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I'm not sure if this qualifies as an Assassin, it should prove difficult with an SSS=1.73 .... It follows the Tetris theme (I didn't have time to colour it , I'll be tempted if you like it ) ...

rcbroughton: This thread gave rise to a great discussion on the nature of Assassins versus regular Killers - by popular demand, I've moved that portion of the discussion to a "sticky" topic here What is an Assassin


Tetris Killer


3x3::k:5382:2835:7188:5121:5121:5121:5383:5896:4869:5382:2835:7188:7188:5121:5383:5383:5896:4869:5382:2835:2835:7188:2562:5383:5896:5896:4869:5382:7698:7698:2562:2562:2562:4362:4362:4869:7698:7698:5137:5137:21:4105:4105:4362:4362:5392:5392:5137:5137:6404:4105:4105:4619:4619:5134:5392:5392:6404:6404:6404:4619:4619:5900:5134:3599:3599:4611:4611:4611:5901:5901:5900:5134:5134:3599:3599:4611:5901:5901:5900:5900:
LBSK<<LNJ^^^<^>^^^^^<^A^>^^^U<>^<H<^>^K<0G<^<L<^^P^^I<K^<>^<>^N^E<I<<N<^^<^<^>^>^



Enjoy

Tarek

Here is a lighter version. SSS=1.22

Tetris Killer V2

3x3::k:6662:4627:5140:3585:3585:3585:4359:5640:6149:6662:4627:5140:5140:3585:4359:4359:5640:6149:6662:4627:4627:5140:3842:4359:5640:5640:6149:6662:4114:4114:3842:3842:3842:5642:5642:6149:4114:4114:6417:6417:21:4617:4617:5642:5642:4112:4112:6417:6417:5892:4617:4617:6411:6411:6158:4112:4112:5892:5892:5892:6411:6411:3084:6158:4367:4367:6915:6915:6915:4365:4365:3084:6158:6158:4367:4367:6915:4365:4365:3084:3084:
QIKE<<HMO^^^<^>^^^^^<^F^>^^^G<>^<M<^>^P<0I<^<G<^^N^^P<O^<>^<>^C^H<R<<H<^^<^<^>^>^



tarek

It's good to see that you've now posted some puzzles with SS scores below two. Maybe next time you produce puzzles at this level you could sign up to post as Assassins. IMHO, just from glancing at the puzzles before I try them, the easier one could have been posted as an Assassin with the harder one as a V2 provided that there was already a volunteer for the following week's Assassin.

Maybe it's a good thing that you didn't colour it. I've just done that on my Excel worksheet and it immediately highlights the hole in the middle.

It was also interesting to note that the first puzzle has four cages which are immediately naked quads but the lighter version doesn't have any. Despite that, the lighter version is definitely the easier of the two.

I have to agree with Andrew that it would have been better to use these Killers as Assassins. By the way, you might want to use the recent SudokuSolver version (3.3.0) for the ratings.

Edit: I made a logical mistake (forgot a combo). Thanks for finding it, manu! My walkthrough should be ok now.

Tetris Killer Walkthrough:

1. R1234 !
a) 11(4) = {1235} locked for N1
b) Innies+Outies C123: -13 = R4C1 - R12C3 -> R4C1 = (1234), R12C3 <> 4
c) 4 locked in 21(4) @ N1 for C1
d) ! Outies R123 = 18(5) = {12348} since R4C1456 = {1234} -> R4C9 = 8; 1,2,3,4 locked for R4; 4 also locked for N5+10(4)
e) 10(4) = {1234} -> CPE: R56C5 <> 1,2,3
f) 28(4): R23C4 <> 6,7 since 4,5 only possible there and R12C3 = {89} blocked by Killer pair (89) of 21(4) @ N1

2. R456
a) Innie of grid = R5C5 = 7
b) 30(4) = {6789} locked for N4; 7 also locked for R4; 8 also locked for R5
c) 5 locked in 17(4) @ R4 for N6 -> 17(4) = 25{19/46} -> 2 locked for R5+N6; R5C89 = (124)

3. R789
a) Innies+Outies N7: -11 = R9C4 - R7C23 -> R9C4 <> 7,8; R7C23 <> 1,2
b) Innies+Outies N9: 1 = R9C6 - R7C78 -> R9C6 <> 1,2,3; R7C78 <> 8,9
c) Outies N9 = 19(2+1): R9C6 <> 5 because R6C89 <> 5,8
d) Outies N9 = 19(2+1): R9C6 <> 4 because R6C89 = {69} blocked by R4C78 = (569)
e) R9C6 <> 8 since it sees all 8 of N9

