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Ed
 Post subject: Assassin 243
PostPosted: Fri Aug 03, 2012 8:12 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Olympic level Assassin! Take your time with this one. It gets a "high" score (low compared to Pinata's puzzle 2!) of 1.85. However, it didn't feel that difficult with an advanced move available. This is a puzzle that my solvers order on Jsudoku solves very easily which is why I tried it.

Assassin 243
Image
code: paste into solver:
3x3::k:8704:8704:8704:6145:6145:7170:7170:7170:7170:8704:8704:6145:2819:2819:6145:7684:7170:7170:8704:7685:7685:7685:2566:7684:7684:7684:7170:4615:7685:3592:7685:2566:7684:6665:1802:1802:4615:3592:7685:7685:6665:6665:6665:3595:3595:4615:1804:3592:1805:1805:4110:4110:2319:3595:4368:1804:4369:4369:4369:4110:2319:2319:3858:4368:3603:2836:2836:3605:2070:2070:3863:3858:4368:3603:3603:3605:3605:2328:2328:3863:3858:
corrected solution: 
+-------+-------+-------+
| 3 9 8 | 6 4 2 | 1 5 7 |
| 1 7 5 | 8 3 9 | 2 6 4 |
| 6 2 4 | 5 1 7 | 8 9 3 |
+-------+-------+-------+
| 2 8 3 | 7 9 4 | 5 1 6 |
| 9 5 1 | 3 6 8 | 7 4 2 |
| 7 4 6 | 2 5 1 | 9 3 8 |
+-------+-------+-------+
| 8 3 9 | 1 7 6 | 4 2 5 |
| 4 6 2 | 9 8 5 | 3 7 1 |
| 5 1 7 | 4 2 3 | 6 8 9 |
+-------+-------+-------+

Cheerio
Ed
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Andrew
 Post subject: Re: Assassin 243
PostPosted: Tue Aug 28, 2012 11:57 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for a really challenging Assassin. Of course V1 Assassins can't be left unsolved; I know that you always solve your killers before you post them.

Because I found it so hard, I suspect that I probably missed the advanced move which you said didn't make it feel difficult.

Maybe if I'd spotted step 23b sooner, I would have found it easier; I'd seen step 23a a lot earlier.

When I first started working on this puzzle I had a mental aberration:
I thought I'd found a 45 which gave R6C7 = R5C5 + 3 (which it is, when the puzzle has been solved). Not sure why I thought I'd thought that. I mention it because it led to the interesting and useful R5C6 + R456C7 = 29 (repeats possible). Then, as shown below, I had another aberration with my original step 25.

Many thanks Ed for pointing out (by PM) that my original step 25 was incorrect. I've added a note about this, showing how I went wrong. Then I’ve re-worked from that stage; I hope I’ve got it right now. I’ve also corrected an earlier typo and added a clarification.

Thanks also Ed for being patient and giving me the chance to re-work my later steps, before you post your optimised walkthrough showing us how this Assassin should be solved.

Here is my walkthrough for Assassin 243:
Prelims

a) R2C45 = {29/38/47/56}, no 1
b) R34C5 = {19/28/37/46}, no 5
c) R4C89 = {16/25/34}, no 7,8,9
d) R67C2 = {16/25/34}, no 7,8,9
e) R6C45 = {16/25/34}, no 7,8,9
f) R8C34 = {29/38/47/56}, no 1
g) R8C67 = {17/26/35}, no 4,8,9
h) R89C8 = {69/78}
i) R9C67 = {18/27/36/45}, no 9
j) 9(3) cage at R6C8 = {126/135/234}, no 7,8,9
k) 26(4) cage at R4C7 = {2789/3689/4589/4679/5678}, no 1
l) 28(7) cage at R1C6 = {1234567}, no 8,9

1. 45 rule on C1 3 outies R1C23 + R2C2 = 24 = {789}, locked for N1
1a. 45 rule on C1 3 innies R123C1 = 10 = {136/145/235}

