Assassin 66

[Andrew]

Finished A66 this evening. Don't often manage to solve them the same day that they are posted. My walkthrough will follow tomorrow after I've checked it and tidied it up.

[mhparker]

Hi Andrew,

Finished A66 this evening. Don't often manage to solve them the same day that they are posted.

That was quick! BTW, if it's just a matter of checking for typos, I'm sure no-one would have minded if you would have posted your WT "as is", especially if accompanied by an appropriate remark to that effect.

I would also be interested to know how you and the other forum members rate this puzzle (which I personally haven't even looked at yet, if one discounts the fact that I stared at it for a few seconds last night!).

[CathyW]

Super quick - though you do have a time advantage!

I've only just printed it out to have a look at in my lunch break. Will let you know how I get on later.

Edit: Took a little bit longer than allotted lunch break but all done! No time now to do WT but will post again once typed up and checked. Rating - 0.5 probably.

[Howard S]

One of the easier ones - I am torn between 0.75 and 1.0

[Andrew]

That was quick! BTW, if it's just a matter of checking for typos, I'm sure no-one would have minded if you would have posted your WT "as is", especially if accompanied by an appropriate remark to that effect.

If it had been just a case of possible typos I would have done that. In the later stages of solving I had spotted several hidden singles and wondered how long they had been there so I wanted to check. As it happened they hadn't been there long but while checking I found one or two others.

I also had to decide whether to move my key step 32 to the earliest position that I might have been able to use it but have decided not to, see comment in the walkthrough.

Super quick - though you do have a time advantage!

Yes I do have a time advantage but only if I start a puzzle on the day that it is posted and manage to solve it the same day. Otherwise people in Europe, for example, have a time advantage over me.

I think I'll rate this as 1.0. Step 32 isn't a difficult one but I found it was hard to spot; I'd got to a stage where I was looking around for the next step and a relationship that I hadn't yet used; there's also step 31 which was easier to see.

I'll be interested to see Cathy's walkthrough and see why she thinks the rating is as low as 0.5.


Here is my walkthrough in TT

1. R34C5 = {49/58/67}, no 1,2,3

2. R5C23 = {14/23}

3. R5C78 = {16/25} (cannot be {34} which clashes with R5C23)
3a. Killer pair 1,2 in R5C23 and R5C78, locked for R5

4. R67C5 = {12}, locked for C5

5. R1C123 = {389/479/569/578}, no 1,2

6. 9(3) cage in N2 = {126/135/234}, no 7,8,9
6a. 1,2 only in R12C4 -> no 6 in R12C4

7. R1C789 = {126/135/234}, no 7,8,9

8. 22(3) cage in N3 = 9{58/67}, 9 locked for N3

9. R6C234 = 9{58/67}, 9 locked for R6

10. R6C678 = {136/145/235} (cannot be {127} which clashes with R6C5), no 7,8,9
10a. Killer pair 5,6 in R6C234 and R6C678, locked for R6

11. R9C123 = {127/136/145/235}, no 8,9

12. R9C789 = {128/137/146/236/245}, no 9

13. 45 rule on R9 3 innies R9C456 = 24 = {789}, locked for R9 and N8
13a. 45 rule on R9 1 innie R9C4 – 6 = 1 outie R8C6 -> R8C6 = {123}
13b. R9C123 (step 11) = {136/145/235}
13c. R9C789 (step 12) = {146/236/245}

14. 45 rule on R1 1 innie R1C6 – 7 = 1 outie R2C4 -> R1C6 = {89}, R2C4 = {12}
14a. 17(3) cage in N2 = {179/269/278/359/368/458}
14b. R1C6 = {89} -> no 8,9 in R2C56
14c. 7 on {179/278} must be in R2C5 -> no 7 in R2C6
14d. R1C123 (step 5) = {479/569/578} (cannot be {389} which clashes with R1C6), no 3

15. 45 rule on N1 1 outie R3C4 – 6 = 1 innie R3C1 -> R3C1 = {123}, R3C4 = {789}

16. 45 rule on N2 3 innies R3C456 = 19 = {379/469/478/568} (cannot be {289} which clashes with 17(3) cage), no 1,2

