Assassin 78

[mhparker]

Hi folks,

Happy to be able to post the first WT for a change!

The puzzle proved to be less difficult than Ruud's comments suggested, but very enjoyable nevertheless. Estimated rating: 1.25.


Assassin 78 Walkthrough

Prelims:

a) 24(3) at R1C1 = {789}, locked for N1
b) 11(3) at R1C9, R2C5 and R8C1 = {128/137/146/236/245} (no 9)
c) 11(2) at R3C7 = {29/38/47/56} (no 1)
d) 7(3) at R4C2 = {124}, locked for N4
e) 21(3) at R4C6 = {489/579/678} (no 1..3)
f) 12(2) at R7C2 = {39/48/57} (no 1,2,6)
g) 22(3) at R7C4 = {589/679}, 9 locked for N8
h) 9(2) at R7C7 = {18/27/36/45} (no 9)

1. Innie/Outie difference (I/O diff.), N1: R4C1 = R1C3 + 1
1a. -> no 1,3 in R1C3; no 8,9 in R4C1

2. I/O diff., N3: R1C6 = R3C9 (no eliminations yet)

3. I/O diff., N7: R7C1 = R9C4 + 1
3a. -> no 1 in R7C1

4. I/O diff., N9: R9C7 = R6C9 + 1
4a. -> no 1 in R9C7; no 9 in R6C9

5. I/O diff., N1245: R146C6 = R7C1 + 22
5a. -> R7C1 = 2; R146C6 = {789}, locked for C6
5b. -> R9C4 = 1 (step 3)
5c. cleanup: no 7 in R8C7; R3C9 = {789} (step 2)

6. Naked triple (NT) at R1C126 = {789}, locked for R1

7. 14(3) at R3C4, 11(2) at R3C7 and R3C9 form hidden killer triple type 1:1:1 on {789}
7a. -> no 7,8,9 in R4C4; no 5,6 in R3C78

8. 1 in R7 locked in N9 -> not elsewhere in N9
8a. cleanup: no 8 in R7C7

9. Outies, N8: R6C6 + R9C7 = 12(2) = [75/84/93]
9a. -> R9C7 = {345}
9b. cleanup: R6C9 = {234} (step 4)

10. 2 unavailable to 11(3) at R8C1 = {137/146} (no 5,8)

11. Split 20(3) at R8C3+R9C23 = {389/569/578} (no 4)
(Note: {479} blocked by 12(2) (Prelim f) or 11(3) (step 10) - take your pick)

12. Split 22(3) at R5C1+R6C12 = {589/679} (no 3)
12a. 9 locked for N4

13. 9 in C3 locked in N7 -> not elsewhere in N7
13a. cleanup: no 3 in R7C3

14. I/O diff., N4: R6C4 = R4C1 + 1
14a. -> no 2,3,5,9 in R6C4

15. 17(3) at R5C3 = {368/458/467}
15a. 4 only available in R6C4
15b. -> no 7 in R6C4
15c. cleanup: no 6 in R4C1 (step 14); no 5 in R1C3 (step 1)

16. 15(4) at R2C1 = {1257/1347/1356}
(Note: {2346} blocked by R1C3 or 7(2) at R2C3 - take your pick)
16a. 1 locked for N1
16b. cleanup: no 6 in R23C3

17. Hidden single (HS) in C3 at R4C3 = 1
17a. -> R45C2 = {24}, locked for C2
17b. cleanup: no 8 in R7C3

18. Innies C12: R79C2 = 10(2) = {37} (no 5,6,8) (last combo), locked for C2 and N7
18a. cleanup: no 4 in R7C3

19. HS in N1 at R1C1 = 7
19a. cleanup: no 7 in R3C9 (step 2)

20. Hidden pair (HP) in C1 at R56C1 = {89} (no 5,6), locked for N4
20a. -> R6C2 = 5 (split 22(3) cage sum)

21. Naked single (NS) at R4C1 = 3
21a. -> R1C3 = 2 (step 1), R6C4 = 4 (step 14)
21b. cleanup: no 5 in R9C7 (step 4)

22. 7(2) at R2C3 = {34} (last combo, or HP(C2)), locked for N1

23. 6 in N4 locked in C3 -> not elsewhere in C3

24. I/O diff., N2: R1C6 = R4C4 + 4
24a. -> R1C6+R4C4 = [95]
24b. -> R3C9 = 9 (step 2)
24c. cleanup: no 2 in R3C78

25. R12C2 = [89]

26. Naked pair (NP) at R46C6 = {78}, locked for N5

27. Split 16(3) at R1C45+R2C4 = {358/367} (no 1,4) (all other combos unplaceable)
27a. must have 1 of {78}, only available in R2C4
27b. -> R2C4 = {78} (no 3,6)
27c. 3 locked in R1C45 for R1 and N2

28. {14} in R1 locked in N3 -> not elsewhere in N3

29. 11(2) at R3C7 = {38} (last combo), locked for R3 and N3

30. R23C3 = [34]

31. Split 14(3) at R1C78+R2C7 = {167} (no 2,4,5) (all other combos unplaceable)
31a. -> R2C7 = 7; R1C78 = {16}, locked for R1 and N3
31b. cleanup: no 2 in R8C7

32. HS in C7 at R6C7 = 2

33. NS at R6C9 = 3
33a. -> R9C7 = 4 (step 4)
33b. cleanup: no 5 in R78C7

34. R12C4 = [38]
34a. -> R1C5 = 5

35. 22(3) at R7C4 = {679} (no 8) (last combo)
35a. {67} locked for N8

36. Outie, N8 (step 9): R6C6 = 8
36a. -> split 9(2) at R7C56 = [45] (last combo/permutation)

The rest is now singles and cage sums.