4. C456 !
a) ! 7 locked in Innies C1234 = 15(4) = 17{25/34} -> 1 locked for C4
b) Killer pair (45) locked in Innies C1234 + 28(4) for C4
c) Innies+Outies N8: -2 = R6C5 - R9C46 -> R6C5 <> 5 since R9C46 >= 8
d) 5 locked in 16(4) @ N5 for C6 -> 16(4) = 5{128/137/146/236} <> 9
e) Innies+Outies N8: -2 = R6C5 - R9C46 -> R9C4 <> 6 because R9C6 >= 6
f) 6 locked in R56C4 @ C4 for N5
g) Killer pair (23) locked in Innies C1234 + R9C4 for C4
h) Naked triple (689) locked in R56C4+R6C5 for N5
i) R6C6 <> 3 since it sees all 3 of N6

5. R456 !
a) Naked triple (689) locked in R5C124 for R5
b) 16(4) = 5{137/146/236} -> R6C7 = (67)
c) ! Innies R6789 = 18(4) <> 5 because R6C47 >= 13
d) 16(4) = 5{137/146/236} -> R5C6 = 5; R5C7 = (34)
e) 20(4) = 6{149/239/248} (step 4f); R6C3 <> 3 since 2 only possible there
f) Innies R6789 = 18(4) = 1{269/278/467} -> 1 locked for R6
g) 1 locked in 17(4) @ N6 = {1259} for R5 -> 9 locked for R4+N6
h) 30(4) = {6789} -> R5C12 = {89} locked for R5
i) R5C4 = 6
j) 3 locked in 10(4) @ N5 for R4+10(4)

6. N478
a) Killer pair (12) locked in 20(4) + R4C1 for N4
b) 5 locked in R6C12 @ N4 for 21(4) -> 21(4) = 35{49/67}
c) Outies N7 = 10(2+1) = 2+{35} -> R9C4 = 2; 3 locked for R6+N4+21(4)
d) Innies+Outies N8: R6C5 = R9C6 = 9
e) R5C3 = 4, R6C4 = 8 -> R6C3 = 2, R6C6 = 1, R5C7 = 3 -> R6C7 = 7, R4C1 = 1
f) 21(4) @ N1 = {1479} -> 7,9 locked for C1+N1
g) Hidden Single: R7C3 = 9 @ C3
h) 21(4) @ N7 = {3459} -> R7C2 = 4
i) 14(4) = 12{38/56} -> 1 locked for N7
j) R5C1 = 8
k) 20(4) @ N7 = {2567} since (78) only possible @ R9C2 -> R9C2 = 7; 5,6 locked for C1+N7

7. C4567
a) 28(4) = {5689} -> 6,8 locked for C3; 5 locked for C4+N2
b) Innies N3 = 11(2) = {29/56}
c) Killer pair (59) locked in Innies N3 + R4C7 for C7
d) 18(4) @ N9 = {1467} since R6C89 = {46} and R7C7 <> 3,5 -> R7C7 = 1, R7C8 = 7
e) 25(4) = {3589} -> R7C4 = 3, R7C6 = 8, R7C5 = 5
f) 23(4) @ N8 = {2489} locked for N9 because R89C7 <> 3,5; 2 also locked for R8

8. N238
a) 10(4) = {1234} -> R3C5 = 1
b) 18(4) = {1467} -> R8C4 = 1, R8C6 = 7; 4,6 locked for C8
c) Outies N3 = 10(2) = {46} locked for C6+N2+21(4)
d) Innies N3 = 11(2) = {29} locked for C7+N3

9. Rest is singles.

Rating: 1.25. I used Killer pairs of large Innies.

So I missed my chance for an Assassin

I would probably want to sign up for 1 assassin & then disappear to improve Generated puzzles design before returning

So ,, where should I sign up ?!

