Assassin 58

[Jean-Christophe]

deleted

[Ruud]

The service provider hosting my websites is currently upgrading MySQL. Because of this, the database server is sometimes slow or not responding at all. I also experienced these problems and complained about it

I hope the site will be back at full speed soon.

Ruud

[CathyW]

Struggling with this one! 31 steps so far and still not a single placement.

Edit: Spoke too soon!! Got a placement on my step 34 and a string of singles on step 38 which led to solution. Will post walkthrough later once I've typed it up and checked through.

[mhparker]

Hi folks,

The V1 had a (probably unintentional) design weakness that was admittedly not easy to spot, but which I stumbled across, and which JC also noticed and exploited. Did you find it?

Time for a V1.5, which I designed to keep with the spirit of the V1, whilst removing the aforementioned weakness. It should be slightly harder than the original was intended to be, but still very do-able. So don't be put off, you can do it!

Here it is:

Assassin 58 V1.5



3x3::k:6912:6912:69125380:5380:5894:58946912231453803854:58946912:4883256336065894:5894:4883:48833092233541302084387738794130:413020844655:4655:46553634:4148:4148:8246:8246261649234148:59508246390549233141:59508246:82462371:4923:5950:5950:5950:

Good luck!

[CathyW]

I seem to have done it the hard way!

In steps 1-16 candidates are entered on to grid:

1. 7(3) N4 = {124} not elsewhere in N4
-> 11(2) N4 = {38/56}

2. Innies N1: r3c23 = 8 = {17/26/35}
-> r4c1234 = 20
-> r4c89 = 13 = [94]/{58/67} -> r5c789 = 16
-> r5c9 = (12345)
-> 28(5) in N1 = {9…}

3. Innies N9: r7c78 = 9 {18/27/36/45}
-> r6c6789 = 19
-> r6c12 = 9 [81/54] -> r6c1 <> 3,6; r5c1 <> 5,8; r6c2 <> 2 -> 11(2) N4 = [38/65]
-> r5c123 = 9 = [324/342/612/621]
-> 2 locked to r5c23 not elsewhere in r5 -> r4c9 <> 7 -> r4c8 <> 6
-> 27(5) in N9 = {9…}

4. Innies N3: r23c7 = 5 = {14/23} -> r2c6+r3c56 = 16
-> 7(2) r2c67 = [61/52]/{34}
-> 30(5) in N3 must have 5

5. Innies N7: r78c3 = 14 = [95]/{68} -> r8c4 = (134)

6. 6(2) r89c1 = {15/24} -> 25(5) in N7 = {37…}

7. Outies - Innies N4: r6c3 - r4c4 = 7
-> r4c4 = (12), r6c3 = (89)
-> r3c3 <> 1,2; r3c2 <> 6,7

8. O-I N6: r6c6 - r4c7 = 3
-> r6c6 = (4…9), r4c7 = (1…6)

9. Split 14(2) r78c3 and r6c3 form Killer Pair -> 8,9 not elsewhere in c3
-> 14(3) r3c3 + r4c34 = [761/752/671/572] -> r4c3 = (567), r3c3 <> 3 -> r3c2 <> 5

10. 7 locked to r4c123, not elsewhere in r4.
-> r4c9 <> 6 -> r5c9 <> 3
-> 12(3) r4c567 = {138/156/246/345} ({129} blocked by r4c4)
-> r4c45 = (1234568)

11. 10(3) r123c4 = {136/145/235} ({127} blocked by r4c4) -> r123c4 = (1…6)

12. r34678c3 Naked Quin {56789} -> r129c3 = (1234) -> r2c2 = (5678)

13. Innies N69: r467c7 = 13
-> r1589c7 = 27 must have 9 in r159c7, not elsewhere in c7
-> 27(4) r1589c7 = {3789/4689/5679} -> r159c7 = (3…9), r8c7 = (3…8) -> r8c8 = (1…6)
-> split 13(3) r467c7 = {148/157/238/256} ({247/346} blocked by split 5(2) r23c7) -> r6c7 = (1…8)

14. 14(3) r3c2 + r4c12 = [167/176/239/293/257/275/356/365] -> r4c12 = (35679)
-> 8 locked to r6c13, not elsewhere in r6 -> r4c7 <> 5 (step 8)