2. 45 rule on R89 2 outies R7C19 = 13 = {49/58/67}, no 1,2,3

3. 45 rule on R6789 3 innies R6C139 = 21 = {489/579/678}, no 1,2,3

4. 45 rule on C6789 1 innie R2C6 = 1 outie R5C5 + 3, no 1,2,3,4 in R2C6, no 7,8,9 in R5C5
4a. 26(4) cage at R4C7 = {2789/3689/4589/4679/5678}
4b. 2 of {2789} must be in R5C5 -> no 2 in R4C7 + R5C67

5. 45 rule on R12 2 outies R3C19 = 1 innie R2C7 + 7
5a. Max R3C19 = 13 -> max R2C7 = 6
5b. R3C78 = {89} (hidden pair in N3), locked for R3 and 30(5) cage at R2C7, no 8,9 in R4C6, clean-up: no 1,2 in R4C5
5c. Killer pair 8,9 in R3C8 and R89C8, locked for C8

6. 45 rule on N3 (using R3C78 = {89} = 17) 1 outie R1C6 = 1 innie R2C7, no 7 in R1C6
[Alternatively 7 in N3 only in …, but R1C6 = R2C7 is potentially simpler for later clean-ups.]

7. 45 rule on R789 2 outies R6C28 = 1 innie R7C6 + 1
7a. Min R6C28 = 3 -> min R7C6 = 2

8. 45 rule on N6 4 innies R456C7 + R6C8 = 24 cannot be {1689} which clashes with R3C7, no 1 in R6C78
8a. R456C7 + R6C8 must contain one of 8,9 (because {4567} only totals 22)
8b. Killer pair 8,9 in R3C7 and R456C7, locked for C7, clean-up: no 1 in R9C6
8c. Hidden killer pair 8,9 in R456C7 and 14(3) cage at R5C8 for N6, R456C7 contains one of 8,9 -> 14(3) cage must contain one of 8,9 = {149/158/239/248}, no 6,7
8d. 7 in N6 only in R456C7, locked for C7, clean-up: no 1 in R8C6, no 2 in R9C6

9. 45 rule on N9 3(1+2) outies R6C8 + R89C6 = 11
9a. Min R6C8 + R8C6 = 4 -> max R9C6 = 7, clean-up: no 1 in R9C7
9b. Min R6C8 + R9C6 = 5 -> max R8C6 = 6, clean-up: no 1 in R8C7
9c. Min R89C6 = 6 (cannot be [23] which would make R89C7 = [66]) -> max R6C8 = 5
9d. R8C34 = {29/38/47} (cannot be {56} which clashes with R8C67), no 5,6 in R8C34

10. Hidden killer pair 8,9 in 14(3) cage at R5C8 and 15(3) cage at R7C9 for C9, 14(3) cage contains one of 8,9 in C9 -> 15(3) cage must contain one of 8,9 = {159/249/258/348} (cannot be {168} which clashes with R89C8), no 6,7, clean-up: no 6,7 in R7C1 (step 2)

11. 7 in N9 only in R89C8 = {78}, locked for C8 and N9 -> R3C78 = [89], clean-up: no 5 in R7C1 (step 2)
11a. 15(3) cage at R7C9 (step 10) = {159/249}, no 3, 9 locked for C9
11b. 14(3) cage at R5C8 (step 8c) = {158/248}, no 3
11c. R4C89 = {16/34} (cannot be {25} which clashes with 14(3) cage), no 2,5 in R4C89

12. 7,9 in N6 only in R456C7, R456C7 + R6C8 = 24 (step 8) = {2679/3579}, no 4
12a. 2 of {2679} must be in R6C8 -> no 2 in R6C7

13. 26(4) cage at R4C7 = {2789/3689/4589/4679/5678}
13a. 8 of {3689/4589/5678} must be in R5C6 -> no 3,5 in R5C6
13b. 5 of {4589/5678} must be in R45C7 (R5C56 cannot be [58] which clashes with R2C6 + R5C5 = [85] (step 4), combo clasher), no 5 in R5C5, clean-up: no 8 in R2C6 (step 4)
13c. R5C56 + R45C7 = {4679} can only be {46}{79}/[49]{67} (cannot be [47]{69} which clashes with R2C6 + R5C5 = [74] (step 4), combo clasher), no 7 in R5C6

