Assassin 67

[Howard S]

This seemed straight forward - certainly easier than 66

1 Cage 17/2 C2 ={98}
2 => Cage 10/2 N1={64I73}
3 Rule 45 N1=> R3C13={94I85} (76 locked in Cage 10/2)
4 Rule 45 C6=> R189C6=24={987}
5 Cage 22/3 C67 = [{98I97}I{5I6}]
6 =>R1C6<>9 =>R12C7={94I86}
7 => Cage 19/3 N3={973I865}
8 Cage 3/2 N3 = {12}
9 => R3C79= 73 (54 not possible due to point 3 above)
10 => Cage 19/3 N3={865}
11 => R12C7={94} => R9C7=6 =>R89C6={97} =>R1C6=8
12 => Cage 10/2 N1={64} => R3C13={85}

Thereafter it is very easy with nothing special required

Solution

312748956
769513428
845692713
193284567
687935241
254176389
936451872
428367195
571829634

Let's hope no typos this week Rating 0.75 max

[CathyW]

Gosh Howard, you were quick off the mark this morning!

I can't say I found it easier than A66 but would agree with the 0.75 rating. Haven't done a WT today - no advanced steps required. All done with a few 45 rules, killer pairs and cage combos.

[Para]

It will definitely score higher than last week's Assassin

I have to agree with Howard that this one was easier than last weeks. Probably a low 0.75 on the rating scale.


Walk-through Assassin 67

1. R12C1, R23C2, R45C8 and R56C5 = {19/28/37/46}: no 5

2. 21(3) at R1C6 = {489/579/678}: no 1,2,3

3. 19(3) at R1C8 = {289/379/469/578}: no 1

4. 9(3) at R2C6 = {126/135/234}: no 7,8,9

5. 11(3) at R3C9 = {128/137/146/236/245}: no 9

6. R67C1 and R78C5 = {29/38/47/56}: no 1

7. R67C2 = {17/26/35}: no 4,8,9

8. R67C8 = {69/78}: no 1,2,3,4,5

9. R89C1 = {18/27/36/45}: no 9

10. 10(3) at R8C2 = {127/136/145/235}: no 8,9

11. 22(3) at R8C6 = {589/679}: no 1,2,3,4

12. R23C8 = {12} -->> locked for C8 and N3
12a. R45C8 = {37/46}: no 8,9
12b. Killer Pair {67} in R45C8 + R67C8 -->> locked for C8

13. R34C5 = {89} -->> locked for C5
13a. R56C5 = {37/46} = {4|7..}: no 1,2
13b. R78C5 = {56}: {47} blocked by R56C6 -->> locked for C5 and N8
13c. R56C5 = {37} -->> locked for C5 and N5

14. R45C2 = {89} -->> locked for C2 and N4
14a. Naked Pair {89} in R4C25 -->> locked for R4
14b. Clean up: R23C2: no 1,2

15. 22(3) at R8C6 = {79}[6]/{89}[5] -->> R9C7 = {56}; R89C6 = {79/89} -->> locked for C6 and N8

16. 45 on C6: 1 innie and 1 outie: R9C7 + 2 = R1C6 -->> R1C6 = {78}
16a. Naked Triple {789} in R189C6 -->> locked for C6

17. 45 on N2: 2 innies and 2 outies: R1C6 + R3C5 = R4C46 + 11: R1C6 + R3C5 = 15/16/17 -->> R4C46 = 5/6 (4 not possible) = {14/15/24}: no 6; R1C6 + R3C5 = [79/89] -->> R3C5 = 9
17a. R4C5 = 8; R45C2 = [98]

18. 45 on N1: 2 innies: R3C13 = 13 = {58}: {67} blocked by R23C2 -->> locked for R3 and N1
18a. Clean up: R12C1: no 2

19. 12(3) at R1C4 needs 2 of {124} in R12C5 -->> 12(3) = [7]{14}/[6]{24}: R1C4 = {67}; R12C5 = {14/24} -->> 4 locked for C5 and N2

20. 45 on C4: 3 innies: R189C4 = 18 = [6]{48}/[7]{38} -->> R89C4 = {38/48}: no 1,2,7; 8 locked for C4 and N8
20a. R1C6 = 8(hidden); R9C7 = 6(step 16); R2C9 = 8(hidden)