15. 14(3) r3c2 + r4c12:
a) if 1{67} -> 14(3) r3c3 + r4c34 = [752]
b) if 2{39} -> 14(3) r3c3 + r4c34 = [671]
c) if 2{57} -> no options for 14(3) r3c3 + r4c34
d) if 3{56} -> 14(3) r3c3 + r4c34 = [572]
-> 14(3) r3c2 + r4c12 can’t be 2{57}
-> r4c3 <> 6

16. r4c1234 = 20 = {39}[71]/{567}2

Enter available candidates in all remaining cells for elimination
r123c1+r1c2 = (1…9); 19(3) in N2 = (2…9); r3c56 = (1…9); 10(2) in N3 = (1…4, 6…9);
r123c8+r3c9 = (1…9); 20(3) in N5 = (3…9); r6c45 = (1…7); r5c8 = (3…9); r6c89 = (1…7,9);
r7c1+r789c2 = (1…9); r7c45 = (1…9); 20(3) in N8 = (3…9); 12(3) in N8 = (1…9);
r9c8+r789c9 = (1…9)

17. 16(3) r6c67 + r7c7 = {178/259/268/349/358/367/457}
({169} blocked by split 13(3) r467c7)
Analysis: r7c7 <> 1 -> r7c8 <> 8

18. Outies r12: r3c1489 = 23

19. Outies r89: r7c1269 = 18

20. 10(3) r123c4 = {136/145/235}. Forms KP with r4c4 -> 1,2 not elsewhere in c4
-> r8c3 <> 8, r7c3 <> 6 -> NP {89} r67c3; NT {567} r348c3

21. 18(3) r7c345 = [891/981/972]/8{37}/8{46}/9{36}/9{45}
-> r7c5 <> 8,9

22. 10(3) r123c4 forms KP with r8c4 -> r5679c4 <> 3,4
-> 18(3) r7c345 = [891/981/972/873/864/963/954] -> r7c5 <> 5,6,7

23. 17(3) r6c345 = [872/863/971/962/953] ([854] blocked by r6c1 -> r6c5 <> 4,5,6,7

24. Split 13(2) r4c89 = [94]/{58}, Split 20(4) r4c1234 = {1379/2567} -> Forms KP on 5 and 9 -> r4c56 <> 5 -> 12(3) r4c567 = {138/246}

25. Innies N8: r7c45 + r8c4 = 13
Max from r7c5 + r8c4 = 7 -> r7c4 <> 5

26. 25(5) in N7 = {13579/13678/23479} - all other combos blocked by must have both 3 and 7 and can’t have both 89/56/14/25/45

27. 12(3) r789c6 = {129/138/147/156/237/246} ({345} blocked by r8c4)

28. Outies N14: r46c4 + r6c5 = 10 = {127/136/235}
-> r4c56 + r6c6 = 15 = {168/249/258/267/348/456}

29. 20(3) in N6 = {389/479/569} ({578} blocked by remaining options for 9(2) r45c9)
-> r6c89 <> 9

30. Innies N14: r346c3 = 21 = {579/678}

31. Split 16(3) r5c789 = {169/349/358}
{178} blocked by options for 20(3); {457} blocked by split 13(2) r4c89
-> r5c78 = (3689)
-> split 16(3) forms KP with r5c1 -> 20(3) r5c456 <> 3,6 -> options {479/578}
-> r6c46 <> 7 -> r4c7 <> 4

32. 10(3) r123c4 forms KP with r6c4 -> r579c4 <> 5,6 (NT {789} r579c4) -> r7c5 <> 4

33. 17(3) r6c345 = [863/953/962] -> r6c5 <> 1
-> 1 locked to r4c456 -> r4c7 <> 1 -> r6c6 <> 4
-> NQ {5689} r6c1346 -> r6c789 <> 5,6
-> r4c56 <> 6 -> r4c7 <> 2 -> r6c6 <> 5

34. 12(3) r4c567 = {18}3/{24}6 -> r4c56 <> 3 -> HS r6c5 = 3

35. 18(3) r7c345 = [972]/{89}1 -> 9 not elsewhere in r7

36. From step 8 options for O-I N6 now:
r6c6 = 6, r4c7 = 3 OR r6c9 = 9, r4c7 = 6
Either case r7c7 <> 6 -> r7c8 <> 3

37. Colouring 9s: [r6c6] =9= [r6c3] =9= [r7c3] =9= [r7c4]
r5c4 and r89c6 see both r6c6 and r7c4 -> r5c4, r89c6 <> 9
-> 9 locked to r79c4 <> r89c5 <> 9

38. Innies c4: r8c4 = 4 -> r8c3 = 5, r7c3 = 9, r6c3 = 8, r4c3 = 7, r3c3 = 6, r4c4 = 1, r6c4 = 6, r6c1 = 5, r5c1 = 6, r6c6 = 9, r4c7 = 6 …

Straightforward combinations and singles from here.