This V2 seems really hard : I have used killer pairs and some cage blockers. I might have missed something since this puzzle seems to be as difficult as many 1.5 I have solved (not able to rate exactly)

Here is my walkthrough :


WALKTHOUGH TETRIS V2




1)Innie for the grid : r5c5=7

2)IO for n9 : r7c78 = 16+r9c6 → r7c78={89} and r9c6=1
→ split cage 8(2) at r6c89 : {17/26/35}

3)IO for n8 : r6c5=r9c4+6 → r9c4={23}, r6c5={89}


4)IO for c1 : r9c2=r56c1+5 → r9c2={89}, r56c1={12/13}
→ 1 locked for c1 and n4 at r56c1

5)Combination for cage 23(4) at n58 : 8{357/456} (r7 c456 cannot contain 1, 8, 9 and 2 from step3) and 9{257} ( r7c456 cannot contains 1,8,9,and 3 from step3)
→ 5 locked for n8 and r7

6)Outies for r89 : r7c19 total 7 : [61] or {34}


7)IO for n7 : total of r7c23=4+r9c4
a) r9c4<=3 → total of r7c23 <=7 : no 7 for r7c23
b) 7 locked in r7c456 for r7 and n8 : combination 8{456} removed for cage 23(4) (step 5)
c) 27(4)={4689} (cannot contain 5 7)
d) r4c9={23} → total of r7c23 = 6/7 : r7c23={24/16/34}


8)Combination for cage 16(4) at n47 : [19]{24} [37]{24} [27]{16} [18]{34} [27]{34}
→ r6c12 contains one of {17} → split cage 8(2) at r6 ={26/35}

9)Outies for r5 = r5c1289 totals 14 : no 9

10)IO for c9 : r56c9=r9c8+9, with r6c9={2356}
a) cage 12(4) at n9 : {1236/1245} → r9c8={23456}
b) r56c9 : combination {56} impossible since it would imply r9c8=2 and both combinations of cage 12(4) would be blocked
c) r9c8 >=2 → total r56c9 >= 11 → r5c9 >= 5 since r6c9 <= 6
d) r5c9 <>5 since total r56c9 >= 11, r6c9 <=6 and combination {56} impossible for r56c9
We deduce r5c9={68}
e) r5c9 <>6 since total r56c9 >= 11, r6c9 <=6 and combination {56} impossible for r56c9
We deduce r5c9=8, r6c9={356} and r9c8={245}
f) No 8 for cage 24(4) at c9 : {2679/3579/4569} → r9c8 <> 4 since {125} blocks all these combinations → r6c89=[53/26]
g) Killer pair {36} at cage 24(4) and r6c9 → no 3 6 for cage 12(4). Deduce cage 12(4) = {1245} - > r7c9={14} and r7c1= {36} (step 6)

11)From step 9, r5c1289={123}8, no 1 at r5c2, no 2 at r5c8 (naked pair {25} at r69c8, 2 and 5 locked for c8)
a) 2 locked for r5 and n4 at r5c12 → r6c1<>2
→ combination {16} removed for r7c23 (step 8)
→ 4 locked for r7 and n8 at r7c23 (step 8)
→ r7c9=1 (HS) , r7c1=6

12)Combinations for cage 24(4) at n7 : 6{37}8 or 6{27}9
→ Naked quad {1237} at r5689c1 → cage 26(4) = {4589}

13)IO for n3 : r4c9= 1 + r12c7 >= 4 : no 1 2 3 at r4c9

14)Naked triple {123} at r5c12+r6c1 : locked for n4

15)a) No 1,3 at r4c78 (no valid combination for cage 22(4) )
b) No 2 at r4c78 since combination {29}[38] for cage 22(4) would block split cage 8(2)
c) Deduce that r4c456= {123} (hidden triple) and r3c5=9

16)r6c5=8 (NS) r7c456={357}, r9c4=2, r7c23={24}, r89c1={37}, r9c2=8

17)Cage 17(4) at n78 = {159}2, r9c89=[54], r8c9=2, r9c3=9 r9c5=6 r6c89=[26] Naked pair {15} at r8c23, r8c5=4

18)Naked pair {37} at r89c1 → r6c1= 1 r6c2=9 r5c12=[23] r5c8=1

19)Last combinations : r4c78={49} r4c23={56} : r4c1=8 r4c9=7 r56c7=[53]

20)Hidden pair for r5 : r5c46={69}, and r5c6=6 (combinations for 18(4) cage) r5c4=9 r6c6= r5c3=4 and r6c34=[75] NS

21)Innies for n3 : r12c7={24} → r23c6={38}, r4c6=2, r23c4={47} r1c6=5, r1c4=6

22) Hidden killer pair {38} locked at r12c3 and r3c3. r12c3 totals 9, so contains one of {38} -> r3c3={38}

23)Naked pair {38} at r3c36 : locked for r3

24)Rest is singles


EDIT : Thanks to Andrew for having pointed out some typos and lack of explanations. There was also a mistake at step 23 (have forgotten an elimination)

Hi,

I won't post any WT for this "V1" because there are many steps similar to Afmob. On the other hand, I 'd like to point out a decisive move that enables me to crack this puzzle in a different way. It' something similar to Ed's technic IOE, but one only obtains an inequality (similar to IOI technic I have used for JFF1)

Following Afmob's WT for instance, one can obtain r56c4=(689) and r6c5=(89) and obtain a naked triple {689}
for n5.