14. 17(3) cage at R7C3 = {179/269/278/368/467} (cannot be {359/458} which clash with R7C19), no 5

15. R6C139 (step 3) = {489/579/678}
15a. 5 of {579} only in R6C9 -> no 5 in R6C13

16. 45 rule on N9 4 innies R7C78 + R89C7 = 15 = {1356/2346}
16a. Killer pair 1,4 in 9(3) cage at R6C8 and 15(3) cage at R7C9, locked for N9, clean-up: no 5 in R9C6

17. 45 rule on R789 4 innies R7C2678 = 15 = {1239/1257/1347/1356/2346} (cannot be {1248} which clashes with 17(3) cage at R7C3), no 8
17a. 8 in C6 only in R56C6, locked for N5, clean-up: no 2 in R3C5

18. 16(3) cage at R6C6 = {169/259/268/349/358/367/457} (cannot be {178} because 1,8 only in R6C6)
18a. Hidden killer triple 7,8,9 in R6C139 and 16(3) cage for R6, R6C139 contains two of 7,8,9 -> 16(3) cage must contain one of 7,8,9 in R6, only one of 7,8,9 in 16(3) cage -> no 7,9 in R7C6

19. R7C2678 (step 17) = {1356/2346}, 3,6 locked for R7
19a. 9(3) cage at R6C8 must contain one of 1,4 in R7C78 -> no 1,4 in R7C26, clean-up: no 3,6 in R6C2
19b. Killer pair 4,5 in R7C19 and R7C2678, locked for R7

20. 17(3) cage at R7C1 = {179/269/278/368/458/467} (cannot be {359} which clashes with R123C1)
20a. 9 of {179/269} must be in R7C1 -> no 9 in R89C1

21. 16(3) cage at R6C6 (step 18) = {169/259/268/349/358/367} (cannot be {457} which clashes with R6C139)

22. 45 rule on N4 3 innies R46C2 + R5C3 = 13
22a. 30(7) cage at R3C2 = {1234569/1234578}
22b. 8 of {1234578} only in R4C2 + R5C3 -> 7 of {1234578} must be in R345C4 (because R4C2 + R5C3 cannot total more than 12), no 7 in R4C2 + R5C3

23. R456C7 + R6C8 (step 12) = {2679/3579}
23a. 45 rule on N9 2 innies R89C7 = 1 outie R6C8 + 6
23b. R6C8 = {235} -> R89C7 = 8,9,11 = {35/36/56} (cannot be {26} which clashes with R456C7 + R6C8 = {679}2, killer combo clash), no 2 in R89C7, clean-up: no 6 in R8C6, no 7 in R9C6

24. R127C7 = {124} (hidden triple in C7), clean-up: R1C6 = {124} (step 6)

[At this stage my original next step was Hidden killer pair 2,4 in 9(3) cage at R6C8 and 15(3) cage at R7C9 for N9, 15(3) cage contains one of 2,4 -> 9(3) cage must contain one of 2,4 = {126/234} (cannot be {135} which doesn’t contain 2 or 4), no 5 in R67C8. Ed pointed out that this is incorrect because 15(3) cage = {159/249} contains both or neither of 2,4. There is, in fact, a hidden killer pair 2,4 in 9(3) cage at R6C8 and 15(3) cage at R7C9 for N9 but it is that 15(3) cage contains both or neither of 2,4 -> 9(3) cage must contain both or neither of 2,4 in R7C78, which doesn’t eliminate any combinations from the 9(3) cage but does provide a different elimination.]