[Jean-Christophe]

deleted

[herschko]

I did not find this one hard at all. All the numbers vell in place right away.

[mhparker]

Hi Herschko,

Welcome to the forum! We need new keen members like yourself!

I did not find this one hard at all. All the numbers vell in place right away.

Assassin 58 had a cage pattern that didn't allow for the creation of a really tough puzzle.

But if you stick around on this forum (maybe helping out with a team-based ("tag") solution), you'll find enough of those as well!

[herschko]

But if you stick around on this forum (maybe helping out with a team-based ("tag") solution), you'll find enough of those as well!

Oh, I have already found enough of those here. Just because I haven't posted before doesn't mean I have been playing.

Just great for my productivity...

[mhparker]

Hi Stephen,

Oh, I have already found enough of those here. Just because I haven't posted before doesn't mean I have been playing.

Just great for my productivity...

You certainly picked a quiet week to join the forum! I think several forum members are on holiday at the moment.

BTW, I've just stumbled across some of your mathematics articles on the internet! Very impressive. Compared to that, AIC notation and the like must be a no brainer!

Good to have you around. Let's see what Ruud serves us up for Assassin 59. Maybe you're lucky and it's a real eeevil one!

[CathyW]

Give us a break Mike! You can have real evil on the V1.5 / V2.

Given the small number of walkthroughs posted perhaps I wasn't the only one who took a long time to solve this week - or perhaps, as you say, some of the other regulars are on holiday.

Welcome to Herschko
From one who struggled for a while, it would be interesting to know how you solved this week's puzzle. JC makes it seem easy by comparison to my walkthrough although I bet no-one else used colouring!

[herschko]

Welcome to Herschko
From one who struggled for a while, it would be interesting to know how you solved this week's puzzle. JC makes it seem easy by comparison to my walkthrough although I bet no-one else used colouring!

Thank you both for the welcome. I take this opportunity to let you know that my favorite type of sudoku is the "greater than killer," found weekly at killersudokuonline.com. I wish I could find more.

I wish I could tell you how I solved a puzzle step by step. I don't quite know how to recover that from a finished puzzle, though I do save intermediate states along the way. I do this by working in Excel. I delete the intermediate worksheets after I am done.

I think I remember this much. Here is some

S

P

O

I

L

E

R



S

P

A

C

E


I use letters to refer to columns, numbers for rows (as in Excel). After the usual limitation of numbers in small cages (e.g., 1245 in A8 and A9), and derived cages (e.g. B3 + C3 = 8), I think what set the whole thing off was one of the relationships like F6 = G4 + 3, derived after we notice that G7 + H7 = 9. I am not sure that was it, though.

[CathyW]

I take this opportunity to let you know that my favorite type of sudoku is the "greater than killer," found weekly at killersudokuonline.com. I wish I could find more.

Oh yes - I enjoy those too, though haven't had so much time to tackle them in the last couple of weeks. I presume you've tried the couple at Miyuki Misawa's site?
http://www7a.biglobe.ne.jp/~sumnumberplace/79790008/
I haven't found any other source of greater than killers.

BTW I think the only way to do a walkthrough is to keep track of the steps as you make them. Quite often takes longer to do the walkthrough than to do the puzzle!!

[Andrew]

Welcome to the forum Herschko!

I seem to have done it the hard way!

I'm sure I did too. I took 69 steps (67 after checking my walkthrough) before I reached "and the rest is naked singles".

Give us a break Mike! You can have real evil on the V1.5 / V2.

Given the small number of walkthroughs posted perhaps I wasn't the only one who took a long time to solve this week - or perhaps, as you say, some of the other regulars are on holiday.

JC makes it seem easy by comparison to my walkthrough although I bet no-one else used colouring!

It took me several hours to solve this one so I feel it was hard enough for a V1. In my opinion V1 Assassins shouldn't become so hard that they drive away solvers like myself. Real evil is fine for V2 and V2+. V1.5 should be somewhere between those levels.

I'll post my walkthrough after I've checked it and also worked through the ones already posted by J-C and Cathy. I know it will be different because I didn't see the weakness that Mike referred to and I didn't use colouring. It's one of the techniques, along with AIC and ALS, that I haven't yet learned. Must find time to study Andrew Stuart's book but there are so many puzzles and other non-Sudoku things to do.