[goooders]

i agree with mhp's rating i suspect the cage pattern could produce something quite nasty however there was one giveaway

[Nasenbaer]

The puzzle proved to be less difficult than Ruud's comments suggested, but very enjoyable nevertheless.

Enjoyable - yes, but I needed more than 4 hours to solve it! Maybe I'm a little rusty.

I think I'll take a closer look at your walkthrough to improve my solving technique.

[Afmob]

I haven't found a fast way to solve it so it took me rather long to solve it. I'm still a bit confused that JSudoku wasn't able to solve it considering it can solve something like the Brick Wall.

Edit: Deleted some steps and correct many typos, thanks Andrew!

A78 Walkthrough:

1. C123
a) 24(3) = {789} locked for N1
b) 7(3) = {124} locked for N4
c) Innies+Outies N1: 1 = R4C1 - R1C3
-> R4C1 <> 8,9; R1C3 <> 1,3
d) Innies+Outies N7: -1 = R9C4 - R7C1
-> R7C1 <> 1, R9C4 <> 9
e) Innies+Outies C123: 3 = R69C4 - R1C3
-> R6C4 <> 9 because R1C3 <= 6

2. R6789
a) 22(3) = 9{58/67} -> 9 locked for N8
b) Innies+Outies N9: -1 = R6C9 - R9C7
-> R9C7 <> 1; R6C9 <> 9
c) Innies+Outies R789: 9 = R6C69 - R7C1
-> R6C69 <> 1 because R7C1 >= 2
d) Innies+Outies R6789: 18 = R5C138 - R6C5
-> R5C8 <> 1; R6C5 <> 7,8,9

3. R1234
a) Innies+Outies R123: -1 = R4C14 - R3C9
-> R3C9 = (56789) since R4C1 >= 3
-> R4C4 <> 6,7,8,9 because R4C1 >= 3
b) Innies+Outies N3: R1C6 = R3C9 = (56789)
c) Innies+Outies R1: 20 = R2C247 - R1C9
-> R1C9 = (1234); R2C47 <> 1,2,3

4. N369
a) Innies+Outies N36: 13 = R14C6 - R6C9
-> R14C6 <> 1,2,3,4,5 because R6C9 >= 2
-> R6C9 = (234)
b) Innies+Outies N9: -1 = R6C9 - R9C7
-> R9C7 = (345)
c) Innies+Outies N3: R1C6 = R3C9 = (6789)

5. N6789
a) Innies+Outies N8: 11 = R6C6+R9C7 - R9C4
-> R6C6 = (789) because R9C7 = (345)
-> R9C4 = (123) because R6C6+R9C7 <= 14
b) Innies+Outies N7: -1 = R9C4 - R7C1
-> R7C1 = (234)
c) ! Innies+Outies N689: 23 = R3C9+R46C6 - R9C4
-> R3C9 <> 6 since R46C6 <= 17
-> R4C6 <> 6 because R3C9 must be 9 like R6C6 -> not possible (step 4c)

6. R1+C6789
a) Innies+Outies N3: R1C6 = R3C9 = (789)
b) Naked triple (789) locked in R146C6 for C6
c) Naked triple (789) locked in R1C126 for R1

7. N258 !
a) 17(4): R9C5 <> 1 because R89C6+R9C7 <= 15
b) 17(3) @ N8: R7C5 <> 1 because R7C6 <> 7,9
c) 7,8,9 locked in 21(5) and R46C6 for N5
d) ! Innies+Outies N25: -2 = R1C3 - R6C4 because of step 6b
-> R1C3 = (24); R6C4 = (46)
e) 17(3) @ N4 = {368/458/467}

8. C123
a) 9 locked in R789C3 for N7
b) 12(2): R7C3 <> 3
c) Innies+Outies N1: 1 = R4C1 - R1C3
-> R4C1 = (35)
d) 15(4) = 36{15/24} -> 6 locked for N1
e) 7(2) <> 1
f) Killer pair (24) locked in 7(2) + R1C3 for C3+N1
g) 2,4 locked in R789C1 for N7
h) R4C3 = 1
i) 12(2) = [39/57/75]
j) Killer pair (59) locked in 12(2) + 21(4) for N7

9. C123
a) 2,4 locked in R789C1 and 11(3) can't have both -> R7C1 = (24)
b) Innies+Outies N7: -1 = R9C4 - R7C1
-> R9C4 = (13)
c) Innies+Outies C12: 3 = R47C3 - R9C2
-> R9C2 = (357) because R47C3 = 1{5/7/9}
d) 1 locked in 11(3) @ N7 -> 11(3) = 1{28/46} because of Killer pair (37) of 11(3)
e) 21(4): R89C3 <> 3 because (89) only possible there and R9C4 <> 5,6,7
f) 3 locked in R79C2 for C2
g) 15(4) = {1356} -> 3 locked for C1
h) 9 locked in 24(4) = 9{258/267/456}

