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I had hoped to post this on Friday, but it took me forever to solve this puzzle. Since there's been no A154 posted, I'll make this the official one!

I recently asked Afmob how he made the "criss-cross" cage pattern he used in A148. (I think other puzzle makers have used similar patterns.) I've always used Sumocue to draw out potential puzzle diagrams, and it's very cumbersome to include such a pattern. Afmob told me to try using JSudoku. Eureka!!!

You may be sorry he shared this with me, once you take a good look at this cage pattern. I went a little nuts with the criss-crosses.

I've used Richard's nifty "colouring" tool in the hopes it will provide some visual clarity [Moderator edit: image no longer available, a coloured version available in hide below].

Enjoy!

Assassin 154


Note: This is NOT a Killer-X


SS score: 1.37

Been away for a long while. Thanks for a nicely easy puzzle as a welcome-back.

_________________
ADYFNC HJPLI BVSM GgK Oa m

I pretty much solved this Assassin the same way as udosuk, so no walkthrough from me.

I would rate this path of solving 1.0 - Hard 1.0 since to get to the important hidden cages (Innies N58, Outies R123) you had to use other hidden cages (Innies R9, Innies N58), so they aren't immediately there.

Thanks Ronnie for a challenging Assassin.

Many of my steps were the same as those used in udosuk's walkthrough but I took longer to find the early key moves and didn't spot the important part of his final breakthrough Outies @ n1: r1c4+r4c14=14; I'd looked at those outies earlier but maybe not after restricting r4c4 to {678}.

I'll rate my walkthrough at least Easy 1.25 because of step 12, which I found difficult to spot and because it's 5(3+2) innies, step 21 and I'd also rate the move I missed at this level.

Here is my walkthrough.

Prelims

a) 7(2) cage in N4 = {16/25/34}, no 7,8,9
b) 11(2) cage in N6 = {29/38/47/56}, no 1
c) R67C3 = {13}, locked for C3, clean-up: no 4,6 in R6C2
d) R67C7 = {17/26/35}, no 4,8,9
e) 19(3) cage in N7 = {289/379/469/478/568}, no 1
f) 11(3) cage in N8 = {128/137/146/236/245}, no 9
g) 30(4) cage at R1C6 = {6789}, CPE no 6,7,8 in R1C9
h) 14(4) cage at R1C9 = {1238/1247/1256/1346/2345}, no 9
i) R5678C5 = {5789}, locked for C5

1. 45 rule on N7 3 innies R7C23 + R8C3 = 9 = {126/135/234}, no 7,8,9
1a. 5 of {135} must be in R8C3 -> no 5 in R7C2

2. 45 rule on R9 3 innies R9C456 = 11 = {128/137/146/236/245}, no 9

3. 45 rule on N69 1 innie R4C9 = 1 outie R9C6 + 7 -> R4C9 = {89}, R9C6 = {12}
3a. 11(3) cage in N8 = {137/146/236/245} (cannot be {128} which clashes with R9C6), no 8
3b. Killer pair 1,2 in 11(3) cage and R9C6, locked for N8

4. 45 rule on C6789 3 innies R238C6 = 20 = {389/479/569/578}, no 1,2
4a. 8,9 of {389} must be in R23C6 -> no 3 in R23C6

5. 45 rule on N6 3 innies R4C9 + R6C79 = 19 = {289/379/469/478/568}, no 1, clean-up: no 7 in R7C7
5a. 8,9 of {289} must be in R46C9 -> no 2 in R6C9

6. 45 rule on N47 1 innie R4C1 = 1 outie R9C4 + 1, no 1,2,3 in R4C1

7. 45 rule on C789 3 outies R149C6 = 9 -> R1C6 = 6, R49C6 = {12}, locked for C6
[This was there straight after the prelims. If not seen then I ought to have spotted it after step 4 from 45 rule on C6.]
7a. 7 of 30(4) cage at R1C6 locked in R2C7 + R3C8, locked for N3
7b. R2C7 + R3C8 + R4C9 = {789}, CPE no 8,9 in R23C9

8. 45 rule on N2 1 remaining innie R1C4 = 1 outie R4C5, no 5,7,8,9 in R1C4, no 6 in R4C5
8a. Naked quad {1234} in R1C45 + R23C5, locked for N2