17. 45 rule on N3 1 outie R3C6 – 1 = 1 innie R3C9 -> no 1 in R3C9

18. 45 rule on N7 3 innies R7C13 + R8C3 = 19 = {289/379/469/478} (cannot be {568} which clashes with R9C789), no 1,5
18a. 45 rule on N7 1 innie R7C1 – 2 = 1 outie R7C4 -> no 2,9 in R7C1, no 3 in R7C4

19. 45 rule on N8 3 innies R7C456 = 12 = {156/246} (cannot be {345} because R7C5 only contains 1,2) = 6{15/24}, no 3, 6 locked for R7 and N8, clean-up: no 4 in R7C4 (step 18a)
19a. R7C5 = {12} -> no 1,2 in R7C46, clean-up: no 3,4 in R7C1 (step 18a)
19b. R8C456 = 3{15/24}, 3 locked for R8

20. 45 rule on N9 1 innie R7C9 – 2 = 1 outie R7C6 -> R7C9 = {78}, no 4 in R7C6

21. Naked pair {56} in R7C46, locked for R7 and N8 -> R7C5 = 1 (step 19), R6C5 = 2
21a. 4 in N8 locked in R8C45, locked for R8
21b. 15(3) cage = 4{29/38), no 7 in R9C4
21c. 18(3) cage = 7{29/38}
[With hindsight it would have been useful to spot step 32 now. It might have made the solution a bit shorter. However since I don’t consider it to have been an “I ought to have seen it now” move, I haven’t moved it to step 22.]

22. Naked pair {78} in R7C19, locked for R7

23. 45 rule on R6 2 remaining innies R6C19 = 11 = {38/47}, no 1

24. 45 rule on R5 2 innies R5C19 = 15 = {69/78}
24a. R5C456 = {369/378/459} (cannot be {468/567} which clash with R5C19)

25. 45 rule on R123 3 innies R3C159 = 12 = {129/138/147/156/237/246/345}
25a. 8 of {138} must be in R3C5 -> no 8 in R3C9, clean-up: no 9 in R3C6 (step 17)

26. 45 rule on N3 3 innies R2C7 + R3C79 = 14 = {158/167/248/347} (cannot be {257/356} which clash with 22(3) cage)
26a. 5 of {158} must be in R3C9 -> no 5 in R23C7

27. 17(3) cage at R7C3 = {269/359/368/458/467} (cannot be {278} because R7C4 only contains 5,6)
27a. R7C4 = {56} -> no 6 in R8C3

28. 15(3) cage at R7C6 = {159/258/267/357/456} (cannot be {249/348} because R7C6 only contains 5,6, cannot be {168} because 1,8 only in R8C7)
28a. 2 of {258/267} must be in R7C7 -> no 2 in R8C7
28b. 9 of {159} must be in R7C7 -> no 9 in R8C7

29. 45 rule on N4 4 outies R37C1 + R46C4 = 23, max R37C1 = 11 -> min R46C4 = 12 -> no 1 in R4C4
29a. 1 in N5 locked in R46C6, locked for C6
29b. 1 in N2 locked in 9(3) cage = 1{26/35}, no 4
29c. 17(3) cage in N2 (step 14a) = {269/278/359/458} (cannot be {368} which clashes with 9(3) cage
29d. 2 of {269} must be in R2C6 -> no 6 in R2C6

30. 45 rule on N6 4 outies R46C6 + R37C9 = 16
30a. Min R46C6 = 4 -> max R37C9 = 12, min R7C9 = 7 -> max R3C9 = 5, clean-up: no 7,8 in R3C6 (step 17)
30b. Min R37C9 = 9 -> max R46C6 = 7, no 7,8,9

31. Hidden killer triple 7,8,9 in R159C6 -> R5C6 = {789}
31a. R5C456 (step 24a) = {369/378/459}
31b. 9 on {369/459}must be in R5C6 -> no 9 in R5C45

32. 45 rule on C123 4 outies R3467C4 = 27 = {5679} (cannot be {3789/4689} which clash with R9C4), locked for C4 -> R9C4 = 8
32a. R9C56 = {79} -> R8C6 = 2

33. Naked pair {34} in R58C4, locked for C4
33a. R12C4 = {12} -> R1C5 = 6

34. 45 rule on C789 4 outies R3467C6 = 15 = {1356} (only remaining combination), locked for C6 -> R2C6 = 4

