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Hi,

I think Udosuk has found a decisive step with this large outie for n8 : not evident to see it !
Here is another way to solve this killer. I think some ideas can be interesting.
Thanks to Ed for some helping aids : once again, he does great things for this forum.

1)Innies for r1 : r1c1289 = h11(4)={1235} locked for r1
2)Innies-outies for n2 = r1c4+r3c6=5+r1c7
=> r3c6<>5 since r1c4<>r1c7
3)a) 5 locked for n2 at 16(3) : {259/358/457}: no 6. 16(3) contains one of {234} so 16(3)+5(2) contains 4. Hidden single for r1 : r1c7=4
b) from step2), r3c6= 9-r1c4=(123), and r1c4<>9, r1c3<>6
4)8(3)n3={125} locked for n3. 3 locked for r1 and n1 at r1c12.
5)a) Outies for c12 : r23c3=h12(2)=[84/75/57]
b) r23c3 contains 5 unless r2c3=8 ie r2c2=5 (cage sum). 5 is locked at r2c23+r3c3 for n1 and r4c2. R34c2<>5 → r3c3<>4, r2c3<>8
6)Naked pair {57} locked for n1 and c3 at r23c3. R1c3<>7, r1c4<>8
7)Innies-outies for n9 : r6c8+r6c9=r9c7+13 : r9c7=(1234) and r6c8+r6c9 >= 14 : contains one of {89}, so r5c7+r6c7 <=16 : r5c6<>5
8)16(3) n2 <> {457} since 7 is locked for n2 and r1 at r1c456 : 16(3) contains one of {23} : 5(2)={14} locked for c4 and n2
9)Innies for n5 : r5c6+r5c6=h12(2)=[39/57]
10)Combinations of 18(3) at n4 : {369/459} : 9 locked for n4 and c3 at r45c3.
11)Combinations for 10(3)n1 with r3c3=(57) = {127/145/235} : r34c2=(1234)
12)Innies-outies for n1 : r4c1+r4c2=4+r1c3=12/13. Since Max r4c1=8 and Max r4c2=4, we deduce that r4c12=[84]

Suddenly, everything become really easy

Here is a V2.5 version of A 171 I have left out, until I find today a way to crack it. The large outie found by udosuk is not valid for
this one, and my solving path had to be quite modified. I had to use a short forcing chain. It is a really hard puzzle, but you should have fun with it. Enjoy !




3x3::k:6656:6656:3842:3842:4868:4868:4868:2055:2055:6656:3338:3338:1292:2061:2061:4879:3344:2055:6656:2579:2579:1292:5398:4879:4879:3344:2330:6656:2579:4637:2590:5398:5398:4879:3344:2330:1828:1828:4637:4637:2590:5673:5673:2859:2859:2093:4910:3375:3632:3632:2590:5673:3636:7477:2093:4910:3375:3375:3632:2363:3636:3636:7477:4927:4910:3375:1346:1346:2363:3909:3909:7477:4927:4927:4938:4938:4938:1869:1869:7477:7477:

Solution :



SSscore : 2.5

Thanks for another nice version, but I'm afraid it is not really that hard. No forcing chain needed at all, and it only takes innie-outies and killer subsets to solve.

I'd think the difficulty is somewhere between your v1 and v2 (with v1 being the hardest among the three). But it's indeed a fun enjoyable puzzle.

No time for a walkthrough from me now, but I'm sure others will show you a decent walkthrough pretty soon.

Added later:

Here are a couple of little tricks that helps, but I'm not sure if they're essential or not:

_________________
ADYFNC HJPLI BVSM GgK Oa m

I don't know if my walkthrough is decent (enough?), but it should give one a good idea how to crack this Killer.

Considering the name of this Killer, I think V1.5 or V2 would have been more appropiate since V2 usually is a tougher version of V1, which could have a score of 1.5 or 2.5 or whatever and if you feel it isn't hard enough then just name it V1.5. But nonetheless, thanks for this fun Killer, manu!