9. R9C5 = 6 (hidden single in C5), clean-up: no 7 in R4C1 (step 6)
9a. 11(3) cage in N8 = {146/236}, no 5,7
9b. R9C456 (step 2) = {146/236} -> R9C46 = 5 = {14/23}, no 5,7,8, clean-up: no 6,8,9 in R4C1 (step 6)
9c. Naked pair {34} in R8C6 and R9C4, locked for N8, CPE no 4 in R8C3
9d. Naked pair {12} in R8C4 + R9C6, CPE no 1,2 in R8C7

10. R238C6 (step 4) = {389/479} (cannot be {569/578} because R8C6 only contains 3,4), no 5, 9 locked for C6 and N2
10a. 5 in N2 locked in R23C4, locked for C4

11. 45 rule on N4 3 innies R4C1 + R6C13 = 14, max R4C1 + R6C3 = 8 -> min R6C1 = 6
11a. R4C1 + R6C13 = {149/158/347} (cannot be {167} because 6,7 only in R6C1, cannot be {356} which clashes with 7(2) cage), no 6

12. 45 rule on N58 5(3+2) innies R4C456 + R9C46 = 16
12a. R9C46 = 5 (step 9b) -> R4C456 = 11 = {128/137/146/236}, no 9
12b. 6,7,8 only in R4C4 -> R4C4 = {678}

13. 9 in C4 locked in R567C4 = {189/279/369}, no 4

14. R9C789 = {159/258/357} (cannot be {249} which clashes with R9C46, cannot be {348} which clashes with R9C4), no 4, 5 locked for R9 and N9, clean-up: no 3 in R6C7
14a. 1 in R9 locked in R9C6789, CPE no 1 in R7C8

15. R9C123 = {289/379/478}
15a. 17(3) cage in N7 = {269/359/458/467} (cannot be {179/278/368} which clash with R9C123), no 1

16. 1 in N7 locked in R7C23, locked for R7, clean-up: no 7 in R6C7
16a. 1 locked in R7C23 + R8C3 (step 1) = {126/135}, no 4

17. 45 rule on N9 3 innies R7C78 + R8C7 = 12 = {237/246}, no 8,9, 2 locked in R7C78, locked for R7 and N9, clean-up: no 8 in R9C789 (step 14)

18. 8 in R9 locked in R9C123, locked for N7
18a. R9C123 (step 15) = {289/478}, no 3

19. R4C9 + R6C79 (step 5) = {289/469/568} (cannot be {379/478} because R6C7 only contains 2,5,6), no 3,7

20. 15(4) cage in N6 = {1239/1257/1347/1356} (cannot be {1248} which clashes with R4C9 + R6C79), no 8

21. 45 rule on R123 5 outies R4C14569 = 24
21a. 45 rule on N3 2 remaining outies R4C69 = 10 = [19/28]
21b. -> R4C145 = 14 = {248/257/347/356} (cannot be {158} which clashes with R4C69, cannot be {167/239} because R4C1 only contains 4,5), no 1, clean-up: no 1 in R1C4 (step 8)
21c. 4 of {347} must be in R4C1 -> no 4 in R4C5; clean-up: no 4 in R1C4 (step 8)

22. R9C4 = 4 (hidden single in C4), R4C1 = 5 (step 6), R9C6 = 1 (step 2), R4C9 = 8 (step 3), R8C46 = [23], R1C4 = 3, R4C56 = [32], R4C4 = 6 (step 21b), clean-up: no 2 in 7(2) cage in N4, no 3 in 11(2) cage in N6, no 7 in R567C4 (step 13), no 7 in R9C123 (step 18a), no 9 in R9C789 (step 14)

23. Naked pair {13} in R6C23, locked for R6 and N4

24. Naked pair {89} in R67C4, locked for C4 -> R5C4 = 1
24a. Naked pair {57} in R23C4, locked for N2
24b. Naked pair {89} in R23C6, locked for C6

25. R4C1 + R6C13 (step 11a) = {158} (last remaining combination) -> R6C13 = [81], R6C2 = 3, R5C3 = 4, R67C4 = [98], R7C3 = 3, clean-up: no 2 in R5C7, no 5 in R6C7, no 7 in R6C8
25a. R7C2 = 1 (hidden single in R7), R8C3 = 5 (step 16a)