21. 21(3) at R1C6 = 8{49}(last combo) -->> R12C7 = {49} -->> locked for C7 and N3

22. 19(3) at R1C8 = [56]8(last combo) -->> R1C89 = [56]
22a. R1C4 = 7; R3C2 = 4(hidden); R2C2 = 6
22b. Clean up: R2C1: no 3; R12C5 = {14} -->> locked for C5 and N2; R67C2: no 2; R8C1: no 3
22c. R9C5 = 2
22d. Clean up: R8C1: no 7; R89C4 = {38} -->> locked for C4 and N8

23. 14(3) at R5C4 = {149} (last combo) -->> locked for C4

24. 12(3) at R5C6 = {56}[1]/{26}[4] -->> R56C6 = {26/56} -->> 6 locked for C6 and N5
24a. R3C4 = 6(hidden); R3C8 = 1(hidden); R2C8 = 2; R2C46 = [53]; R3C6 = 2; R4C46 = [24]
24b. R7C46 = [41]

25. 45 on C9: 1 innies: R9C9 = 4
25a. 16(3) at R8C8 = 4{39}: R89C8 = {39} -->> locked for C8 and N9
25b. R45C8 = [64](last combo); R6C9 = 9(hidden); R56C4 = [91]

26. 16(3) at R6C9 = 9{25} (last combo) -->> R78C9 = {25} -->> locked for C9 and N9
26a. R8C7 = 1(hidden)

27. 14(3) at R3C7 = {257}(last combo) -->> R345C7 = [752]
27a. R78C7 = [38]; R78C8 = [87]; R56C5 = [37]; R67C2 = [53]; R56C6 = [56]; R3C9 = 3

28. R67C1 = [29](last combo)

And the rest is naked and hidden singles.

greetings

Para

[Andrew]

I agree with Howard and Para. Definitely easier than A66. I used less steps, slightly easier ones and had less notes about relationships below my working diagram for A67 than I did for A66. I'd put it between 0.75 and 1.0. Maybe when giving ratings we forget that Mike has defined typical recent Assassins as 1.25.

This was another one that I solved in one session, apart from a break for dinner, so that makes it easier than average Assassins over the last few months.

Here is my walkthrough.
Thanks Para for the comments and corrections.

1. R12C1 = {19/28/37/46}, no 5

2. R23C2 = {19/28/37/46} no 5

3. R23C8 = {12}, locked for C8 and N3

4. R34C5 = {89}, locked for C5

5. R45C2 = {89}, locked for C2 and N4, clean-up: no 1,2 in R23C2

6. R45C8 = {37/46}, no 5,8,9

7. R56C5 = {37/46}, no 1,2,5

8. R67C1 = [29/38]/{47/56}, no 1, no 2,3 in R7C1

9. R67C2 = {17/26/35}, no 4

10. R67C8 = {69/78}

11. R78C5 = {47/56}, no 1,2,3
[Para commented this should be R78C5 = {56} (only remaining combination, {47} clashes with R56C5), locked for C5. I ought to have spotted that. I saw it the other way round in step 20, only just after the preliminary steps, so this didn’t really affect the solution path.]

12. R89C1 = {18/27/36/45}, no 9

13. 21(3) cage at R1C6 = {489/579/678}, no 1,2,3

14. R234C6 = {126/135/234}, no 7,8,9

15. R345C9 = {128/137/146/236/245}, no 9

16. 10(3) cage at R8C2 = {127/136/145/235}, no 8,9

17. 22(3) cage at R8C6 = 9{58/67}
17a. CPE no 9 in R9C4

18. Naked pair {89} in R4C25, locked for R4

19. Killer pair 6,7 in R45C8 and R67C8, locked for C8

20. R56C5 (step 7) = {37} (cannot be {46} which clashes with R78C5), locked for C5 and N5, clean-up: no 4 in R78C5 = {56}, locked for C5 and N8
[Alternatively 45 rule on C5 3 innies R129C5 = 7 = {124}, locked for C5]

21. 22(3) cage at R8C6 (step 17) = 9{58/67}
21a. R89C6 = {79/89} -> R9C7 = {56}
21b. 9 locked in R89C6, locked for C6 and N8

22. 45 rule on C2 3 innies R189C2 = 10 = {127/145/235} (cannot be {136} which clashes with R67C2), no 6