25. Hidden killer pair 2,4 in 9(3) cage at R6C8 and 15(3) cage at R7C9 for N9, 15(3) cage contains both or neither of 2,4 -> 9(3) cage at R6C8 must contain both or neither of 2,4 in R7C78
25a. R7C2678 (step 19) = {1356/2346}
25b. 2,4 of {2346} must be in R7C78 (because of hidden killer pair) -> no 2 in R7C26, clean-up: no 5 in R6C2
25c. 1 of {1356} must be in R7C7 -> no 1 in R7C8

26. R89C7 (step 23b) = {35/36/56} = [35/53/36/63/65] (cannot be [56] because R89C6 cannot be [33]) -> R89C6 = [54/36/53/26/24]
26a. 45 rule on N3 3 outies R134C6 = 13 = {157/247} (cannot be {256/346} which clashes with R89C6), no 3,6, 7 locked for C6, clean-up: no 4 in R5C5 (step 4)
26b. 1 of {157} must be in R1C6 -> no 1 in R34C6
26c. R89C6 = [36/53/26/24] (cannot be [54] which clashes with R134C6) -> R89C7 = [53/36/63/65]

27. 26(4) cage at R4C7 = {2789/3689/4679/5678} (cannot be {4589} because R5C5 only contains 2,3,6)
27a. 4,8 only in R5C6 -> R5C6 = {48}

28. R89C6 (step 26c) = [36/53/26/24]
28a. Consider combinations for R134C6 (step 26a) = {157/247}
R134C6 = {157} => R89C6 = [26/24] (cannot be [36] which clashes with R7C6 which only contains 3,6 when R134C6 = {157}), 2 locked for C6
or R134C6 = {247}, 2 locked for C6
-> 2 must be in R134C6 + R8C6, locked for C6

29. 16(3) cage at R6C6 (step 21) = {169/349/358/367}
29a. 1,4 of {169/349} must be in R6C6 -> no 9 in R6C6
29b. 8 of {358} must be in R6C6 -> no 5 in R6C6
29c. 5 of {358} must be in R7C6 (R6C67 cannot be [85] which clashes with R6C139) -> no 5 in R6C7
29d. 7,9 of {169/367} must be in R6C7 -> no 6 in R6C7

30. 45 rule on R789 4 outies R6C2678 = 17 = {1259/1349/1367/1457/2357} (cannot be {1268} because 6,8 only in R6C6, cannot be {1358/2456} which clash with R6C45, cannot be {2348} because no 2,3,4,8 in R6C7), no 8
30a. 7,9 only in R6C7 -> R6C7 = {79}
30b. 5 of {1259/2357} must be in R6C8 -> no 2 in R6C8

31. R25C6 = [98] (hidden pair in C5), R5C5 = 6 (step 4), R6C9 = 8 (hidden single in N6), clean-up: no 2,5 in R2C4, no 2 in R2C5, no 4 in R34C5, no 1 in R6C45
31a. Killer pair 3,5 in R6C45 and R6C8, locked for R6
[Seems to be cracked at last.]

32. 9(3) cage at R6C8 = {135/234} (cannot be {126} because R6C8 only contains 3,5), no 6

33. 6 in N6 only in R4C89 = {16}, locked for R4 and N6
33a. R5C89 = {24} (hidden pair in N6)

34. 16(3) cage at R6C6 (step 29) = {169/349/367}, no 5

35. R89C6 (step 26c) = [53/26/24] (cannot be [36] which clashes with R7C6, no 3 in R8C6, clean-up: no 5 in R8C7
35a. 3 in C7 only in R79C6, locked for C6, clean-up: no 8 in R8C3

36. 15(3) cage at R7C9 (step 11a) = {159} (only remaining combination, cannot be {249} which clashes with R5C9), locked for C9 and N9 -> R4C89 = [16], clean-up: no 4 in R9C6
36a. R7C78 = {24} (hidden pair in N9), locked for R7, R6C8 = 3 (step 32), clean-up: no 4 in R6C45
36b. Naked pair {25} in R6C45, locked for N5
36c. Naked pair {36} in R9C67, locked for R9
36d. Naked pair {24} in R57C8, locked for C8