35. 17(3) cage in N2 = [854] (only remaining permutation), R3C6 = 3, R3C9 = 2 (step 17), R3C1= 1, R3C4 = 7 (step 15), R3C5 = 9, R9C56 = [79], R5C6 = 7, R4C5 = 4, R5C45 = [38], R8C45 = [43], clean-up: no 2 in R5C23
[I should also have included clean-up: no 8 in R3C8 (step 8) but this got fixed in step 40.]
35a. R23C3 = 11 = [38/65]

36. Naked pair {14} in R5C23, locked for R5 and N4, clean-up: no 6 in R5C78

37. Naked pair {25} in R5C78, locked for N6

38. R1C789 (step 7) = {135} (only remaining permutation), locked for R1 and N3 -> R12C4 = [21]
[R1C4 had been a hidden single since step 35; missed that one!]

39. Naked triple {479} in R1C123, locked for N1

40. R3C7 = 4 (hidden single in R3), R2C7 = 8, R3C8 = 6

41. R34567C9 = {23489/23678} (cannot be {12689} because 1 would have to be in R4C9 when the only remaining 6,9 are both in R5C9) = 238{49/67}, no 1, 3,8 locked for C9
41a. 9 of {23489} must be in R5C9 -> no 9 in R4C9
41b. 6 of {23678} must be in R5C9 -> no 6 in R4C9

42. Killer pair 7,9 in R2C9 and R34567C9, locked for C9

43. R4C234 = {256} (only remaining combination, cannot be {238} because R4C4 only contains 5,6,9), locked for R4 -> R4C6 = 1, R6C4 = 9 (hidden single in C4)
43a. R4C78 = 17 = [98] (only remaining permutation), R5C9 = 6, R5C1 = 9, R467C9 = {378} (step 41) -> R7C9 = 8, R46C9 = {37}, locked for C9 and N6 -> R2C89 = [79], R6C78 = [14] -> R6C6 = 5, R7C46 [56], R4C4 = 6, R7C1 = 7, R46C1 = [38], R46C9 = [73], R1C1 = 4

44. R9C9 = 4 (hidden single in C9)
44a. R9C78 (step 13c) = {25}/[61], no 3
44b. R9C123 (step 13b) = 3{16/25}, 3 locked for N7

45. Killer pair 1,5 in R8C9 and R9C78, locked for N9 -> R8C78 = [79], R8C3 = 8
[R8C7 had been a hidden single for at least a couple of steps.]

46. R9C7 = 6 (hidden single in C7), R9C8 = 1

47. Naked triple {235} in R9C123, locked for N7

and the rest is naked singles and cage sums

[CathyW]

And here's my WT in 22 steps (though it's not to the point of all singles)! 0.5 because I only used Innies, Outies, Outies-Innies, cage combinations, killer combos and combination analysis and because it only took me just over an hour including writing down my steps as I did them, though it's taken me as long again to type it up and check through!

Prelims

a) 20(3) N1 – no 1 or 2
b) 9(3) N2 & N3 = {126/135/234}
c) 22(3) N3 = {589/679} 9 n/e N3
d) 13(2) r34c5 = {49/58/67}
e) 5(2) r5c23 = {14/23}
f) 7(2) r5c78 = {16/25} ({34} blocked by 5(2)) -> 5(2) and 7(2) form KP 1,2 n/e r5
g) 22(3) r6c234 = {589/679} 9 n/e r6
h) 3(2) r67c5 = {12} n/e c5 -> 10(3) r6c678 = {136/145/235} ({127} blocked by r6c5}
-> 10(3) and r6c5 form KP 1,2 -> r6c19 <> 1,2


1. Innies r5: r5c19 = 15 = {69/78}
-> 18(3) r5c456 = {369/378/459} ({468/567} blocked by split 15(2))

2. Innies r9: r9c456 = 24 = {789} n/e r9/N8
-> r8c6 = (123)
-> 10(3) r9c123 = {136/145/235}, 11(3) r9c789 = {146/236/245}