From this situation, using Innies-Outies for n7, we have r7c23 = 11+r9c4 so r7c2, r7c3 <>r9c4. We deduce that digit at r9c4 is locked for n7 and c1 at r78c1, so r9c4 <>r4c1.
Using now Innies-Outies for n47, we have r5c3+r6c3 = 5 + r9c4 - r4c1, so r5c3+r6c3 <> 5 since r9c4 <>r4c1.
We deduce that r56c4 <> 15 , so r6c5<>8 since r56c4<>{69} : r6c5=9, and so on.. . The puzzle becomes smoother from this point.

Cheers,

manu

I finished Tetris Killer v2 over a week ago, soon after Manu's walkthrough was posted, but waited until Richard had moved the interesting What is an Assassin? discussion to its own thread.

I'll rate Tetris Killer v2 at 1.25 to Hard 1.25 the way I solved it, because of some of the combination eliminations and for the hidden killer triple in step 12a; Manu's walkthrough should probably be rated at 1.5.

Here is my walkthrough. I found things hard going in the middle until I spotted the simple step 20; the rest was easy.

Prelims

a) R1234C1 = {2789/3689/4589/4679/5678}, no 1
b) 14(4) cage in N2 = {1238/1247/1256/1346/2345}, no 9
c) 27(4) cage in N8 = {3789/4689/5679}, no 1,2, 9 locked for N8
d) 12(4) cage in N9 = {1236/1245}, no 7,8,9, 1,2 locked for N9

1. 45 rule on whole grid 1 innie R5C5 = 7

2. 45 rule on R89 2 outies R7C19 = 7 = {16/25/34}, no 7,8,9

3. 45 rule on R1234 4 outies R5C1289 = 14 = {1238/1256/1346/2345}, no 9
3a. Max R5C89 = 11 (from the combinations of R5C1289) -> min R4C78 = 11, no 1

4. 45 rule on N9 2 innies R7C78 = 1 outie R9C6 + 16 -> R9C6 = 1, R7C78 = 17 = {89}, locked for R7, N9 and 25(4) cage at R6C8
4a. R7C78 = 17 -> R6C89 = 8 = {17/26/35}, no 4
4b. 1 in N9 locked in R78C9, locked for C9, clean-up: no 7 in R6C8

5. 45 rule on N8 1 outie R6C5 = 1 remaining innie R9C4 + 6, R6C5 = {89}, R9C4 = {23}

6. 23(4) cage at R6C5 = {2579/3578} (cannot be {2489} because 8,9 only in R6C5, cannot be {2678/3479/3569} which clash with 27(4) cage in N8, cannot be {4568} which clash with R7C19), no 4,6, 5,7 locked in R7C456, locked for R7 and N8, clean-up: no 2 in R7C19 (step 2), no 3 in 27(4) cage in N8

7. 45 rule on C789 4 innies R1256C7 = 14 = {1238/1247/1256/1346/2345}, no 9
7a. 9 in N6 locked in R4C789, locked for R4

8. 45 rule on N3 1 outie R4C9 = 2 innies R12C7 + 1
8a. Min R12C7 = 3 -> min R4C9 = 4
8b. Max R4C9 = 9 -> max R12C7 = 8, no 8

9. 12(4) cage in N9 = {1236/1245}
9a. 6 of {1236} must be in R9C89 (R9C89 cannot be {23} which clashes with R9C4), no 6 in R78C9, clean-up: no 1 in R7C1 (step 2)
9b. 6 in R7 locked in R7C123, locked for N7

10. 45 rule on C1 1 outie R9C2 = 2 innies R56C1 + 5
10a. Min R56C1 = 3 -> min R9C2 = 8
10b. R9C2 = {89} -> R56C1 = 3,4 = {12/13}, 1 locked for C1 and N4
10c. 1 in R4 locked in R4C456, locked for N5 and 15(4) cage at R3C5

11. 45 rule on N7 2 innies R7C23 = 1 outie R9C4 + 4
11a. R9C4 = {23} -> R7C23 = 6,7 = {16/24/34}
11b. R7C23 = 6,7 -> R6C12 = 9,10
11c. Max R6C1 = 3 -> min R6C2 = 6
11d. 16(4) cage at R6C1 = {1249/1267/1348/2347}
11e. 7,8,9 only in R6C2 -> R6C2 = {789}