A171 V2.5 Walkthrough

1. C789 !
a) ! Innies+Outies N69: 8 = R59C6 - R4C789 -> R59C6 >= 14 <> 1,2,3,4 must have one of (89) -> R5C6 = (89)
and R59C6 <= 15 -> R4C789 = 6/7 = 12{3/4} -> 1,2 locked for R4+N6
b) 1 locked in R9C789 @ R9 for N9
c) Outies C89 = 9(2) = [27/36]
d) 22(3) = {589} since {679} blocked by R8C7 = (67) -> 5 locked for C7+N6; CPE: R5C89 <> 8,9
e) 11(2) = {47} locked for R5+N6
f) 7(2) = [52/61]
g) 4 locked in R123C7 @ C7 for N3
h) 8(3) = {125} locked for N3
i) 13(3) = 3{19/28} -> 3 locked for C8
j) 15(2) = [69/78]
k) Innies C89 = 20(3) = {569} since (457) only possible @ R7C8 -> R7C8 = 5, R8C8 = 9, R6C8 = 6
l) Cage sums: R7C7 = 3, R8C7 = 6

2. R123
a) Hidden Single: R3C9 = 6 @ N3 -> R4C9 = 3
b) 13(3) = {238} -> R4C8 = 2; 8 locked for C8+N3
c) R4C7 = 1, R9C7 = 2 -> R9C6 = 5
d) 19(4) = {1279} since (38) only possible @ R3C6 -> R3C6 = 2; 7,9 locked for C3
e) 5(2) = {14} locked for C4+N2
f) 8(2) = {35} -> R2C6 = 3, R2C5 = 5
g) R2C8 = 8, R3C8 = 3
h) 10(3) = {145} -> 1 locked for R3+N1; CPE: R12C2 <> 4,5

3. C3456
a) 9(2) = {18} locked for C6+N8
b) Innies R1234 = 14(2) = [86/95]
c) 10(3) @ N5 = {145} since R4C4 = (56) and R6C6 = (47) -> R4C4 = 5, R5C5 = 1, R6C6 = 4
d) 18(3) = {369} -> R4C3 = 9; 3,6 locked for R5

4. R456+N2
a) 7(2) = {25} locked for R5+N4
b) 8(2) = {17} locked for C1
c) 7 locked in 21(3) @ R4 for N5+21(3) -> 21(3) = {678} -> R3C5 = 8; 6 locked for R4+N5
d) R5C4 = 3
e) 14(3) @ N5 = {248} -> R6C5 = 2, R6C4 = 8, R7C5 = 4
f) 19(3) @ N2 = {469} -> R1C7 = 4; 6,9 locked for R1

5. Rest is singles.

Rating: (Hard?) 1.0. I used IOD of large Innies/Outies.

All apologies guys for the level of this puzzle. I have realized just before Udosuk send his post that there was a much more easy way to solve this killer. I was confident about the SudokuSolver score and did not search an easier way; in fact the solving path is really different from V1 or V2. So, let us consider this puzzle as a completely different one (let's say : alt version) and have pleasure with it.

Yeah it's a pretty decent walkthrough. In fact the way you cleaned it up makes it even easier than V2, so it could be renamed as a "V0.5" for this series I guess.

Here is another way to do your first step, which makes it even more straight forward (and it's sort of similar to my critical move for "V2"):

_________________
ADYFNC HJPLI BVSM GgK Oa m

Thanks manu for another nice variant!

Thanks udosuk for making that statement. When I first saw the SS score I was inclined to give this one a miss because I've got so many other unfinished puzzles. However after reading that comment I decided to give it a try.

Unlike both udosuk and Afmob I found this one the hardest of the three A171 puzzles. I'll take udosuk's latest comment "so it could be renamed as a "V0.5" for this series I guess" as being a bit "tongue in cheek". Afmob's first step was impressive, only an optimised walkthrough could start with a move like that. I never spotted it when I was solving this puzzle.

Here is my walkthrough. I've realised that I missed a couple of simple locked steps, involving 1 in R9 and later 1 in C1, which I hope didn't make too much difference.