10. C12 !
a) ! Innies+Outies C1: 5 = R368C2 - R1C1
-> R1C1 <> 9 since R368C2 would be 14(3) with 9 locked -> not possible because of 7(3)
b) 24(3) = {789} -> 9 locked for C2
c) ! Innies+Outies C1: 5 = R368C2 - R1C1
-> R1C1 <> 8 since R368C2 would be 13(3) with 8 locked -> not possible because of 7(3)
d) 24(3) = {789} -> R1C1 = 7, {89} locked for C2

11. N5
a) 7 locked in R46C6
b) 21(5) = 1{2369/2459/3458}; {12468} impossible because R6C4 = (46)
c) Killer pair {46} locked in 21(5) + R6C4

12. N3689 !
a) Innies+Outies N3: R1C6 = R3C9 = (89)
b) ! Innies+Outies N689: 23 = R3C9+R46C6 - R9C4
-> R9C4 <> 3 because R46C6 would be {89} -> blocked by R1C6 = (89)
c) R9C4 = 1
d) 21(4) = 1{389/578} because {1569} is blocked by Killer pair (59) of 12(2) @ N7
-> 8 locked for C3+N7

13. C123
a) 11(3) = {146} locked for N7
b) R7C1 = 2
c) 17(3) = {467} -> R6C4 = 4, {67} locked for C3+N7
d) R6C2 = 5, R4C1 = 3
e) 15(4) = {1356} -> 5 locked for N1
f) 7(2) = {34} locked for N1
g) R1C3 = 2

14. N5
a) 21(5) = {12369} locked
b) R4C4 = 5
c) Naked pair (78) locked in R46C6 for C6
d) R1C6 = 9 -> R3C9 = 9 (step 12a)

15. C789
a) 11(2) = {38/47} because {56} blocked by 15(4) = {1356} @ R3
b) 2 locked in 11(3) for R2 -> 11(3) = 2{18/36/45}
c) Innies+Outies N36: 13 = R14C6 - R6C9
-> R6C9 <> 2 because R14C6 >= 16
-> R6C9 = 3 -> R4C6 = 7
d) R6C6 = 8
e) Innies+Outies N9: -1 = R6C9 - R9C7 -> R9C7 = 4
f) R9C1 = 6, R8C2 = 1, R8C1 = 4, R3C2 = 6
g) 13(3) = {148/157/247/256}
h) 9 locked in 21(3) = {579} -> R4C7 = 9, R5C7 = 5
i) 24(4) = 69{18/27} -> 6 locked for N6
j) 13(3) = 4{18/27} -> R5C8 = 4
k) 13(3) = {247} -> {27} locked for R6+N6

16. N23
a) 11(2) = {38} locked for R3+N3
b) 23(4) = {1679} -> R2C7 = 7, {16} locked for R1+N3
c) 18(4) = {2358} -> R1C4 = 3, R2C4 = 8, R1C5 = 5

17. N89
a) 22(3) = {679} locked for N8
b) 17(3) = {458} -> R7C5 = 4, R7C6 = 5
c) R7C3 = 9 -> R7C2 = 3
d) 19(4) = 38{17/26} -> 8 locked for N9
e) 9(2) = [63] -> R7C7 = 6, R8C7 = 3

18. Rest is singles.

By the way, I have never used so much Innies+Outies Difference to solve a Killer.

[Para]

Hi

I did this one, but no posting a walk-through. Took me a while to solve till i found one step(I/O Diff N3689: R146C6 = R9C4 + 23) and then it was smooth sailing. This step was there from the beginning(see Mike's walk-through(it is similar to his step 5). So could have gone a lot faster. I had almost made it to this step through some detours. I didn't feel like posting my walk-through as it is completely inefficient and if i am going to rewrite it it is more like writing a walk-through on the solution than the way i solved it.
I think 1.25 is probably a fair rating, but it takes a very odd move to crack it which you normally don't look for. I have tried making a puzzle which has an even crazier move to crack it, but it won't stick.

greetings

Para

[gary w]

Hi,

Given Ruud's comment I approached this one with some trepidation but it turned out to be fairly standard..took me about 2 hours.Once i'ld noticed O-I on nonets 1245 -> r146c6=r7c1+22 and from the IO of N7 r7c1=r9c4+1 thus r7c1=2 and r9c4=1.Also r146c6={789}.
Then all the IO (lots of them in this puzzle!) of N12 mean that r1c3,r4c14,r6c4 are all "tied together" and together with the I N5=24 and r46c6=7/8,7/9,8/9 this enabled a placement of r1c3=2 after which the puzzle came out quite readily..

Of course when I looked at the other guys' wts the moves had pretty much been used by them.

Regards

Gary

[mhparker]

Hi all,

i suspect the cage pattern could produce something quite nasty

Right on! This puzzle was incredibly difficult to find a suitable V2 for, the vast majority of successful attempts (not that there were many...) being direct candidates for the Unsolvables list. Fortunately, this puzzle isn't one of them :


Assassin 78 V2 (Est. rating: 1.75)

It takes a clever move to get the ball in motion, but once it's gained momentum, this puzzle should reward you by staying interesting until near the end.