26. Naked pair {57} in R5C6 + R6C5, locked for N5 -> R5C5 = 8, R6C6 = 4, clean-up: no 7 in R5C7
26a. Naked triple {256} in R6C789, locked for R6 and N6 -> R6C5 = 7, R57C6 = [57], R78C5 = [59], R5C7 = 9, R6C8 = 2, R67C7 = [62], R6C9 = 5, R2C7 = 7, R3C8 = 9, R23C4 = [57], R8C7 = 4, R4C7 = 1, R7C89 = [69], R7C1 = 4
26b. Naked pair {37} in R5C89, locked for R5 and N6 -> R4C8 = 4
26c. Naked pair {67} in R8C12 -> R8C89 = [81], R1C9 = 4
26d. Naked pair {37} in R59C9, locked for C9

27. R23C9 = {26} = 8 -> R1C78 = 9 = [81], R1C5 = 2, R2C8 = 3, R3C7 = 5

28. R23C1 = [13] (hidden pair in C1) = 4 -> R1C23 = 14 = [59]

and the rest is naked singles

Me too! I missed Andrew's step 12 (udosuk's line 11) . Always struggle to find innies. Have to go out and look for them.

Do you use Shift with click to make the cages? Perhaps JSudoku is even easier. Never tried.

Thanks Ronnie.
Ed

Everything seems quiet around here, so I thought I'd try to liven it up a bit! Keep everyone occupied until manu's 156 and of course Ed's Anniversary 157.

Here's a slightly harder version of A154, let's call it V1.5 It has a slightly altered cage pattern and different solution from the V1.

Assassin 154 V1.5




Code string:

3x3::k:5376:4609:4609:4099:5636:7173:4358:4358:3592:4609:5376:4099:5636:5636:5636:7173:3592:4358:4609:4099:5376:4885:4885:4885:3592:7173:4358:4099:5660:5660:5376:4885:3592:4385:4385:7173:5660:5660:1830:5159:5160:4649:2858:4385:4385:5677:1830:1071:5159:5160:4649:1587:2858:4661:4406:5677:1071:5159:5160:4649:1587:4661:5182:4406:4406:5677:4162:4162:4162:4661:5182:5182:4936:4936:4936:5677:4162:4661:3406:3406:3406:



SS score: 1.59

Enjoy!

Sorry about the twitter message...it came from imageshack. I'll once again have to learn how to do images better

Ronnie

Thanks for providing us with a V2, Ronnie! I used lots of combo clashes to solve this Killer, so maybe someone can find a neater way to crack it.

A154 V1.5 Walkthrough:

1. N7
a) 4(2) = {13} locked for C3
b) Innies N7 = 9(3) <> 7,8,9
c) 22(4): R6C1+R9C4 <> 1,2,3,4 because R7C2+R8C3 @ Innies N7 <= 8

2. C789
a) Outies C789 = 9(3) <> 7,8,9; R49C6 = (123) since R1C6 = (456)
b) Innies+Outies N69: -5 = R9C6 - R4C9 -> R4C9 = (678)
c) Outies N3 = 14(3): R1C6 <> 6 since R4C9 = (678) and 28(4) cannot have 6 and 7
d) 28(4) = 89{47/56} -> 9 locked for N3; CPE: R123C9 <> 8; R2C7+R3C8 <> 4,5 since R1C6 = (45)
e) Outies N9 = 12(2+1): R6C9 <> 1,2,3 since R6C7+R9C6 <= 8
f) Outies C789 = 9(3) = 3{15/24} -> 3 locked for C6

3. C123 !
a) Outies C123 = 11(3) <> 9; R14C4 = (1234) since R9C4 >= 5
b) Outies N1 = 10(3) <> 8,9; R4C1 <> 1,2,3 since R14C4 @ Outies C123 <= 6
c) 22(4) @ N7: R6C1 <> 5 because R6C9 <= 8 and R7C2+R8C3 @ Innies N7 <= 8
d) Innies N7 = 9(3) must have one of (25) but cannot have both of them which must be in R7C2 or R8C3
e) 22(4) = {1579/2389/2479/3568/4567} since other combos clash with step 3d
f) 22(4) <> {4567} since R7C2+R8C3 @ Innies N7 would be >= 9
g) Innies N7 = 9(3) must have one of (456) which can only be placed in R7C2 or R8C3
h) 22(4) <> {2389} since it contains no (456)
i) 22(4) = {1579/2479/3568} -> R7C2+R8C3 = {15/24/35}, R9C4 <> 5
j) Innies N7 = 3{15/24} (from step 3i) -> 3 locked for R7+N7