3. O-I N1: r3c4 – r3c1 = 6 -> r3c4 = (789), r3c1 = (123)

4. O-I N3: r3c6 – r3c9 = 1 -> r3c6 = (2…9), r3c9 = (1…8)

5. Innies N2: r3c456 = 19. Min from r3c45 = 7+4 = 11 -> r3c6 max 8 (i.e. <> 9) -> r3c9 <> 8

6. Innies r4: r4c159 = 14

7. Innies r6: r6c159 = 13

8. O-I N7: r7c1 – r7c4 = 2 -> r7c1 = (3…8), r7c4 = (1…6)

9. O-I N9: r7c9 – r7c6 = 2 -> r7c9 = (3…8), r7c6 = (1…6)

10. Innies r123: r3c159 = 12 = {129/138/147/156/237/246/345}

11. Innies r789: r7c159 = 16 = {178/268} 8 locked to r7c19 n/e r7
-> r7c19 <> 3,4,5
clean up: r7c46 <> 1,2,3 (from steps 8 and 9)

12. Innies N8: r7c456 = 12 = {156/246} -> 6 locked to r7c46 n/e r7/N8
-> r7c19 = {78} -> r7c5 = 1, r6c5 = 2
-> r7c46 = {56} -> r7c2378 = {2349}
-> r8c456 = {234} -> r8c123789 = {156789}

13. 10(3) r6c678 = {136/145} Killer combo with 22(3) -> r6c19 <> 5,6 -> r6c19 = {38/47}
-> r5c19 <> {78} since r7c19 = {78} (would block both options for r6c19)
-> r5c19 = {69} -> 7(2) = {25} n/e N6, 5(2) = {14} n/e N4 -> r6c9 <> 7, 18(3) = {378} n/e N5 -> r3c5 <> 5,6
Options for 10(3): If {145}, r6c6 = 5 -> r6c6 <> 4

14. 17(3) r7c34+r8c3: Max from r7c34 = 9+6 = 15 -> r8c3 <> 1
Min from r7c4+r8c3 = 5+6 = 11 -> r7c3 <> 9
-> 17(3) = {269/359/368/458/467}
Combo analysis: r8c3 <> 5,6

15. 18(3) N8 = {279/378} -> r9c4 <> 7 -> 15(3) N8 = {834/924}

16. 15(3) r7c67 + r8c7 = [591/528/537/546/645/627] -> r8c7 <> 9

17. Outies c123: r3467c4 = 27 = {4689/5679}
Combo analysis: r3c4 <> 9 -> r3c1 <> 3
-> split 27(4) = [8496]/7{569}
How did I manage to miss the conflict with r9c4 here?! Thanks to Andrew for pointing it out.

18. 28(5) r34567c1 = {13789/14689/23689/24589/24679/25678} ({15679} not possible)
Combo analysis: r4c1 <> 2,6,7,8

19. Split 19(3) r3c456 = [793/784/892/874/847]
-> r3c6 <> 5,6,8 -> r3c9 <> 4,5,7

20. Split 14(3) r4c159 = [347/356/563/941] -> r4c9 = (1367)

21. 26(5) r34567c9 = {13679/14678/23489/23678} ({12689} not possible)
Combo analysis: r3c9 <> 3 -> r3c6 <> 4
-> 9(3) r1c789 = {135/234} ({126} blocked by r3c9)
-> 3 locked to r1c789 n/e r1/N3 -> 20(3) r1c123 = {479/469/578}

22. 15(3) r2c7 + r3c67 = {258/267/348} since {456} no longer possible and {357} would be blocked by combo with 22(3). If {267}, r3c6 = 2 (r23c7 can't be {26} blocked by combo with r3c9 and 9(3)) -> r3c6 <> 7 -> r3c9 <> 6.
-> NP {12} r3c19
-> r3c6 = 3 -> r23c7 = {48} n/e N3/c7
-> r3c9 = 2, r3c1 = 1
-> r3c4 = 7, r3c5 = 9, r4c5 = 4

Fairly straightforward from here with cage combos and singles

[Andrew]

0.5 because I only used Innies, Outies, Outies-Innies, cage combinations, killer combos and combination analysis and because it only took me just over an hour including writing down my steps as I did them

I also used the same types of moves but still rate this puzzle at 1.0. It's a matter of perception of the level of difficulty. It took me somewhat longer but if it took Cathy just over an hour then surely it was at least 0.75.

Cathy's second line in her step 13 was neat! That certainly wasn't a rating 0.5 step!