3x3::k:4096:4096:4354:4354:4354:6149:6149:61494873:40964354:4109:4109:61493080:4873:4873334941092328:6682:4873:4636:463664312336:6682:6682:4132:4636:4134:6431:6431:64314139:6682:4132:4132:4134:4134:64314139:4139:5685:4132:4151:415126103388:5685:56853903:44173897:64682374:56854417:4417:4417:6468:6468:6468:2374

Good luck, team!

[Para]

Hi all

Woke up early and didn't feel like going to sleep again so solved Mike's V2 instead. It's a bit of an annoying killer because the end is so tedious. Mostly because it seems a bit useless work when you really did all the fun bits already. And if it would take 3 or less steps to break it down, it actually took me 7 steps. Furthermore it is a fun killer, so don't be disheartened or anything, would have been nicer without the last 7 steps though.
I am going to rate it a 1.5, although i actually want to rate it something like a 1.65 but as this isn't a category it will be a 1.5. The reason for 1.5 and not 1.75 is that it misses that extra bit that tends to be in my 1.75 walk-throughs. This usually is one creative step, an extra special set of contradictions on a 45-test/cage combinations or just one higher technique like a killer x-wing. I kinda feel it is comparable to A66V1.5 as a walk-through and that is a 1.5. I know i am way of what Sudoku Solver thinks, but i think it is just because there are loads of small steps that Sudoku Solver does that i didn't implement in my walk-through as they are completely unnecessary. But as i said it is really a 1.65 so a high 1.5.

Walk-through Assassin78V2

1. R23C3 = {29/38/47/56}: no 1

2. R3C78 = {18/27/36/45}: no 9

3. 26(4) at R3C9 = {2789/3689/4589/4679/5678}: no 1

4. 9(3) at R4C6 and R8c8 = {126/135/234}: no 7,8,9

5. 10(3) at R6C6 = {127/136/145/235}: no 8,9

6. R78C7 = {49/58/67}: no 1,2,3

7. R7C23 = {79} -> locked for N7 and R7
7a. 7 and 9 in N9 locked within R8C79 + R9C7: pointing -> R8C6: no 7,9
7b. Clean up: R8C7: no 4,6

8. 45 on N1: 1 innie and 1 outie: R1C3 + 1 = R4C1: R1C3: no 9; R4C1: no 1

9. 45 on N2: 1 innie and 2 outies: R1C6 + 1 = R1C3 + R4C4: R4C4: no 1(IOU)

10. 45 on N3: 1 innie and 1 outie: R1C6 = R3C9: R1C6: no 1

11. 45 on N4: 1 innie and 2 outies: R4C1 + 5 = R6C4 + R7C1: R6C4: no 5(IOU)

12. 45 on N6: 1 innie and 2 outies: R6C9 + 6 = R4C6 + R3C9: R4C6: no 6(IOU)
12a. 45 on N6: 3 innies and 1 outie: R45C7 + R6C9 = R3C9 + 3: R3C9: no 2
12b. Clean up: R1C6: no 2(step 10)

13. 45 on N7: 1 innie and 1 outie: R7C1 + 3 = R9C4: R7C1: no 7; R9C4: no 1,2,3

14. 45 on N8: 1 innie and 2 outies: R9C4 + 5 = R6C6 + R9C7: R6C6: no 5(IOU)

15. 45 on N9: 1 innie and 1 outie: R6C9 + 1 = R9C7: R6C9: no 9; R9C7: no 1

16. 45 on R89: 4 innies: R8C4579 = 24
16a. 7 and 9 in R89 locked within R8C4579 -> R8C4579 = {2679/3579}: no 1,4,8
16b. Clean up: R7C7: no 5

17. 45 on R89: 1 innie and 2 outies: R7C47 = R8C9 + 4: R7C4: no 4(IOU)
17a. 45 on R89: 2 innies and 1 outie: R7C4 + 9 = R8C79: Max R8C79 = 16 -> Max R7C4 = 7: R7C4: no 8

18. 15(3) at R7C4 = {159/267/357}: 15(3) needs one of {79} in R8C45
18a. Hidden Killer Pair {79} in R8: R8C45 needs one of {79} and R8C79 needs one of {79}
18b. Hidden Killer Pair {79} in N9: R8C79 needs one of {79} and R9C7 needs one of {79} -> R9C7 = {79}
18c. Clean up: R6C9 = {68}

19. 22(4) at R6C9 = [6]{178/349/358}/[8]{149/167/239/347/356}:[6]{259/457}/[8]{257} blocked by R89C7: R7C89 + R8C9 needs one of {579}
19a. Killer Triple {579} in "R7C89 + R8C9" + R89C7 -> locked for N9
19b. 9(3) at R8C8 = {126/234} = {1|4..},{3|6..}: 2 locked for N9
19c. 22(4) at R6C9 = [6]{178/349/358}/[8]{167/347}: [8]{149/356} blocked by 9(3) at R8C8: 7 only in R8C9 -> R8C9: no 6

20. R8C4579 = {3579}: no 2,6: R8C45 needs one of {79} and {26} only in R8C45 so {2679} blocked: {3579} locked for R8
20a. 15(3) at R7C4 = [1]{59}/[3]{57}/[5]{37}: R7C4: no 2,6; 5 locked for N8
20b. 10(3) at R6C6 = [7]{12}/{136}: no 4; R6C6: no 2; 1 locked within cage -> pointing: R89C6: no 1
20c. Clean up: R7C1: no 2