37. R7C19 (step 2) = {58} (only remaining combination) -> R7C1 = 8, R7C9 = 5, clean-up: no 2 in R6C2
37a. R7C1 = 8 -> R89C1 = 9 = {27/45} (cannot be {36} which clashes with R7C2), no 1,3,6
37b. R123C1 (step 1a) = {136/145} (cannot be {235} which clashes with R89C1), no 2, 1 locked for C1 and N1

38. R5C56 = [68] = 14 -> R45C7 = 12 = {57}, locked for C7 -> R6C7 = 9

39. R6C9 = 8 -> R6C139 (step 3) = {678} (only remaining combination) -> R6C12 = {67}, locked for R6 and N4

40. 9 in C1 only in R45C1, locked for N4
40a. R46C2 + R5C3 = 13 (step 22) = {148} (only remaining combination, cannot be {238} because R6C2 only contains 1,4) -> R4C2 = 8, R5C3 = 1, R6C2 = 4, R7C2 = 3, R12C2 = [97], R1C3 = 8, R67C6 = [16], R9C67 = [36], R8C7 = 3, R8C6 = 5, R5C2 = 5, R45C7 = [57], clean-up: no 4 in R2C45, no 1 in R2C7 (step 6), no 8 in R8C4, no 4 in R9C1 (step 37a)

41. R1C7 = 1 (hidden single in C7)

42. 24(4) cage at R1C4 contains 9 = {2679/4569} (cannot be {3579} which clashes with R2C45), CPE no 6 in R1C1 + R2C4, clean-up: no 5 in R2C5
42a. Naked pair {38} in R2C45, locked for R2 and N2, clean-up: no 7 in R4C5
42b. Naked pair {24} in R2C79, locked for R2 and N3
42c. Naked pair {39} in R4C5 + R5C4, locked for N5

43. 30(7) cage at R3C2 contains 8 = {1234578} (only remaining combination), no 6,9 -> R3C2 = 2, R5C4 = 3, R2C45 = [83], R4C5 = 9, R3C5 = 1, R7C5 = 7, R7C34 = [91]

44. 45 rule on N8 1 remaining innie R8C4 = 9, R8C3 = 2

45. 45 rule on N1 2 remaining innies R23C3 = 9 = [54]

and the rest is naked singles.

Rating Comment:
It was difficult to decide what rating to give my walkthrough for A243. I'll go for Hard 1.5, based on my hardest steps, the difficulty in finding steps and the length of my walkthrough.
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Ed
 Post subject: Re: Assassin 243
PostPosted: Thu Sep 06, 2012 9:58 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
This is how I cracked this one. Andrew did the earlier placements a slightly different way, then we kept making key eliminations in the same areas but for different reasons. Really pleased that Andrew found a way to use the weird 30(7) cage at r3c2 (his step 22). I was hoping to find a puzzles that required that cage but this one won out. As usual, this optimised walkthrough makes it seem a lot easier than it felt - very, very tough.

A243
26 steps:
Please let me know if anything could be clearer or is incorrect. [Thanks Andrew!]

1. 28(7)r1c6 = {1234567}(no 8,9)
1a. 7(2)n6: no 7,8,9
1b. -> hidden killer pair 8,9 in c9 because 14(3) and 15(3) cages cannot have both of 8&9
1c. 14(3)n6 must have 8/9 = {149/158/239/248}(no 6,7)
1d. cannot have both 8&9 -> 8 or 9 must be in c9 -> no 8,9 in r5c8
1e. 15(3)n9 must have 8/9 -> max. other two cells = 7 (ie no 7 in r789c9)

2. 9(3)r6c8: no 7,8,9
2a. 7 in n6 only in c7: 7 locked for c7

3. 7 in n9 only in 15(2) = {78} only: both locked for n9 and c8

4. Hidden single 9 in c8 -> r3c8 = 9

5. "45" on c1: 3 outies r12c2+r1c3 = 24 = {789} only: all locked for n1

6. "45" on r12: 2 outies r3c19 - 7 = 1 innie r2c7
6a. max. r3c19 = 13 -> max. r2c7 = 6 (no 8)