12. 17(4) cage at R8C2 = {1259/1358/2348/2357} (cannot be {1349} which clashes with R7C23, cannot be {1457} because R9C4 only contains 2,3)
12a. Hidden killer triple 1,2,3 in R7C23, 17(4) cage at R8C2 (contains two of 1,2,3, one within N7 and one at R9C4) and R789C1 for N7 -> R789C1 must contain one of 2,3
12b. Killer triple 1,2,3 in R56C1 and R789C1, locked for C1

13. 45 rule on N1 2 innies R12C3 = 1 outie R4C1 + 1
13a. Max R4C1 = 8 -> max R12C3 = 9, no 9

14. 45 rule on R123 2 outies R4C19 = 1 innie R3C5 + 6
14a. Min R4C19 = 9 -> min R3C5 = 3

15. 45 rule on C9 2 innies R56C9 = 1 outie R9C8 + 9
15a. Min R9C8 = 2 -> min R56C9 = 11, no 2,3 in R5C9, no 2 in R6C9, clean-up: no 6 in R6C8 (step 4a)

16. R5C1289 (step 3) = {1238/1256/1346/2345}
16a. 8 of {1238} must be in R5C9 -> no 8 in R5C28

17. 4 in R6 locked in R6C3467
17a. 45 rule on R6789 4 innies R6C3467 = 19 = {1459/1468/2458/2467/3457}
17b. Killer triple 7,8,9 in R6C2, R6C3467 and R6C5, locked for R6, clean-up: no 4 in R5C9 (step 15a), no 1 in R6C8 (step 4a)

18. Max R56C9 = 14 -> max R9C8 = 5 (step 15)
18a. R56C9 cannot total 12 -> no 3 in R9C8 (step 15)
18b. 12(4) cage in N9 = {1236/1245}
18c. 6 of {1236} must be in R9C9 -> no 3 in R9C9
[There’s a forcing chain possible here
R9C8 = 2 => R56C9 = 11 (step 15) = {38/56} -> 12(4) cage in N9 = {1245} (cannot be {1236} which clashes with R56C9)
R9C8 = {45} => 12(4) cage in N9 = {1245}
-> 12(4) cage in N9 = {1245}, locked for N9
but I’ll try to avoid using it to keep the rating down. Step 22 shows that it wasn’t needed]

19. 22(4) cage in N6 = {1489/1579/1678/3478} (cannot be {2389/2569/2578/3469/3568/4567} which clash with R6C89, cannot be {2479} because R5C9 only contains 5,6,8), no 2
19a. 5 of {1579} must be in R5C9 -> no 5 in R4C78 + R5C8
19b. 1 of {1678} must be in R5C8 -> no 6 in R5C8

20. 7,9 in C9 locked in R1234C9 = {2679/3579}, no 4,8

21. R5C9 = 8 (hidden single in C9)
21a. R5C1289 (step 3) = {1238} (only remaining combination) -> R5C128 = {123}, locked for R5
21b. Naked triple {123} in R5C12 + R6C1, locked for N4
21c. 2 in N6 locked in R6C78, locked for R6

22. 1,4 in C9 locked in R789C9, locked for N9
22a. 12(4) cage in N9 = {1245} (only remaining combination), locked for N9, clean-up: no 4 in R7C1 (step 2)
22b. R56C9 = R9C8 + 9 (step 15) -> R6C9 = R9C8 + 1, no 5 in R6C9, clean-up: no 3 in R6C8 (step 4a)

23. 22(4) cage in N6 (step 19) = {1489/1678/3478}
23a. R5C8 = {13} -> no 3 in R4C78

24. R4C456 = {123} (hidden triple in R4), locked for N5, R3C5 = 9 (cage sum), R6C5 = 8
24a. Naked pair {46} in R89C5, locked for C5 and N8
24b. Naked pair {89} in R8C46, locked for R8

25. R3C5 = 9 -> R4C19 = 15 (step 14) = [69/87]

26. R6C12 (step 11b) = 10 (cannot be 9 because R6C12 are both odd) -> R7C23 = 6 = {24}, locked for R7 and N7 -> R7C9 = 1, R7C1 = 6 (step 2), R4C1 = 8, R4C9 = 7 (step 25), R9C4 = 2 (step 11), R9C89 = [54], R8C9 = 2, R6C8 = 2, R6C9 = 6 (step 4a), R89C5 = [46]