21. 2 in R7 locked within 10(3) cage at R6C6: 10(3) = [7]{12}: R6C6 = 7; R7C56 = {12} -> locked for R7 and N8
21a. 15(3) at R7C4 = {357} -> locked for N8; 7 locked for R8
21b. R9C7 = 7(hidden); R6C9 = 6(step 15); R9C4 = 9(step 14); R7C1 = 6(step 13)
21c. Clean up: R1C3: no 5; R1C6: no 6; R3C9: no 7; R3C8: no 2

22. Hidden Triple {126} in N9: R8C8 + R9C89 = {126}
22a. 6 in N9 locked for C8
22b. Clean up: R3C7: no 3

23. 15(3) at R8C1 = {28}[5]/{48}[3]: no 1; R8C12 = {28/48}: 8 locked for N7 and R8; R9C1 = {35}

24. 45 on N6: 2 outies: R3C9 + R4C6 = 12 = [93/84]: R3C9 = {89}; R4C6 = {34}
24a. 26(4) at R3C9 = {2789/4589}: no 3; {2|4..},{2|5..} in N6
24b. 9(3) at R4C6 = [3]{15}/[4]{23} = {2|5..} in N6: [3]{24} blocked by 26(4) at R3C9: R45C7: no 4
24c. Killer Pair {25} in R45C7 + (R4C89 + R5C9) -> locked for N6
24d. 16(3) at R5C8 = [7]{18}/{349}: R5C8: no 1,8
24e. Clean up: R1C6 = {89}

25. 45 on N4: 1 innie and 1 outie: R4C1 = R6C4 + 1: R4c1: no 7,8
25a. Clean up: R1C3: no 6,7

26. 45 on N36: 2 outies: R14C6 = [93]: [84] blocked by R89C6
26a. R3C9 = 9(step 10)
26b. R45C7 = {15}(last combo in 9(3)) -> locked for C7 and N6
26c. R78C7 = [49]
26d. 16(3) at R5C8 = {4[3]9}(last combo): R6C7 = 5; R56C8 = {49} -> locked for C8 and N6
26e. Naked Triple {268} in R123C7 -> locked for N3
26f. Clean up: R3C8: no 3; R4C1: no 4; R6C4: no 2; R1C3: no 2,3; R2C3: no 2

27. 45 on N2: 2 outies: R1C3 + R4C4 = 10 = [46/82]: R1C3 = {48}; R4C4 = {26}
27a. Clean up: R4C1: no 2; R6C4: no 1

28. 24(4) at R1C6 = 9{6[1]8/2[5]8/2[7]6}: no 3

29. 13(3) at R3C4 = {38/47/56}[2]/{25/34}[6]: no 1

30. 9 in C1 locked for 19(4) at R2C1: 19(4) = {1279/1369/1459/2359]: no 8

31. 16(4) at R5C1 = 6{127/145/235} = {5|7..} in N4: no 8,9
31a. 16(3) at R5C3 = [718/628/358]: [754] blocked by 16(4); [394] blocked by R6C8: R5C3 = {367}; R6C3 = {125}; R6C4 = 8
31b. R4C1 = 9; R1C3 = 8; R4C4 = 2(all on 45's); R5C9 = 2(hidden); R9C9 = 1; R8C3 = 1(hidden)
31c. R5C2 = 8(hidden); R8C1 = 8(hidden)
31d. Naked Pair {78} in R4C89 -> locked for R4
31e. Clean up: R23C3: no 3; R5C3: no 7
31f. R5C1 = 7(hidden)

32. R6C12 = {12}(last combo within 16(4)) -> locked for R6 and N4
32a. R56C3 = [35]
32b. Clean up: R23C3: no 6
32c. R4C3 = 6(hidden); R4C2 = 4; R8C2 = 2; R9C123 = [534]; R6C12 = [21]
32d. R89C8 = [62]; R8C6 = 4; R3C3 = 2(hidden); R2C3 = 9; R7C23 = [97];
32e. Clean up: R3C8: no 7

33. 16(3) at R1C1 = [3]{67}/[4]{57}: no 1; 7 locked for N1
33a. 7 in R3 locked within 13(3) at R3C4: 13(3) = 2{47} -> R3C45 = {47} -> locked for R3 and N2

34. 16(3) at R2C5 = {6[2]8}/[3]{58}:[2]{68} blocked by R9C6: no 1; R2C5: no 2,5; R2C6: no 6

35. 24(4) at R1C6 = 9[258]/{2[7]6}: [618] blocked by R3C7: no 1
35a. 1 in R1 locked for N2
35b. 17(4) at R1C3 = [126]/[1]{35}: {3[1]5} blocked by R7C4: R1C4 = 1; R1C5: no 6

36. 45 on R12: 3 innies: R2C156 = 12 = [138/165/462/435]: R2C1: no 3; R2C5: no 8
36a. R9C5 = 8(hidden); R9C6 = 6
36b. Naked Pair {15} in R5C67 -> locked for R5
36c. 6 in N2 locked for R2

37. Hidden Pair {28} in R2 -> R2C67 = {28}
37a. R2C156 = [138/462] = {3|4..}

38. 12(3) at R1C9 = [417]/[345]: [714] blocked by R2C1; [4]{35} blocked by R2C45; [534] blocked by R2C156: R1C9: no 5,7; R2C8: no 3,7; R2C9: no 3,5
38a. 5 in N3 locked for C8
38b. 3 in R2 locked for N2
38c. Clean up: R2C4: no 5
38d. 5 in C4 locked for N8

39. 24(4) at R1C6 = 9[672]: [258] blocked by R1C5

And the rest is all naked singles.