BTW I think the only way to do a walkthrough is to keep track of the steps as you make them. Quite often takes longer to do the walkthrough than to do the puzzle!!

That's the way I've always done them. I type my steps into a Word file while I'm solving the puzzle on an Excel grid. At one time they used to be exactly how I solved the puzzle. Now if I see something that I ought to have seen earlier I usually put it in there and check if any later steps need to be changed, which often means that I have to work through the diagram from the start or, at least, from the basic candidates. Then after I've finished I always work through my walkthrough at least once even if I'm not going to post it to this forum.

[Andrew]

As promised in my previous message, I've now looked at the walkthroughs posted by J-C and Cathy and then checked my own one. Sorry for the delay; I only found time to look at them this evening.

J-C's step 2 was very powerful! I assume this must be what Mike called the Achilles Heel. I also liked his step 18c.

My walkthrough was more like Cathy's although there are quite a lot of differences. Here is mine.

1. R12C9 = {19/28/37/46}, no 5

2. R2C23 = {18/27/36/45}, no 9

3. R2C67 = {16/25/34}, no 7,8,9

4. R45C9 = {18/27/36/45}, no 9

5. R56C1 = {29/38/47/56}, no 1

6. R89C1 = {15/24}

7. R8C34 = {18/27/36/45}, no 9

8. R8C78 = {18/27/36/45}, no 9

9. R123C4 = {127/136/145/235}, no 8,9

10. 19(3) cage at R1C5 = {289/379/469/478/568}, no 1

11. 7(3) cage at R5C2 = {124}, locked for N4, clean-up: no 7,9 in R56C1

12. 20(3) cage at R4C8 = {389/479/569/578}, no 1,2

13. R5C456 = {389/479/569/578}, no 1,2

14. 20(3) cage at R8C5 = {389/479/569/578}, no 1,2

15. 45 rule on N1 2 innies R3C23 = 8 = {17/26/35}, no 4,8,9
15a. 9 in N1 locked in 28(5) cage

16. 45 rule on N3 2 innies R23C7 = 5 = {14/23}, clean-up: no 1,2 in R2C6
16a. 5 in N3 locked in 30(5) cage

17. 45 rule on N7 2 innies R78C3 = 14 = {68}/[95], clean-up: R8C4 = {134}

18. 45 rule on N9 2 innies R7C78 = 9 = {18/27/36/45}, no 9
18a. 9 in N9 locked in 27(5) cage

19. 45 rule on R1234 2 innies R4C89 = 13 = {58/67}/[94], no 1,2,3, clean-up: no 6,7,8 in R5C9

20. 45 rule on R6789 2 innies R6C12 = 9 = [54/81], clean-up: R5C1 = {36}

21. 2 in N4 locked in R5C23, locked for R5, clean-up: no 7 in R4C9, no 6 in R4C8 (step 19)

22. 45 rule on C123 3 innies R678C3 – 21 = 1 outie R4C4
22a. Max R678C3 = 24 -> max R4C4 = 3
22b. Min R678C3 = 22, no 3 in R6C3
22c. R678C3 = {589/679/689/789} = 9{58/67/68/78}
22d. 9 locked in R67C3, locked for C3

23. Killer quad 1/2/3/4 locked in R123C4 (contains two of 1,2,3,4, step 9), R4C4 and R8C4, locked for C4

24. Max R4C4 = 3 -> min R34C3 = 11, no 1,2, clean-up: no 6,7 in R3C2 (step 15)
24a. Max R3C3 + R4C4 = 10, no 3 in R4C3
24b. Max R4C34 = [83] = 11 but that would make 14(3) cage [383] which isn’t allowed
24c. Max R4C34 = 10 -> no 3 in R3C3 clean-up: no 5 in R3C2 (step 15)

25. Naked quint {56789} in R34678C3, locked for C3, clean-up: R2C2 = {5678}
[Later I spotted 45 rule on C12 4 outies R1259C3 = 10 = {1234}, locked for C3, which could have been done immediately after the preliminary steps.]