4. R678
a) 17(3) <> 5 since {458} blocked by Killer pair (45) of Innies N7
b) Innies R9 = 13(3): R9C5 <> 6,7,8,9 since R9C4 >= 6; R9C5 <> 1 since R9C46 <= 11
c) Hidden Killer pair (13) in 13(3) for R9 since Innies R9 = 13(3) cannot be {139}
-> 13(3) <> 2{47/56}
d) 13(3) = {139/157/238/346} because {148} blocked by Killer pair (48) of 19(3)
e) Innies N9 = 12(3) <> 3,8 because 3{18/27/45} blocked by Killer pairs (13,35,37) of 13(3)
f) R7C8+R8C7 <> 1 since they see all 1 of R9
g) Innies N9 = 12(3): R7C7 <> 5 because 1 only possible there
h) 6(2): R6C7 <> 1

5. N479 !
a) Outies R1234 = 14(4) <> 9
b) R7C8+R8C7 <> 9 since it sees all 9 of C9
c) Hidden Killer pair (12) in 13(3) for N9 since Innies N9 cannot be {129}
-> 13(3) = {139/157/238} <> 4,6
d) Innies N9 = 12(3) = {147/156/246} with R7C8+R8C7 = {26/46/47/56} since R7C7 = (124)
e) 18(4) = {1269/1467/2367/2457/3456} <> 8 since other combos clash with step 5d
f) ! Outies N9 = 12(2+1): R9C6 <> 2 because R6C79 can only be [46] and this leaves
no combo for 18(4) since 1,3 only possible @ R9C6

6. R789
a) 13(3) = {157/238} since {139} blocked by R9C6 = (13)
b) 9 locked in 19(3) @ R9 = 9{28/46} for N7
c) 5 locked in Innies N7 = 9(3) = {135} -> R8C3 = 5; 1 locked for R7+N7
d) 6(2) = {24} locked for C7
e) 1 locked in 13(3) @ N9 = {157} locked for R9+N9
f) R9C6 = 3, R8C7 = 6
g) 16(4) = {1249} locked for N8; 9 also locked for R8
h) 20(3) = {389} -> R7C9 = 9; 8 locked for R8
i) 22(4) = {3568} since R9C4 = (68) -> R7C2 = 3

7. R456
a) R7C3 = 1, R6C3 = 3
b) Innies N4 = 13(2): R4C1 = (57)
c) 7(2) = [25/61]
d) Killer pair (56) locked in 7(2) + Innies N4 for N4
e) 22(4) @ R4C2 = 49{18/27} -> 9 locked for R4
f) 9 locked in 11(2) @ N6 = {29} -> R5C7 = 9, R6C8 = 2
g) R7C8 = 4 -> R6C9 = 5, R6C2 = 1 -> R5C3 = 6, R6C7 = 4, R6C1 = 8, R9C4 = 6
h) Innie N6 = R4C9 = 8
i) Innie N4 = R4C1 = 5

8. R123+N4
a) 28(4) = {4789} since R2C7 = 7 -> R1C6 = 4, R2C7 = 7, R3C8 = 9
b) Outie N3 = R4C6 = 2
c) 18(3) = {567} locked for C6 since {189} blocked by R8C6 = (19); R6C6 = 6
d) Naked pair (79) locked in R6C45 for N5
e) R5C6 = 5, R7C6 = 7
f) Both 20(3) = 8{39/57} since R7C45 = (58) -> 8 locked for C45
g) Outies C123 = 5(2) = [14/23]
h) 16(4) = 15{28/46} -> R1C4 = 1
i) Outie N1 = R4C4 = 4

9. C123
a) 17(3) = {467} -> R7C1 = 6; 4 locked for R8+N7
b) Hidden Single: R2C3 = 4 @ C3 -> R3C2 = 6
c) 21(4) = {2478} since R3C3 = (278) -> 2,7,8 locked for N1

10. N2
a) R3C6 = 8
b) 19(4) = {1378} -> R4C5 = 1; 3,7 locked for R3+N2

11. Rest is singles.

Rating: 1.5. I used small combo analysis.