Solution:

Code: Select all

.---------.---------.---------.
| 4  5  8 | 1  2  9 | 6  7  3 |
| 1  7  9 | 6  3  8 | 2  5  4 |
| 3  6  2 | 7  4  5 | 8  1  9 |
:---------+---------+---------:
| 9  4  6 | 2  5  3 | 1  8  7 |
| 7  8  3 | 4  6  1 | 5  9  2 |
| 2  1  5 | 8  9  7 | 3  4  6 |
:---------+---------+---------:
| 6  9  7 | 5  1  2 | 4  3  8 |
| 8  2  1 | 3  7  4 | 9  6  5 |
| 5  3  4 | 9  8  6 | 7  2  1 |
'---------'---------'---------'

greetings

Para

[mhparker]

Woke up early and didn't feel like going to sleep again so solved Mike's V2 instead.

Wow, that was quick! I was concerned that it may be too difficult, and was even wondering whether it would be necessary to drop a vague hint! Just "stepped by", fearing the worst, only to find out that it's already history!

Impressive stuff.

P.S. Please don't let that put the rest of you off attempting it yourselves and/or taking a look at Para's WT (after which my next puzzle will feel like a piece of cake, won't it? ).

[Andrew]

Congratulations to all who managed to solve Assassin 78. I must admit I was really struggling until I got a hint from Afmob. It was a good hint, just enough to make me think how to use it. Many thanks for that! After that it was pretty straightforward with the work I'd already done being helpful.

Really nice walkthrough, Mike! You got to the heart of things very quickly.

Here is my walkthrough for Assassin 78, including the hint after step 23.
Many thanks to Para for corrections and feedback.

Prelims

a) R23C3 = {16/25/34}, no 7,8,9
b) R3C78 = {29/38/47/56}, no 1
c) R7C23 = {39/48/56}, no 1,2,6
d) R78C7 = {18/27/36/45}, no 9
e) 24(3) cage in N1 = {789}, locked for N1
f) 11(3) cage in N2 = {128/137/146/236/245}, no 9
g) 11(3) cage in N3 = {128/137/146/236/245}, no 9
h) 7(3) cage in N4 = {124}, locked for N4
i) 21(3) cage at R4C6 = {489/579/678}, no 1,2,3
j) 11(3) cage in N7 = {128/137/146/236/245}, no 9
k) 22(3) cage in N8 = 9{58/67}, 9 locked for N8

1. 45 rule on N1 1 outie R4C1 = 1 innie R1C3 + 1, no 1,3 in R1C3, no 8,9 in R4C1

2. 45 rule on N12 1 innies R1C6 = 2 outies R4C14 + 1
2a. Min R4C14 = 4 -> min R1C6 = 5
2b. Max R1C6 = 9 -> max R4C14 = 8, no 6,7,8,9 in R4C4

3. 45 rule on N9 1 innie R9C7 = 1 outie R6C9 + 1, no 9 in R6C9, no 1 in R9C7

4. 45 rule on N89 2 outies R6C69 = 1 innie R9C4 + 10
4a. Min R9C4 = 1 -> min R6C69 = 11, no 1, no 2 in R6C6, clean-up: no 2 in R9C7 (step 3)
4b. Max R6C69 = 17 -> max R9C4 = 7

5. 45 rule on N7 1 innie R7C1 = 1 outie R9C4 + 1, no 1,9 in R7C1

6. 45 rule on N4 2 outies R6C4 + R7C1 = 1 innie R4C1 + 3
6a. Max R4C1 = 7 -> max R6C4 + R7C1 = 10, no 9 in R6C4
6b. IOU no 3 in R6C4

7. 45 rule on N6 2 outies R3C9 + R4C6 = 1 innie R6C9 + 13
7a. Min R6C9 = 2 -> min R3C9 + R4C6 = 15, no 1,2,3,4,5
7b. Max R3C9 + R4C6 = 18 -> max R6C9 = 5, clean-up: no 7,8,9 in R9C7 (step 3)
7c. Min R6C69 = 11 (step 4a), no 3,4,5 in R6C6

8. 45 rule on N3 1 outie R1C6 = 1 innie R3C9 -> R1C6 = {6789}

9. 45 rule on N8 2 outies R6C6 + R9C7 = 1 innie R9C4 + 11, max R6C6 + R9C7 = 15 -> max R9C4 = 4, clean=up: no 6,7,8 in R7C1 (step 5)

10. 45 rule on C789 2 outies R14C6 = 1 innie R9C7 + 12
10a. Max R14C6 = 17 -> max R9C7 = 5, clean-up: no 5 in R6C9 (step 3)
10b. Max R6C6 + R9C7 = 14 -> max R9C4 = 3 (step 9), clean-up: no 5 in R7C1 (step 5)
10c. Min R6C69 = 11 (step 4a), no 6 in R6C6
Para: "I think you missed the interactions between some 45-tests.
Because you said maximum of R6C6 + R9C7 was maximum 14: [95], but R9C6 = 5 means R14C6 = {89}, so really maximum was 12([75/84/93] if you use 45 on C789) and that gets you the same as in step 24."
Neat! That would have made the solution a lot quicker.