7. Hidden single 8 in n3 -> r3c7 = 8

8. r1c6 sees all n3 except r2c7+r3c78: can't repeat in the latter two (no common digits) -> r1c6=r2c7 (no 7) [Andrew saw this using "45" on n3: an easier way]
8a. "45" on c89: 3 outies r1c67+r7c7 = 7
8b. r1c6=r2c7 -> r127c7 = 7 = {124}, locked for c7
8c. r1c6 = (124)

9. 8(2)r8c6 = {35}[26](no 1,4,7,8,9; no 6 in r8c6)
9a. 9(2)r9c6 = {36}/[45](no 1,2,7,8,9; no 5 in r9c6)
9b. 8(2) is 1 less than 9(2) -> r89c6 cannot have a difference of -1 since it forces r89c7 to be equal (CCC)(no eliminations yet)

10. "45" on n3: 3 outies r134c6 = 13
10a. but {256} forces r89c6 = [34] which is blocked (step 9b)
10b. {346} blocked by r9c6 = (346)
10c. = {157/247}(no 3,6)
10d. must have 7 -> 7 locked for c6

11. "45" on c6789: 1 outie r5c5 + 3 = 1 innie r2c6
11a. no 1,2,3 in r2c6: no 4,7,8,9 in r5c5

12. 26(4)r4c7: {4589} blocked by 4&8 only in r5c6
12a. = {2789/3689/4679/5678}(no 1)
12b. must have 4 or 8 -> r5c6 = (48)
12c. no 4 in r2c6 (IODc6789 = +3)

13. "45" on n6789: 2 outies r6c26 + 7 = 2 innies r45c7
13a. max. r45c7 = 16 -> max. r6c26 = 9 (no 9)
13b. 7(2)r6c2: no 7,8,9

14. "45" on n6: 4 innies r456c7+r6c8 = 24 and must have 7 & 9 for c7 -> other two cells = 8 = {35/26}(no 1,4)
14a. 2 in {26} must be in r6c8 -> no 6 in r6c8
14b. 9 locked for n6

15. "45" on r789: 2 outies r6c28 - 1 = 1 innie r7c6
15a. no way for r6c28 to sum to 10 -> no 9 in r7c6

16. Hidden single 9 in c6 -> r2c6 = 9
16a. -> r5c5 = 6 (IODc6789 = +3)

17. 7(2)n5 = {25/34}(no 1,7,8,9)
17a. Combined half-cage with r6c8 -> 3 locked for r6
17b. no 4 in r7c2

18. Combined half-cage h13(3)r134c6+r5c6 = {247[8]}/{157}(4/8) = [1/8, 4/5..]
18a. -> 16(3)r6c6: r6c7+r67c6 = [7]{18} blocked
18b. [7]{36} blocked by no 3 or 6 only in r6c6
18c. [7]{45} blocked by h13(3)r134c7 = [4/5..]
18d. -> 16(3) = {169/259/268/349/358}(no 7)

19. 7 in n6 only in 26(4)r4c7 = {4679/5678}(no 3)
19a. 3 in c7 only in n9: 3 locked for n9

20. "45" on r6789: 3 innies r6c139 = 21 = {489/579/678}(no 1,2)

21. 1 in r6 in 16(3)r6c6 = [196](step 18d) or in 7(2)r6c2 -> 6 locked in r7c26 for r7 (Locking Cages)

22. 9(3)r6c8 = {135/234}
22a. must have 3 -> r6c8 = 3

23. "45" on n9: 2 remaining innies r89c7 = 9 and must have 3 for n9 = {36} only: 6 locked for c7 & n9
23a. no 3 in r8c6; no 4 in r9c6

24. 7(2)n5 = {25} only: both locked for r6 and n5
24a. no 2,5 in r7c2

25. "45" on n6: 1 remaining outie r5c6+1 = 1 remaining innie r6c7 = [89] only

26. 6 in n6 only in 7(2) = {16}: both locked for r4 and n6



on from there.
Cheerio
Ed
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