Thanks Ronnie, for this puzzle that was resisting a lot !
It has got me thinking a lot because there are a lot of moves you need before cracking it.
I did not find an easier way than Afmob 's solution, but it is a different approach, so I post my wt

The hardest move is 2)d) : a short forcing chain that enables to get some time. I would have liked to avoid it, but this wt would be much longer without it.
Steps 2)d, 3)f) and 3)g) use the interesting cage pattern at n7 and n9 (cells r9c4 and r9c6 see many other ones)

Walkthrough A.154 V1.5


1)a) Outies for n7 : r6c1+r6c3+r9c4=17.
b) Max r6c3=3 → min r6c1+r9c4=14 : r6c1=(56789), r9c4=(56789)
c) IO for n47 : r9c4=1+r4c1 → r4c1 = (45678)
d) Outies for n1 : r4c1+r4c4+r1c4=10 = h10(3) (all these cells see each over)
→ r4c1<>8 → (step c)) r9c4<>9
e) r4c1 <> 4 since it would force r14c4 to be {15} (step d) ) and r9c4 to be 5 (step c)) which is not possible. Deduce (step c)) that r9c4 <> 5.

2)a) Outies for c789 : r1c6+r4c6+r9c6=9 with r1c6 >= 4 (cage 28(4)) → r1c6=(456), r4c6=(123) and r9c6=(123)
b) IO for n69 : r4c9=5+ r9c6 → r4c9=(678)
c) Outies for n9 : r6c7+r6c9+r9c6=12
d) Let us focus on cell r9c6 :
- If r9c6=1 or 2, this digit is locked for n9 at r7c7 (not at (20(3) and see all other cells), so
r9c6+r6c7=6 →(step c)) r6c9=6
- If r9c6 = 3, then r4c9=8
The conclusion is : r4c9=8 or r6c9=6 : we deduce r4c9<>6 →(step b)) r9c6 <> 1

3)a) Outies for r123 : r4c14569 total 20.
b) Min r4c4+r4c5+r4c6=6 → max r4c1 + r4c9 =14 : r4c1<>7 since r4c19 can't be [78]
→ (step 1)c) r9c4 <> 8
c) Innies for r9 : r9c456 = h13(3) : [652/643/742].
d) We deduce from c) that r9c5<>1 → 1 locked for r9 at n9 : 13(3)={139/148/157} : no 2,6.
e) Innies for n7 : r7c2+r7c3+r8c3 = h9(3).
f) Hidden killer pair {26} locked for r9 at r9c12346 → Cells r9c1234 contain at least one of {26} → CPE : r7c2+r8c3 cannot be {26}. We deduce that h9(3) at n7 cannot be {126}.
h9(3) = 3{15/24} : 3 locked for n7 at h9(3)
g) 3 is locked for r9 at r9c6789 → (CPE) r7c8, r8c7 <> 3
h) Innies of n9 : r7c7+r7c8+r8c7 = h9(3). No 1,3 for these cells → {246} locked for n9.
i) 6(2) at 6 = {24} locked for c7 → r8c7=6. R6c9<>6 → r9c6<>2 (step 2)d) : r9c6=3

4)a) r4c9=8 (step 2)b)
b) h13(3) at n9 = [643] (step 3)c)
c) Step 1)a) → r6c1+r6c3=11 : r6c1=8, r6c3=3 → r7c3=1
d) Innie for n4 : r4c1=5
e) Last combos : 22(4) at n478 = [8356] ; 7(2) at n4 = [61]
f) Hidden single for r7 : r7c1=6
g) Step 3)a) → r4c456 total 7 ={124} : r4c4=4, r4c56={12} locked for n5/r4
h) Step 1)d) → r1c4=1
i) Hidden singles : r4c8=6 then r4c7=3 → r4c23={79} locked for n4 → r5c12={24} locked for r5
j) Last combos at n6 : 17(4)={1367} with r5c89={45} locked for n6/r5, and 11(2)={29} with r5c7=9, r6c8=2. 6(2)=[42], and r7c8=4. R6c9=5
k) No 1,2,3,4 at r567c6 : 18(3)=[567]
l) r1c6=4 → r4c6=2 from step 2)a). r4c5=1
m) Last combo for 28(4) at n3 : {4789} : r2c7=7, r3c8=8
n) Hidden pair {24} locked for n3/c9 at r23c9. Hidden single for c9 : r1c9=6
o) Last combination for 17(4) at n3 : {2348} : r1c7=8, r1c8=3
p) Hidden pair {13} locked at r23c1 for c1/n1
q) Last combination for cage 18(4) at n1 : {1359} : r1c2=5, r1c3=9
r) 4 is locked for n1 at cells r2c3+r3c2 : 16(4)={1456} : r3c2=6, r2c3=4
s) Combination of cage 20(3) at n9 : {389} since 3 is locked at cage 20(3) for n9. r8c8=8, r8c9=3, r7c9=9.