27. R7C1 = 6, R89C1 both odd -> R9C2 must be even -> R9C2 = 8 -> R56C1 = 3 (step 10) = [21], R5C2 = 3, R5C8 = 1

28. Naked pair {49} in R4C78, locked for R4 and N6 -> R56C7 = [53], R89C7 = [67], R8C8 = 3

29. R6C12 = 10 (step 26) -> R6C2 = 9 (cage sum), R6C6 = 4, R6C34 = [75], R5C6 = 6 (cage sum), R5C34 = [49], R7C23 = [42], R8C46 = [89]

30. R1234C1 = {4589} (only remaining combination) -> R123C1 = {459}, locked for C1 and N1 -> R89C1= [73], R9C3 = 9

31. 45 rule on N1 2 remaining outies R23C4 = 11 = {47}, locked for C4 and N2 -> R7C4 = 3, R7C56 = [57], R4C4 = 1, R1C4 = 6

32. R1C4 = 6 -> 14(4) cage in N2 = {1256} (only remaining combination) -> R1C6 = 5, R12C5 = {12}, locked for C5 and N2 -> R4C56 = [32]

33. 45 rule on N3 2 remaining innies R12C7 = 6 = {24}, locked for C7 and N3 -> R4C78 = [94], R7C78 = [89], R3C7 = 1

34. R3C2 = 2 (hidden single in R3)

35. 45 rule on C12 2 remaining outies R34C3 = 1 innie R8C2 + 8
35a. R8C2 = {15} -> R34C3 = 9,13 = [36/85]
[Alternatively R23C4 = {47} = 11 -> R12C3 = 9 = {18}/[36]
Hidden killer pair 3,8 in R12C3 and R3C3 for C3 -> R3C3 = {38}]

36. Naked pair {38} in R3C36, locked for R3 -> R3C9 = 5, R3C1 = 4, R12C1 = [95], R12C9 = [39], R23C4 = [47], R3C8 = 6, R12C7 = [42], R12C5 = [21]

37. R23C4 = [47] = 11 -> R12C3 = 9 = [18] (cannot be {36} because 3,6 only in R2C3)

and the rest is naked singles

Here is another puzzle from my unsolved backlog; I managed to solve the Lite version when it was active but had got stuck on the original Tetris Killer. Having gone through Afmob's walkthrough it looks as if some parts of the solving path are fairly narrow but my key breakthrough using 45 rule on N69 was very different.


Here is my walkthrough for Tetris Killer.

Prelims

a) 11(4) cage in N1 = {1235}
b) 28(4) cage at R1C3 = {4789/5689}, no 1,2,3
c) 10(4) cage at R3C5 = {1234}
d) 30(4) cage in N4 = {6789}
e) 14(4) cage at R8C2 = {1238/1247/1256/1346/2345}, no 9

Steps resulting from Prelims
1a. 11(4) cage in N1 = {1235}, locked for N1
1b. 10(4) cage at R3C5 = {1234}, CPE no 1,2,3,4 in R56C5
1c. 30(4) cage in N4 = {6789}, locked for N4

2. 45 rule on whole grid 1 innie R5C5 = 7
2a. 7 in N4 only in R4C23, locked for R4
2b. 7 in N6 only in R6C789, CPE no 7 in R7C7

3. 45 rule on N1 2 innies R12C3 = 1 outie R4C1 + 13
3a. Max R12C3 = 17 -> max R4C1 = 4
3b. Min R12C3 = 14, no 4
3c. 4 in N1 only in R123C1, locked for C1
3d. 4,5 in N4 only in R5C3 + R6C23, CPE no 4,5 in R6C4 and R7C3
3e. 5 in C1 only in R6789C1, CPE no 5 in R7C2

4. Naked quad {1234} in R4C1456, locked for R4
4a. 4 in R4 only in R4C456, locked for N5 and 10(4) cage at R3C5, no 4 in R3C5
4b. 5 in R4 only in R4C789, locked for N6

5. 45 rule on R1234 4 innies R4C2378 = 27 = {5679} (only remaining combination), locked for R4 -> R4C9 = 8
5a. R4C9 = 8 -> R123C9 = 11, no 9
5b. 8 in N4 only in R5C12, locked for R5

6. 45 rule on N7 2 innies R7C23 = 1 outie R9C4 + 11
6a. Max R7C23 = 17 -> max R9C4 = 6
6b. Min R7C23 = 12, no 1,2