[CathyW]

Ok, I'll concede 0.75. Perhaps I just got better at spotting conflicting combinations! (Or not as I now see I missed one in my step 17!)

[Para]

Hi

I used a similar step to Cathy's Step 13. Just the different way around. I missed a lot in the beginning which made my solving a bit harder. Missed Innies R9 and Innies N8, worked everything out through Innie R789 combined with I/O N7/N9. The way i went about it was more a 1.0.

I think rating difficulties are harder to interpret, when the difficulty fluxuates a lot. When handling harder puzzles previously, this one seems easier than it actually is. Maybe i forgot to look for the obvious after doing some easier Killers without PM's.

My step was:

R7C19 = {78}; R6C19 = {38/47}
Either 28(5) at R3C1 or 26(5) at R3C9 contains both {78}. When 28(5) has both {78} -> 28(5) = {13789}: R5C1 = 9; 26(5) has both {78} -> 26(5) = {14678/23678} : {24578} blocked because R5C9 is minimal 6: R5C9 = 6. Either Way R5C19 = [96]

greetings

Para

[sudokuEd]

Thanks everyone for giving your ratings. I'm still spending every spare second trying to find a way to get a numeric/software rating. My prediction for A66 was a solid mid 1.25 ...hmmmmm. Way off again. Back to tweaking.

Richard has been working tirelessly on this. He's made a wonderful spreadsheet, playing with Sudoku Solver's output and getting some sensible weightings.
We are aiming to get with-in .25 of the most efficient solution in the .75-1.75 categories. Each week's puzzles seems to throw up new challenges. Will go public when we are happy - or ready to give up . So..... will be staying low for a while yet. Will keep lurking though .

Cheers
Ed

[azpaull]

I have to admit, that this was the first Assassin in several weeks that I have been able to do on my own (without using a walk-through). So, either I am learning all the tricks from you walk-through experts, or it was easier than most. (Or, both, I suppose.) I'll give it a 0.75.

By the way, let me thank you all for your walk-throughs and your commentary.

And, I may not converse here frequently from here on out, but I shall no longer be exclusively a lurker!

[sudokuEd]

let me thank you all for your walk-throughs and your commentary.

Yippee! Thanks azpaull - you've lifted me out of my ratings gloom. Been waiting and waiting for the 2nd generation of assassinators .

Become verbose if you like - I'll take over the lurking duties .

Cheers
Ed

[mhparker]

I'm still spending every spare second trying to find a way to get a numeric/software rating. My prediction for A66 was a solid mid 1.25 ...hmmmmm. Way off again. Back to tweaking.
...
We are aiming to get with-in .25 of the most efficient solution in the .75-1.75 categories.

Actually, you weren't far off the mark there IMO. I would agree with Andrew and Para here and plump for a 1.0 rating, which still makes this Assassin one of the easier ones.

In the meantime, I would be interested to know what rating Richard's software would give to this:


Assassin 66 V1.5



3x3::k:30723072:4355:4355282228222825:5131:435535895904:5904:76985131:513120635904:4890:7698:4636:4636:46364384:4384:4384:4890:76982853:5159:5159:51592858:4890:769820942865:4658:4658:4658:4890:7698287228653643:5693:48903383390636525693:5693:4680:4680:468036522894:2894

For the rest of us, there's only one way to find out...

[CathyW]

Welcome Azpaull! Look forward to further posts from you in the near future.

Thanks for the V1.5 Mike.
Edit: Definitely much harder - at least a 1.5. So far, after 37 steps, I have some early placements and rows 1,2,3 down to pairs and triples but currently stuck. Will persevere a bit longer.

Edit 2: 48 steps and Rating up to 2 probably. Either needs hypotheticals or I'm missing something.

Edit 3: See Para's WT on the next page - very clever.

[Andrew]

I'd also like to welcome Azpaull! As well as further posts from you, good luck when you decide to post your first walkthrough.

I only saw that Mike had posted A66V1.5 when I saw Cathy's post; the time difference worked against me!

I've started it but only done 25 steps so far, including preliminaries. As Cathy's TT implies, there's an easy start before one has to do real thinking.

Since this is a puzzle from Mike, I'll assume that it doesn't need hypotheticals but instead probably requires an advance move, possibly something I haven't yet learned. Still I'll keep on trying later; I need a break from the computer now.