The rest is naked and hidden singles

Having caught up with my backlog of unfinished V1s (A161 and A165) last month, I had a look to see if there were any other of Ronnie's puzzles that I hadn't yet done. I found that I'd got stuck on A154 V1.5 and hadn't yet started A150 V2 so I had a go at both of them in the last few days.

I'd got as far as step 21 and had a note of the innies in step 23 (I'd also used 45 rule on N58 for A154) but until this week I hadn't worked out how I could use them. Then after steps 24, 25 and 28 the puzzle was cracked.

Maybe manu's step 2d is that way? It's a neat way, combining a "clone" and a short forcing chain. Many of my steps are similar to those used by Afmob but my breakthrough is different.


Here is my walkthrough for A154 V1.5.

Prelims

a) 7(2) cage in N4 = {16/25/34}, no 7,8,9
b) 11(2) cage in N6 = {29/38/47/56}, no 1
c) R67C3 = {13}
d) R67C7 = {15/24}
e) 20(3) cage at R5C4 = {389/479/569/578}, no 1,2
f) 20(3) cage at R5C5 = {389/479/569/578}, no 1,2
g) 19(3) cage in N7 = {289/379/469/478/568}, no 1
h) 20(3) cage in N9 = {389/479/569/578}, no 1,2
i) 28(4) cage at R1C6 = {4789/5689}, no 1,2,3
j) 14(4) cage at R1C9 = {1238/1247/1256/1346/2345}, no 9

1. Immediate follow-up steps
1a. Naked pair {13} in R67C3, locked for C3, clean-up: no 4,6 in R6C2
1b. 28(4) cage at R1C6 = {4789/5689}, CPE no 8 in R1C9

2. 45 rule on C123 3 outies R149C4 = 11 = {128/137/146/236/245}, no 9

3. 45 rule on C789 3 outies R149C6 = 9 = {126/135/234}, no 7,8,9
3a. R1C6 = {456} -> no 4,5,6 in R49C6
3b. 8,9 of 28(4) cage at R1C6 only in R2C7 + R3C8 + R4C9, CPE no 8,9 in R23C9

4. 45 rule on N7 3 innies R7C23 + R8C3 = 9 = {126/135/234}, no 7,8,9
4a. 45 rule on N7 3(2+1) outies R6C13 + R9C4 = 17
4b. Max R6C13 = 12 -> min R9C4 = 5
4c. Max R9C4 = 8 -> min R6C13 = 9, min R6C1 = 6

5. R149C4 (step 2) = {128/137/146/236/245}
5a. R9C4 = {5678} -> no 5,6,7,8 in R14C4

6. 45 rule on N9 3(2+1) outies R6C79 + R9C6 = 12
6a. Max R6C7 + R9C6 = 8 -> min R6C9 = 4

7. 45 rule on R1234 4 outies R5C1289 = 14 = {1238/1247/1256/1346/2345}, no 9

8. 45 rule on R9 3 innies R9C456 = 13
8a. Max R9C46 = 11 -> min R9C5 = 2
8b. Min R9C46 = 6 -> max R9C5 = 7
8c. 1 in R9 only in R9C6789, CPE no 1 in R7C8 + R8C7

9. 45 rule on N47 1 outie R9C4 = 1 innie R4C1 + 1 -> R4C1 = {4567}

10. 45 rule on N69 1 innie R4C9 = 1 outie R9C6 + 5 -> R4C9 = {678}
10a. 9 of 28(4) cage at R1C6 only in R2C7 + R3C8, locked for N3

11. 45 rule on N1 3(2+1) outies R1C4 + R4C14 = 10 = {127/136/145/235} (normal combinations apply because all three cells are common peers)
11a. 5 of {145} must be in R4C1 -> no 4 in R4C1, clean-up: no 5 in R9C4 (step 9)