7. 45 rule on R89 2 outies R7C19 = 8 = {17/26/35}, no 4,8,9

8. 45 rule on N9 1 outie R9C6 = 2 outies R7C78 + 1
8a. Min R7C78 = 3 -> min R9C6 = 4
8b. Max R7C78 = 8, no 8,9
8c. 8 in N9 only in R89C78, CPE no 8 in R9C6

9. 45 rule on N3 2 remaining outies R23C6 = 10 = {19/28/37/46}, no 5
9a. R23C6 = 10 -> R12C7 = 11 = {29/38/47/56}, no 1

10. 5 locked in 17(4) cage at R4C7 = {1259/2456}, no 3, 2 only in R5C89, locked for R5 and N6
10a. R4C78 = {569} -> no 6,9 in R5C89
10b. 3 in N6 only in R5C7 + R6C789, CPE no 3 in R6C6 and R7C7

11. 45 rule on C1 2 innies R56C1 = 1 outie R9C2 + 4
11a. Min R56C1 = 7 -> min R9C2 = 3

12. 45 rule on C9 2 innies R56C9 = 1 outie R9C8 + 3
12a. R56C9 cannot total 12 -> no 9 in R9C8

13. 28(4) cage at R1C3 = {4789/5689}
13a. R12C3 = R4C1 + 13 (step 3)
13b. Max R4C1 = 3 -> max R12C3 = 16 -> R12C3 cannot contain both of 8,9
13c. Hidden killer pair 8,9 in R12C3 and R23C4 for 28(4) cage -> R12C3 and R23C4 must each contain one of 8,9
13d. R23C4 must contain one of 4,5 and one of 8,9 -> no 6,7 in R23C4

14. Hidden killer quad 1,2,3,5 in R4C1, R6C1 and R789C1 for C1 -> R789C1 must contain two of 1,2,3,5
14a. 20(4) cage in N7 cannot contain more than two of 1,2,3,5 -> no 3,5 in R9C2

15. 20(4) cage at R5C3 = {1469/1568/2369/2459/2468/3458} (cannot be {1289} which clashes with R23C4)
15a. Killer pair 8,9 in R23C4 and R56C4, locked for C4
15b. Max R56C3 = 9 -> min R56C4 = 11, no 1

16. 7 in C4 only in R178C4
16a. 45 rule on C1234 4 innies R1478C4 = 15 = {1257/1347}, no 6, 1 locked for C4
16b. Killer pair 4,5 in R1478C4 and R23C4, locked for C4
16c. 5 in N5 only in R5C6 + R6C56, CPE no 5 in R7C6

17. R7C23 = R9C4 + 11 (step 6)
17a. Min R9C4 = 2 -> min R7C23 = 13, no 3
17b. Naked quad {6789} in R1247C3, locked for C3

18. 20(4) cage at R5C3 (step 15) = {1469/1568/2369/2459/2468/3458}
18a. 3 of {2369} must be in R5C3, 3 of {3458} must be in R5C4 -> no 3 in R6C34

19. 16(4) cage at R5C6 = {1249/1267/1348/1357/1456/2356} (cannot be {1258} because 2,8 only in R6C6, cannot be {2347} which clashes with R4C456, ALS block)
19a. 9 of {1249} must be in R5C6 (R5C67 cannot be [14] which clashes with R5C89, ALS block, R56C6 cannot be [12] which clashes with R4C456, ALS block) -> no 9 in R5C7 + R6C67
19b. 2 of {1267/2356} must be in R6C6, 6 of {1456} must be in R56C7 (R56C7 cannot be {14} which clashes with R5C89, ALS block), no 6 in R6C6

20. Hidden killer quad 1,2,3,5 in R789C1 and R8C23 + R9C3 for N7 -> R789C1 contains two of 1,2,3,5 (step 14) -> R8C23 + R9C3 must contain two of 1,2,3,5
20a. 14(4) cage at R8C2 = {1238/1256/1346/2345} (cannot be {1247} which only contains one of 1,2,3,5 in R8C23 + R9C3), no 7

21. 45 rule on N69 2 remaining innies R56C7 = 1 outie R9C6 + 1
21a. Min R9C6 = 4 -> min R56C7 = 5
21b. R56C7 cannot be {14} which clashes with R5C89 (ALS block) -> min R56C7 = 7 -> min R9C6 = 6

22. 45 rule on N8 2 innies R9C46 = 1 outie R6C5 + 2
22a. Min R9C46 = 8 -> min R6C5 = 6
22b. Max R9C46 = 11 -> no 6 in R9C4