26. 45 rule on N4 3 outies R3C23 + R4C4 – 1 = 1 innie R6C3
26a. R3C23 = 8 (step 15) -> R6C3 – 7 = R4C4 -> R4C4 = {12}, R6C3 = {89}
26b. R678C3 (step 22c) = 9{58/68}, 8 locked for C3

27. R6C345 = {179/269/278/359/368} (cannot be {458} which clashes with R6C1, cannot be {467} because no 4,6,7 in R6C3) -> R6C4 = {567}, R6C5 = {123}

28. 45 rule on N6 3 outies R6C6 + R7C78 – 12 = 1 innie R4C7
28a. R7C78 = 9 (step18) -> R6C6 – 3 = R4C7, no 1,2,3 in R6C6, no 7,8,9 in R4C7

29. 7 in N4 locked in R4C123, locked for R4, clean-up: no 6 in R4C9 (step 19), no 3 in R5C9

30. R4C4 = {12} -> R4C567 must contain 1 or 2 = {138/156/246} (cannot be {129/345}), no 9

31. R123C4 (step 9) = {136/145/235} (cannot be {127} which clashes with R4C4), no 7
31a. Killer pair 1/2 in R123C4 and R4C4, locked for C4, clean-up: no 8 in R8C3, no 6 in R7C3 (step 17)

32. R789C6 = {129/138/147/156/237/246} (cannot be {345} which clashes with R8C4)

33. 20(3) cage at R4C8 (step 13) = {389/479/569} (cannot be {578} which clashes with R45C9) = 9{38/47/56}, 9 locked for N6
33a. 12(3) cage at R6C8 cannot be {129}

34. R48C4 = 5 = {14/23}, here’s how
34a. If R4C4 = 1 => R34C3 = {67} => R8C3 = 5 => R8C4 = 4
34b. If R4C4 = 2 => R34C3 = {57} => R8C3 = 6 => R8C3 = 3
[Later I spotted the more direct 14(3)cage at R3C3 + R8C34 = 23, R348C3 = {567} = 18 -> R48C4 = 5.]
34c. R123C4 (step 31) = {145/235} (cannot be {136} which clashes with R48C4) = 5{14/23}, no 6, 5 locked for C4 and N2, clean-up: no 2 in R2C7, no 3 in R3C7 (step 16)
34d. R6C345 (step 27) = {179/269/278/368}

35. R7C345 = {189/279/369/378/468} (cannot be {459} because no 4,5 in R7C3, cannot be {567} because no 5,6,7 in R7C3) -> R7C5 = {1234}

36. R789C6 (step 32) = {129/138/147/156/237/246}.
36a. If {147} => R8C4 = 3 => R7C5 = 2 => R7C4 = 7 (step 35) clashes with R789C6
36b. If {156} and R8C4 = 3 => 20(3) cage = {479} => R7C5 = 2 => R7C4 = 7 (step 35) clashes with 20(3) cage
36c. R789C6 = {129/138/156/237/246} and {156} combination cannot be with R8C3 = 3

37. 25(5) cage in N7 contains 3,7 and must have 1/2 and 8/9, valid combinations 37{159/168/249} (cannot be {23578} which clashes with R89C1)
37a. If {13678} => R78C3 = [95] => R8C4 = 4 => R89C1 = [24]
[If {13579} R89C1 is {24}; step 37a is a restriction, not an elimination.]

38. 45 rule on C89 4 outies R1589C7 = 27 = 9{378/468/567}, no 1,2, clean-up: no 7,8 in R8C8

39. 14(3) at R3C2 = {158/167/239/257/356}
39a. If {158} => R3C2 = 1 => R4C12 = {58} clashes with R6C1)
If {167} => R3C2 = 1 => R4C12 = {67} => R56C1 = [38] => R6C2 = 1 (step 20) clashes with R3C2
If {257} => R3C2 = 2, R3C3 = 6 (step 15), R4C12 = {57} => R4C3 = 6 clashes with R3C3
39b. 14(3) = {239/356}, no 1,7,8, clean-up: no 7 in R3C3
39c. 8 in N4 locked in R6C13, locked for R6, clean-up: no 5 in R4C7 (step 28a)

40. R4C3 = 7 (hidden single in R4/C3/N4)

41. Consider the remaining combinations for 14(3) at R3C2 = {239/356} (step 39b)
41a. If {239} => R3C2 = 2 => R4C12 = {39} => R56C1 = [65] => R6C2 = 4 (step 20) => R5C2 = 1
If {356} => R3C2 = 3 => R4C12 = {56} => R56C1 = [38] => R6C2 = 1 (step 20)
41b. 1 in N4 locked in R56C2, locked for C2