12. 45 rule on N3 2 innies R2C7 + R3C8 = 1 outie R4C6 + 14
12a. Min R2C7 + R3C8 = 15, no 4,5
12b. 28(4) cage at R1C6 = {4789/5689}
12c. 4,5 only in R1C6 -> R1C6 = {45}

13. R149C6 (step 3) = {135/234}, 3 locked for C6

14. 45 rule on N2 2 innies R1C46 = 1 outie R4C5 + 4
14a. Max R1C46 = 9 -> max R4C5 = 5

15. 45 rule on N5 3 outies R7C456 = 3 innies R4C456 + 13
15a. Min R4C456 = 6 -> min R7C456 = 19, no 1

16. 45 rule on N7 2 outies R6C1 + R9C4 = 1 innie R7C3 + 13
16a. R7C3 = {13} -> R6C1 + R9C4 = 14,16 = [68/86/97], no 7 in R6C1
16b. R6C1 + R9C4 = 14,16 -> R7C2 + R8C3 = 6,8
16c. 22(4) cage at R6C1 = {68}[35]/[97][15]/[97]{24} -> no 5,6 in R7C2, no 6 in R8C3
16d. R7C23 + R8C3 (step 4) = {135/234}, 3 only in R7C23, locked for R7 and N7

17. 45 rule on N1 2 innies R2C3 + R3C2 = 1 outie R4C4 + 6
17a. Max R4C4 = 4 -> max R2C3 + R3C2 = 10, no 9 in R3C2

18. 45 rule on R4C14569 = 20 = {12368/12458/12467/13457/23456}
18a. 5 of {12458/13457/23456} must be in R4C1 -> no 5 in R4C5
18b. R1C46 (step 14) = R4C5 + 4
18c. Max R4C5 = 4 -> max R1C46 = 8, no 4 in R1C4

19. R9C456 = 13 (step 8) = {148/157/238/247/256/346}
19a. R9C4 = {678} -> no 6,7 in R9C5

20. 19(3) cage in N7 = {289/469/478/568}
20a. 17(3) cage in N7 = {179/269/278/467} (cannot be {458} which clashes with 19(3) cage), no 5
20b. R9C456 = (step 19) = {157/238/247/256/346} (cannot be {148} which clashes with 19(3) cage)

21. 13(3) cage at R9C7 = {139/157/238/346} (cannot be {148} which clashes with 19(3) cage at R9C1, cannot be {247/256} which clash with R9C456)
21a. 45 rule on N9 3 innies R7C78 + R8C7 = 12 = {129/147/156/246} (cannot be {138/237/345} which clash with 13(3) cage), no 3,8
21b. 1 of {156} must be in R7C7 -> no 5 in R7C7, clean-up: no 1 in R6C7
21c. 18(4) cage at R6C9 = {1269/1359/1467/2349/2367/2457/3456} cannot be {1368} because 1,3 only in R9C6, cannot be {1278/1458/2358} because R7C8 + R8C7 = {25/27/45} aren’t consistent with any combinations for R7C78 + R8C7 -> no 8 in R6C9
[This is how far I’d got when this puzzle first appeared. I had a note for the innies in step 23, which I’d used for A154, but at that time hadn’t worked out how to use them for this puzzle.]

22. 45 rule on N9 3 innies R7C78 + R8C7 (step 21a) = {129/147/156/246}
22a. 6 of {156/246} must be in R8C7 (R78C7 cannot be {15/24} because of CCC with R67C6), no 6 in R7C8
22b. 5 of {156} must be in R7C8 -> no 5 in R8C7

23. 45 rule on N58 5(3+2) innies R4C456 + R9C46 = 16 must contain at least one 1 in R4C456 + R9C6 (if R4C456 = {234} = 9 -> R9C46 = 7 can only be [61]), CPE no 1 in R56C6
23a. 1 in N5 only in R4C456, locked for R4
23b. 1 in R6 only in R6C23, locked for N4

24. Hidden killer triple 1,2,3 in 22(4) cage, 7(2) cage and R6C6 for N4, 7(2) cage contains one of 1,2,3, R6C6 = {13} -> 22(4) cage must contain one of 2,3
24a. 22(4) cage in N4 = {2479/2569/2578/3469/3478} (cannot be {3568/4567} which clash with 7(2) cage, cannot be {2389} which contains two of 2,3)