23. Killer pair 2,3 in R1478C4 and R9C4, locked for C4

24. 6 in C4 only in R56C4, locked for N5
24a. Naked triple {689} in R5C124, locked for R5
24b. Naked triple {689} in R56C4 + R6C5, locked for N5
24c. R9C46 = R6C5 + 2 (step 22)
24d. Min R6C5 = 8 -> min R9C46 = 10, no 6 in R9C6

25. 5 in N5 only in R56C6, locked for C6
25a. 16(4) cage at R5C6 (step 19) must contain 5 = {1357/1456/2356}
25b. R56C7 = R9C6 + 1 (step 21)
25c. R9C6 = {79} -> R56C7 = 8,10
25d. 16(4) cage at R5C6 = {1357/1456} (cannot be {2356} because R56C7 must total 8 or 10 and 2,5 only in R56C6), no 2
25e. 6,7 only in R6C7 -> R6C7 = {67}
25f. 2 in N5 only in R4C456, locked for R4 and 10(4) cage in R3C5, no 2 in R3C5

26. 45 rule on N7 3(2+1) outies R6C12 + R9C4 = 10
26a. R9C4 = {23} -> R6C12 = 7,8 = {25/34/35}, no 1

27. 20(4) cage at R5C3 (step 15) must contain 6 = {1469/1568/2468} (cannot be {2369} which clashes with R6C12), no 3

28. 3 in R5 only in R5C67 -> 16(4) cage at R5C6 (step 25d) = {1357} (only remaining combination) -> R6C7 = 7, R5C7 = {13}, clean-up: no 4 in R12C7 (step 9a)

29. 45 rule on R6789 3 remaining innies R6C346 = 11 = {128/146} (cannot be {245} because 2,4 only in R6C3) -> R6C6 = 1, R6C34 = [28/46], R5C67 = [53], clean-up: no 9 in R23C6 (step 9), no 8 in R12C7 (step 9a)

30. Naked triple {234} in R4C456, locked for R4 and 10(4) cage at R3C5 -> R3C5 = 1, R4C1 = 1, R56C3 = [42], clean-up: no 7 in R7C9 (step 7)
30a. 20(4) cage at R5C3 (step 27) = {2468} (only remaining combination) -> R56C4 = [68], R6C5 = 9

31. R6C12 = {35} = 8 -> R9C4 = 2 (step 26)
31a. R9C46 = R6C5 + 2 (step 22), R6C5 = 9, R9C4 = 2 -> R9C6 = 9
31b. R8C9 = 9 (hidden single in N9)

32. Naked pair {46} in R6C89, locked for N6 and 18(4) cage at R6C8, no 4,6 in R7C78
32a. Naked pair {59} in R4C78, locked for R4
32b. R6C89 = {46} = 10 -> R7C78 = 8 = [17/53], no 2, no 1,5 in R7C8

33. R7C23 = R9C4 + 11 (step 6)
33a. R9C4 = 2 -> R7C23 = 13
33b. 9 in N7 only in R7C23 -> R7C23 = [49]

34. R5C2 = 9 (hidden single in C2), R5C1 = 8

35. 14(4) cage at R8C2 (step 20a) = {1238/1256}
35a. 6,8 only in R8C2 -> R8C2 = {68}

36. 21(4) cage at R1C1 = {1479} (only remaining combination), 7 locked for N1 and C1, clean-up: no 1 in R7C9 (step 7)

37. Naked pair {68} in R12C3, locked for C3 -> R4C23 = [67], R89C2 = [87]
37a. 7 in N9 only in R78C8, locked for C8

38. 7 in N3 only in 19(4) cage at R1C9 = {1378} (only remaining combination), 1,3 locked for C9 and N3 -> R5C89 = [12], clean-up: no 5,6 in R7C1 (step 7)

39. 5 in C9 only in R79C9, locked for N9 -> R7C7 = 1, R7C8 = 7 (step 32b)

40. R12C3 = {68} = 14 -> R23C4 = 14 = {59}, locked for C4 and N2 -> R7C4 = 3, R7C1 = 2, R7C9 = 6 (step 7), R7C56 = [58], R4C4 = 4, R1C4 = 7, R8C4 = 1, clean-up: no 2,3 in R23C6 (step 9)

41. Naked pair {46} in R23C6, locked for C6, N2 and 21(4) cage at R1C7, no 6 in R12C7, clean-up: no 5 in R12C7 (step 9a)

42. 14(4) cage at R8C2 (step 35) = {1238} (only remaining combination) -> R89C3 = [31]

43. Naked pair {29} in R12C7, locked for C7 and N3 -> R4C7 = 5, R8C7 = 4

and the rest is naked singles.