42. Killer pair 5/9 in R4C12 and R4C89, locked for R4
42a. R4C567 (step 30) = {138/246}

43. R3C567 = {149/167/248/347} (cannot be {239} which clashes with R3C2)
43a. If {149} and R3C7 = 1 => R3C56 = {49} => R2C67 = [34], R2C6 and R3C56 clash with R123C4
If {248} and R3C7 = 2 => R3C56 = {48} => R2C7 = 3 => R2C6 = 4 clashes with R3C56
43b. No 2 in R3C7, clean-up: no 3 in R2C7 (step 16), no 4 in R2C6

44. Naked pair {14} in R23C7, locked for C7 and N3, clean-up: no 6,9 in R12C9, no 4,7 in R6C6 (step 28a), no 5,8 in R7C8 (step 18)

45. 45 rule on C789 5 innies R23467C7 = 18, must contain 1,4 in R23C7 = 124{38/56}, no 7, clean-up: no 2 in R7C8 (step 18)

46. 16(3) cage at R6C6 = {259/268/358}
46a. For {268} R6C6 = 6 -> no 6 in R67C7, clean-up: no 3 in R7C8 (step 18)
46b. For {358} R6C6 = 5, R67C7 = [38] -> no 3 in R7C7, clean-up: no 6 in R7C8 (step 18)

47. R4C567 (step 42a) = {138/246}
47a. If {138} R4C7 = 3 -> no 3 in R4C56

48. 12(3) at R6C8 = {147/156/237/246/345}
48a. If {147} R7C8 cannot be 7 because R6C89 = {14} clashes with R6C2
If {156} R7C8 = 1 => R6C89 = {56} => R7C7 = 8 => R6C67 = [53/62], R6C6 clashes with R6C89
If {237} R7C8 = 7 => R6C89 = {23}, R7C7 = 2, R6C67 = [95] clashes with R6C13 which cannot both be 8
If {246} R7C8 = 4 => R6C89 = {26}, R7C7 = 5, R6C67 = [92] clashes with R6C89
If {345} R7C8 = 4 => R6C89 = {35}, R7C7 = 5, R6C67 = [92] => R6C3 = 8 => R6C1 = 5 clashes with R6C89
48b. 12(3) at R6C8 = {147}, R7C8 = {14}, R6C89 = {147} -> no 4 in R5C8, clean-up: no 2 in R7C7 (step 18)
48c. 7 locked in R6C89, locked for R6 and N6 -> R6C4 = 6 -> R6C35 = [83/92], no 1

49. Naked triple {589} in R6C136, locked for R6

50. R4C567 (step 42a) = {138/246}
50a. 6 only in R4C7 -> no 2 in R4C7

51. R6C7 = 2 (hidden single in C7) -> R6C5 = 3, R6C3 = 8, R6C1 = 5, R6C6 = 9, R7C7 = 5, R5C1 = 6, R7C8 = 4 (step 18), R4C7 = 6 (step 28a), R7C3 = 9, clean-up: no 3 in R8C8, no 1 in R89C1

52. Naked pair {17} in R6C89, locked for R6 and N6 -> R6C2 = 4, R5C23 = [12], clean-up: no 7 in R2C2, no 8 in R4C9

53. R9C4 = 9 (hidden single in C4)

54. R8C9 = 9 (hidden single in N9)

55. R4C7 = 6 -> R4C56 = {24} (step 50), locked for R4 and N5 -> R4C4 = 1, R3C3 = 6, R8C3 = 5, R8C4 = 4, R89C1 = [24], R45C9 = [54], R4C8 = 8 (hidden single in R4), clean-up: no 7 in R8C7

56. R4C12 = {39} -> R3C2 = 2

57. R123C4 = {235}, locked for N2 -> R2C67 = [61], R3C7 = 4, clean-up: no 8 in R2C2, no 3 in R2C3 -> R2C23 = [54]

58. R3C7 = 4 -> R3C56 = [91]

59. R1C8 = 6 (hidden single in R1) -> R8C78 = [81], R6C89 = [71]

60. Naked pair {35} in R3C48, locked for R3

61. Killer pair 7/8 in R12C9 and R3C9, locked for C9 and N3

62. R9C7 = 7 (hidden single in C7)

63. R3C8 = 5 (hidden single in C8) -> R3C4 = 3, R12C4 = [52]

64. R1C9 = 2 (hidden single in R1), R23C9 = [87], R3C1 = 8, R2C5 = 7

65. R9C8 = 2 (hidden single in C8)

66. R7C5 = 1 (hidden single in C5), R7C4 = 8, R5C4 = 7

67. R9C3 = 1 (hidden single in R9)

and the rest is naked singles


Now to try to find time to look at Mike's v1.5