11. 45 rule on C89 2 outies R36C7 = 1 innie R1C8 + 4
11a. IOU no 4 in R6C7

12. 45 rule on N5 4 innies R46C46 = 24 = {1689/2589/2679/3489/3579/3678/4569/4578}
12a. 1 of {1689} must be in R4C4 -> no 1 in R6C4

13. 17(3) cage at R5C3 = {269/278/359/368/458/467}
13a. 2,4 of {278/467} must be in R6C4 -> no 7 in R6C4

14. 45 rule on R1 3 outies R2C247 = 1 innie R1C9 + 20
14a. Min R1C9 = 1 -> min R2C247 = 21, no 1,2,3
14b. Max R2C247 = 24 -> max R1C9 = 4

15. Deleted. It was incorrect and also happened to be unnecessary. When I originally went through my walkthrough before posting it I thought it was probably unnecessary but hadn't seen the flaw which Para pointed out.

16. 45 rule on R89 2 outies R7C47 = 1 innie R8C9 + 6
16a. IOU no 6 in R7C4

17. 45 rule on R12 2 outies R3C36 = 1 innie R2C1 + 4
17a. IOU no 4 in R3C6

18. 45 rule on R6789 3 outies R5C138 = 1 innie R6C5 + 18
18a. Min R6C5 = 1 -> min R5C138 = 19, no 1
18b. Max R5C138 = 24 -> max R6C5 = 6

19. Min R9C7 = 3 -> min R14C6 = 15 (step 10) -> max R67C6 = 15 -> no 1 in R7C5

20. 17(4) cage at R8C6 = {1268/1358/1367/1457/2348/2357/2456}, must contain at least one of 5,6,7,8 in R8C6 + R9C56

21. 17(3) cage at R6C6 = {179/269/278/359/368/458/467}, must contain one of 5,6,7,8 in R7C56
21a. Hidden killer quad 5,6,7,8 in N8 -> 17(4) cage at R8C6 can only contain one of 5,6,7,8 in R8C6 + R9C56 and can also contain 5 in R9C7 = {1358/1457/2348/2357/2456} (cannot be {1268/1367} which contain two of 6,7,8)
21b. 6,7,8 of {1358/1457/2357/2456} must be in R8C6 +R9C56 -> no 5 in R8C6 + R9C56

22. 17(4) cage at R8C6 = {1358/1457/2348/2357/2456}
22a. If {1358} => R9C4 = 2 => no {278} in 17(3) cage at R6C6
22b. If {1457} => 22(3) cage = {589} => no {278} in 17(3) cage at R6C6
22c. If {2348/2357/2456} => no {278} in 17(3) cage at R6C6
22d. -> no {278} in 17(3) cage at R6C6 -> no 8 in R7C56 (8 of {368/458} must be in R6C6)

23. 17(3) cage at R6C6 = {179/269/359/368/458/467}
23a. {179} must be [971] and 7 of {467} must be in R6C6 -> no 7 in R7C6

At this stage I was struggling and Afmob gave me the hint that Mike had used a breakthrough step using 4 combined nonets. I ought to have thought to look for something larger than 2 combined nonets; I have used a L-shaped group of 3 nonets at least once in the past.

24. 45 rule on N3689 3 outies R146C6 = 1 innie R9C4 + 23 -> R146C6 = 24 = {789}, R9C4 = 1, R7C1 = 2 (step 5), clean-up: no 6 in R3C9 (step 8), no 7 in R7C5 (step 23), no 7 in R8C7
24a. Naked triple {789} in R146C6, locked for C6
24b. R5C1 + R6C12 = 22 = 9{58/67}, no 3, 9 locked for N4

25. Naked triple {789} in R1C126, locked for R1

26. 1 in N7 locked in R8C12, locked for R8, clean-up: no 8 in R7C7
26a. 11(3) cage in N7 = 1{37/46}, no 5,8
26b. R8C3 + R9C23 = 20 = {389/569/578} (cannot be {479} which clashes with 11(3) cage), no 4

27. Deleted

28. 45 rule on C123 1 remaining outie R6C4 = 1 innie R1C3 + 2 -> R1C3 = {246}, R6C4 = {468}, clean-up: R4C1 = {357} (step 1)

29. R46C46 (step 12) = {2679/3489/3678/4578}
29a. Two of 7,8,9 must be in R46C6 -> no 8 in R6C4, clean-up: no 6 in R1C3 (step 28), no 7 in R4C1 (step 1)
29b. No combinations with R46C4 = {46} -> no 4 in R4C4
Step 29a inserted and original 29a renumbered.
Thanks Para for sorting out the errors in steps 27 and 28; I’d done my mental arithmetic the wrong way round in step 27 which, when corrected, was superseded by step 28.

30. R1C6 = R4C14 + 1 (step 2)
30a. R4C14 cannot total 6 -> no 7 in R1C6, clean-up: no 7 in R3C9 (step 8)
30b. 7 in R1 locked in R1C12 -> no 7 in R2C2
30c. 7 in C6 locked in R46C6, locked for N5
Para: "You could also have locked the 5 in R4C14 for R4 in this step".