25. 45 rule on N4 3 innies R4C1 + R6C13 = 16 = {169/178/358} (cannot be {367} which clashes with 22(4) cage)
25a. 8,9 only in R6C1 -> R6C1 = {89}
25b. R6C1 + R9C4 (step 16a) = [86/97] -> R9C4 = {67}, clean-up: no 7 in R4C1 (step 9)
[Alternatively hidden killer pair 8,9 in 22(4) cage and R6C1 for N4, 22(4) cage contains one of 8,9 -> R6C1 must contain one of 8,9 -> R6C1 = {89}]
25c. R4C1 + R6C13 = {169/358}
25d. R4C1 + R9C4 = [56/67], CPE no 6 in R9C1

26. 7 in N4 only in 22(4) cage (step 24a) = {2479/2578/3478}, no 6
26a. 6 in N4 only in R4C1 + R5C3, CPE no 6 in R2C3

27. R9C456 (step 19) = {157/247/256/346}
27a. 4,5 only in R9C5 -> R9C5 = {45}

28. 1 in R4 only in R4C456
28a. R4C14569 (step 18) = {12368/12458/12467/13457}
28b. 7,8 only in R4C9 -> R4C9 = {78}, clean-up: no 1 in R9C6 (step 10)

29. 1 in R9 only in R9C789, locked for N9, clean-up: no 5 in R6C7

30. R7C78 + R8C7 (step 21a) = {246} (only remaining combination) -> R8C7 = 6, R7C78 = {24} (locked for R7 and N9), clean-up: no 5 in R6C8

31. Naked pair {13} in R7C23, locked for N7, R8C3 = 5 (step 4), clean-up: no 2 in R6C2

32. Naked pair {24} in R67C7, locked for C7, clean-up: no 7,9 in R6C8

33. 18(4) cage at R6C9 (step 21c) = {2367/3456} -> R9C6 = 3, R4C9 = 8 (step 10), clean-up: no 3 in 11(2) cage in N6
33a. 5,7 of 18(4) cage only in R6C9 -> R6C9 = {57}

34. 3 in N9 only in 20(3) cage = {389} (only remaining combination) -> R7C9 = 9, R8C89 = [83]

35. Naked triple {157} in R9C789, locked for R9 -> R9C5 = 4, R9C4 = 6, R4C1 = 5 (step 9), clean-up: no 2 in R5C3

36. Naked triple {578} in R7C456, locked for R7 and N8 -> R7C1 = 6
36a. R4C14569 (step 28a) = {12458} (only remaining combination) -> R4C456 = {124} -> R4C4 = 4, R1C4 = 1 (step 2), R4C56 = {12}, locked for R4 and N5, CPE no 2 in R3C6

37. R4C8 = 6 (hidden single in R4), clean-up: no 5 in R5C7
37a. Naked pair {24} in R6C78, locked for N6
37b. Naked pair {24} in R67C8, locked for C8

38. Naked pair {79} in R25C7, locked for C7 -> R4C7 = 3

39. Naked pair {79} in R4C23, locked for N4 -> R6C1 = 8, R6C3 = 3 (step 25), R7C23 = [31], R6C2 = 1, R5C3 = 6

40. R4C78 = [36] = 9 -> R5C89 = 8 = {17}, locked for R5 and N6 -> R5C7 = 9, R6C8 = 2, R67C7 = [42], R7C8 = 4, R6C9 = 5, R2C7 = 7, R3C8 = 9, R1C6 = 4 (cage sum)

41. R4C6 = 2 (step 3), R1C9 = 6 -> R2C8 + R3C7 = 6 = {15}, locked for N3 -> R1C78 = [83], R4C5 = 1

42. Naked pair {29} in R8C45, locked for R8 -> R8C6 = 1

43. R23C1 = {13} (hidden pair in C1) = 4 -> R1C23 = 14 = [59], R4C23 = [97]

44. R2C3 = 4 (hidden single in C3), R3C2 = 6 (cage sum), R23C9 = [24], R2C2 = 8, R3C3 = 2, R1C1 = 7, R1C5 = 2, R8C45 = [29]

45. 22(4) cage in N2 = {2569} (only remaining combination) -> R2C456 = {569}, locked for R2 and N2

46. 45 rule on C6 2 remaining innies R23C6 = 17 = [98]

and the rest is naked singles.