = r589c1 = +13(3)
This cannot contain both (35)
-> 9(3)n7 cannot be [{35}1]
-> 1 in c2 only in n1 (in r123c2)

4. Since r5c3 from (56) -> 2 not in 26(4)n4
-> 2 in c2 only in r1239c2
But 2 not in r9c2 since that puts r89c1 = {34}, 4 in r12c3, and 1 in r3c2 which leaves no solution for 7(2)n1
-> 2 in c2 only in n1 (in r123c2)

5! -> 7(2)n1 from {16} or {25}
-> 6 not in 20(3)c2 (it would be {569})
-> (HS 6 in n7) r7c1 = 6

That essentially cracks it.

6. -> r6c1 = 3
-> r3c3 = 3
-> r9c2 = 3
-> (IOD c1) r5c1 = 7
Also r89c1 from {24} or {15}
-> 23(4)c1 either [{589}1] or [{489}2]
-> r12c3 = {47} and r1c4 = 8
-> 23(4)c1 = [{589}1]
-> 7(2)n1 = {16}
-> 10(3)r3c2 = [235] and r5c3 = 6
Also 3(2)r6c3 = [21]
Also r45c2 = {49}
-> 20(3)c2 = [8{57}]
Also r89c3 = {89} and r8c4 = 2
-> 9(3)n7 = [423]

7. Also 5(2)c4 = [14]
-> 20(3)c4 = {569}
-> r59c4 = [37]

8. Outies c789 = r18c6 = +3(2) = [21]
-> Remaining Innies c6 = r59c6 = +14(2)
-> 14(3)c6 = {347}
-> 1 in n2 only in 17(3)n2 = {179}
-> 14(3)c6 = [347]
Also 20(3)c4 = [{56}9]
-> r45c2 = [49]
Also (Remaining Innies n5 = r6c56 = +11(2)) r6c56 = {56}
-> 17(4)n5 = [2348]
-> 14(2)r6c6 = [59]
-> 21(3)n8 = [786]
-> 14(3)c5 = [6{35}]
Also 14(4)n6 = [6{125}]
etc.
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Ed
PostPosted: Sun Oct 16, 2022 5:28 am 
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Really well done both. I got a long way in but couldn't finally crack it. Enjoyed Andrew's WT especially 2c, 3c and 4g. Well spotted on those. But wellbeback's step 4 (no !) is a cracker. Makes a huge difference. Much better than the best of the archive WTs. Mike might have talked his way up a bit compared to step 4 in wellbeback's. Great work!

Cheers
Ed
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Ed
PostPosted: Sun Nov 13, 2022 3:34 am 
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Here's another way of expressing wellbeback's step 4. I wish I'd found that elimination.
from here end of step 3: 
.-------------------------------.-------------------------------.-------------------------------.
| 23456789  123456    4789      | 23456789  123456789 123456789 | 123456789 1234      123456789 |
| 23456789  123456    4789      | 3456789   123456789 123456789 | 123456789 1234      123456789 |
| 23456789  12        356       | 3456789   123456789 123456789 | 23456789  23456789  123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 123456789 23456789  356       | 3456789   123456789 123456789 | 23456789  12345678  123456789 |
| 23456789  23456789  56        | 123456789 123456789 123456789 | 12345678  12345678  12345678  |
| 12345678  3456789   12        | 1234      123456789 5689      | 12345678  3456789   23456789  |
:-------------------------------+-------------------------------+-------------------------------:
| 1245678   456789    12        | 1234      123456789 5689      | 12345678  3456789   23456789  |
| 12345     456789    4789      | 23456789  123456789 12345678  | 12345678  3456789   123456789 |
| 12345     2345      4789      | 456789    456789    456789    | 12345678  123456789 123456789 |
'-------------------------------.-------------------------------.-------------------------------'

4a. 4 in c3 in r1289c3 -> the 7(2)r1c2 and 9(3)r8c1 cannot both be 4
4b. 2 in 9(3)n7 = {234} only: ie 2 must also have 4
4c. and 2 in r9c2 -> r123c2 = {34}[1]
4d. -> 2 in r9c2 breaks 4a.
4e. -> no 2 in r9c2

Very elegant, I think!
(then need to return to start of wellbeback's step 4 to get some other important eliminations)
Cheers
Ed
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