31. 15(4) cage at R2C1 = {1356/2346}, 6 locked for N1, clean-up: no 1 in R23C3

32. Killer pair 2,4 in R1C3 and R23C3, locked for C3 and N1 -> R4C1 = 1, clean-up: no 8 in R7C2

33. Naked pair {24} in R45C2, locked for C2, clean-up: no 8 in R7C3

34. 8 in N7 locked in R8C3 + R9C23 = {389/578}, no 6

35. 6 in N7 locked in 11(3) cage = {146}

36. Grouped X-Wing for 6 in 15(4) cage at R2C1 and 11(3) cage in N7, locked for C12, clean-up: no 7 in 24(4) cage at R5C1 (step 24b)
Para: "That grouped x-wing is doing it the hard way as the 6 in C3 is locked for N4. If there's a workable grouped x-wing in which both cage are completely within one nonet (each) then there is always an easier locked candidates move available".
Agreed. I just happened to spot the grouped X-wing.
36a. Naked triple {589} in R5C1 + R6C12, locked for N4 -> R4C1 = 3, R1C3 = 2 (step 1), R6C4 = 4 (step 28), clean-up: no 5 in R23C3, no 5 in R9C7 (step 3)

37. 17(4) cage at R8C6 (step 22) = {2348} (only remaining combination) -> R9C5 = 8, clean-up: no 5 in 22(3) cage in N8
37a. 2 locked in R89C6, locked for C6

38. Naked triple {679} in 22(3) cage, locked for N8
[I missed 6 locked in R8C45 for R8 here. Fortunately it didn’t make much difference.]

39. 5 in N8 locked in R7C56, locked for R7, clean-up: no 7 in R7C23, no 4 in R8C7
39a. 17(3) cage at R6C6 (step 23) = {359/458}, no 7

40. R4C6 = 7 (hidden single in C6), R45C7 = 14 = {59/68}, no 4

41. Naked pair {34} in R23C3, locked for C3 -> R7C23 = [39], R7C4 = 7, clean-up: no 2,6 in R8C7

42. Naked pair {67} in R56C3, locked for C3 -> R9C23 = [75], R8C3 = 8, clean-up: no 1 in R7C7

43. Naked pair {45} in R7C56, locked for R7 and N8 -> R78C7 = [63], R9C7 = 4, R89C6 = [23], R6C9 = 3 (step 3), R9C1 = 6, R8C12 = [41], clean-up: no 5,7,8 in R3C8, no 8 in R45C7 (step 40)

44. Naked pair {15} in R23C1, locked for C1 and N1 -> R3C2 = 6, clean-up: no 5 in R3C7

45. Naked pair {89} in R12C2, locked for C2 and N1 -> R1C1 = 7, R6C2 = 5

46. R8C9 = 7 (cage sum), R8C8 = 5 (hidden single in R8)

47. R46C46 (step 29) = {4578} (only remaining combination) -> R4C4 = 5, R6C6 = 8, R1C6 = 9, R12C2 = [89], R45C7 = [95], R56C1 = [89], R1C7 = 1, R1C9 = 4, R3C9 = 9 (step 8), R9C89 = [92], clean-up: no 2,7 in R3C7, no 2 in R3C8

and the rest is naked singles

[gary w]

Well,just in time before no.79 I finally cracked Mike's vicious creation.
Found I needed lotsof innies/outies as per v1 but also the innies on r78 finally got me going (see Para's step 16).
But it didn't give up without a fight..a hard slog right to the end.
Re Para's wt.. 26d r6c7 should read =3 not 5 and also I wasn't sure where the step 26f r3c8<>8 came from..it's 1.30 am so probably missed it somewhere.


Hope 79 isn't too demanding!!

Regards

Gary

[CathyW]

I'll second that! I'd been looking at 78 on and off all week and still didn't crack it. (Had to cheat and look at the posted WTs )

[sudokuEd]

The reason for 1.5 and not 1.75 is that it misses that extra bit that tends to be in my 1.75 walk-throughs. This usually is one creative step

Step 7 (Para's WT) is the key step - though not the type of 'creative step' Para is talking about. Without this elimination, SudokuSolver can't even solve it using the basic-Killer-techniques-plus-"45 extreme"! (found this out while researching a [future] reply to Andrew on the rating assassins thread).

Para calls this step "pointing" and not CPE: not sure if there's a reason for that (I've always thought of them as identical). Incidently, SudokuSolver only gets this elimination with what it calls "Jigsaw locked candidates" [edit: Richard has since explained to me that this is because Para's step 7 is a "grouped" CPE move].

gary w didn't comment on this step. Did you find this step gary? I know I often still miss these type of CPE moves but would not call it a "1.75" move in isolation.

vicious

What rating would you give to 'vicious' (nice quote for the sticky: thanks ) gary?

I wish I could make a comment on the whole puzzle and Para's rating of it as a high 1.5... but haven't tried it unfortunately. Great work Para and gary w!

Cheers
Ed

[gary w]

I did find Para's step 7.I hope it doesn't sound really arrogant if I say it didn't seem too difficult a move??!!

Regards

Gary