23. 45 rule on C4 1 innie R1C4 – 5 = 1 outie R9C5 -> R1C4 = {679}
[Alternatively R1C4 comes from remaining combinations for 12(3) cage]

24. 45 rule on C7 1 outie R1C6 – 2 = 1 innie R9C7 -> R1C6 = {78}
24a. Naked triple {789} in R189C6, locked for C6

25. 45 rule on C7 3 innies R129C7 = 19 = {49}6/{68}5 (cannot be {58}6 which clashes with 21(3) cage at R1C6)
25a. R12C7 = {49/68}, no 5,7

26. 45 rule on C8 1 innie R1C8 – 1 = 1 outie R9C9 -> R9C9 = {23478}

27. 45 rule on N1 2 innies R3C13 = 13 = {49/58} (cannot be {67} which clashes with R23C2)
27a. Killer pair 8,9 in R3C13 and R3C5, locked for R3

28. 12(3) cage in N1 = {129/156/237/246} (cannot be {138} which clashes with all combinations for R23C2 together with R3C13, cannot be {147} which clashes with R23C2, cannot be {345} which clashes with R3C13), no 8

29. 45 rule on N3 2 innies R3C79 – 2 = 1 outie R1C6 -> R3C79 = 9 or 10 = {36/37/46} (cannot be {45} which clashes with R3C13), no 5
[Para pointed out that R3C79 cannot be {46} either because this clashes with R12C7. Well spotted! It’s so easy to forget which combinations remain from previous steps, particularly ones like this that don’t have a fixed total for these two cells. He added "Get's eliminated in 29a though" so it didn’t matter this time.]
29a. 5 in N3 locked in 19(3) cage = {568} (only remaining combination), locked for N3, 6 locked in R12C9, locked for C9, clean-up: R9C9 = {47} (step 26)

30. Naked pair {49} in R12C7, locked for C7 and N3 -> R1C6 = 8 (cage sum), R34C5 = [98], R45C2 = [98], R1C89 = [56], R2C9 = 8, R9C7 = 6 (step 24), R9C9 = 4 (step 26), clean-up: no 2 in R1C1, no 2,4 in R2C1, no 4 in R3C13 (step 26), no 9 in R6C8, no 3,5 in R8C1

31. R9C9 = 4 -> R89C8 = 12 = {39}, locked for C8 and N9, clean-up: no 7 in R45C8, no 6 in R6C8

32. R6C9 = 9 (hidden single in C9), R78C9 = 7 = {25} (only remaining combination), locked for C9 and N9
32a. R5C4 = 9 (hidden single in R5)

33. 1 in N9 locked in R78C7, locked for C7
33a. R678C7 = {138} (only remaining combination) -> R6C7 = 3, R78C7 = {18}, locked for N9 -> R7C8 = 7, R6C8 = 8, R3C79 = [73], R56C5 = [37], clean-up: no 3,7 in R2C2, no 4 in R6C1, no 1 in R6C2, no 4,8 in R7C1, no 1,5 in R7C2
33b. Naked pair {46} in R23C2, locked for C2 and N1, clean-up: no 2 in R67C2 = [53], no 6 in R7C1, no 6 in R8C1

34. 10(3) cage in N7 = {127} (only remaining combination), locked for N7, clean-up: no 8 in R89C1 = [45], R3C1 = 8, R3C3 = 5, R7C1 = 9, R6C1 = 2, clean-up: no 1 in R12C1
34a. Naked pair {37} in R12C1, locked for C1 and N1

35. Naked triple {127} in R9C235, locked for R9 -> R89C6 = [79], R89C8 = [93], R9C4 = 8
35a. R8C4 = 3 (hidden single in R8), R9C5 = 2 (cage sum), R1C4 = 7 (step 23), R12C1 = [37]
35b. R8C2 = 2 (hidden single in N7), R1C2 = 1, R9C23 = [71], R78C9 = [25], R78C5 = [56], R78C3 = [68], R78C7 = [81], R6C3 = 4, R45C3 = [37], R45C9 = [71], R45C1 = [16], R45C8 = [64], R12C5 = [41], R12C7 = [94], R12C3 = [29], R23C2 = [64], R23C8 = [21], R2C46 = [53]

36. R2C6 = 3 -> R34C6 = 6 = [24]

and the rest is naked singles

There were several hidden singles near the end and probably others that I missed which may have made the solution slightly more direct. No need to point them out to me unless I missed any before step 30.