Prelims

a) R1C34 = {69/78}
b) R2C23 = {49/58/67}, no 1,2,3
c) R23C4 = {14/23}
d) R2C56 = {17/26/35}, no 4,8,9
e) R34C9 = {18/27/36/45}, no 9
f) R5C12 = {16/25/34}, no 7,8,9
g) R5C89 = {29/38/47/56}, no 1
h) R67C1 = {17/26/35}, no 4,8,9
i) R78C6 = {18/27/36/45}, no 9
j) R8C45 = {14/23}
k) R8C78 = {69/78}
l) R9C67 = {16/25/34}, no 7,8,9
m) 19(3) cage at R1C5 = {289/379/469/478/568}, no 1
n) 8(3) cage in N3 = {125/134}
o) 10(3) cage at R3C2 = {127/136/145/235}, no 8,9
p) 21(3) cage at R3C5 = {489/579/678}, no 1,2,3
q) 10(3) cage in N5 = {127/136/145/235}, no 8,9
r) 22(3) cage at R5C6 = {589/679}
s) 19(3) cage at R6C2 = {289/379/469/478/568}, no 1
t) 19(3) cage at R8C1 = {289/379/469/478/568}, no 1
u) 19(3) cage at R9C3 = {289/379/469/478/568}, no 1
v) 13(4) cage at R6C3 = {1237/1246/1345}, no 8,9

Steps resulting from Prelims
1a. 8(3) cage in N3 = {125/134}, 1 locked for N3, clean-up: no 8 in R4C9
1b. 22(3) cage at R5C6 = {589/679}, CPE no 9 in R5C89, clean-up: no 2 in R5C89

2. 45 rule on R1234 2 innies R4C34 = 14 = [86/95]
2a. 10(3) cage in N5 = {136/145/235} (cannot be {127} because R4C4 only contains 5,6), no 7
2b. R4C4 = {56} -> no 5,6 in R5C5 + R6C6

3. 45 rule on R6789 2 innies R6C67 = 9 = [18/27/36/45], no 9
3a. 9 in 22(3) cage locked in R5C67, locked for R5

4. 45 rule on R1 4 innies R1C1289 = 11 = {1235}, locked for R1
4a. 8(3) cage in N3 = {125/134}
4b. 4 of {134} must be in R2C9 -> no 3 in R2C9

5. 45 rule on C12 2 outies R23C3 = 12 = [57/75/84/93], no 1,2,6, no 4 in R2C3, clean-up: no 7,9 in R2C3
5a. Min R3C3 = 3 -> max R34C2 = 7, no 7

6. 45 rule on C89 2 outies R78C7 = 9 = [18/27/36], clean-up: no 6 in R8C8

7. 45 rule on N9 2 outies R6C89 = 1 innie R9C7 + 13
7a. Max R6C89 = 17 -> max R9C7 = 4, clean-up: no 1,2 in R9C6
7b. Min R6C89 = 14, no 1,2,3,4
7c. R6C89 = 14 ... 17 must contain at least one of 8,9
7d. 22(3) cage at R5C6 = {589/679}
7e. 5 of {589} must be in R56C7 (R56C7 cannot be {89} which clashes with R6C89), no 5 in R5C6

8. R5C89 = {38/47} (cannot be {56} because of clash with R5C7 + R6C789, ALS block), no 5,6
8a. R5C12 = {16/25} (cannot be {34} which clashes with R5C12), no 3,4
8b. Killer quint 5,6,7,8,9 in R5C7, R5C89 and R6C789, locked for N6, clean-up: no 2,3,4 in R3C9
8c. 1,2 in N6 locked in R4C789, locked for R4

9. 10(3) cage at R3C2 = {136/145/235} (cannot be {127} because 1,2 only in R3C2), no 7, clean-up: no 5 in R2C3 (step 5), no 8 in R2C3
9a. 1,2 only in R3C2 -> R3C2 = {12}

10. Hidden killer triple 7,8,9 in 19(3) cage at R6C2 and R9C2 for C2, 19(3) cage at R6C2 cannot contain all of 7,8,9 -> R9C2 = {789}
10a. 19(3) cage at R6C2 must contain two of {789} = {289/379/478} (cannot be {469/568} which only contain one of 7,8,9), no 5,6

11. 45 rule on N1 2 outies R4C12 = 1 innie R1C3 + 4
11a. Min R1C3 = 6 -> min R4C12 = 10, no 3 in R4C1
11b. R4C1 cannot be 5 (because R4C12 = [56] clashes with R4C4)

12. 5 in N6 locked in R5C7 + R6C789
12a. {589} can only be [895/958/985] -> R6C89 cannot be {89} because either it clashes with R56C7 or there is no 5 in N6
12b. Max R6C89 = 16 -> max R9C7 = 3 (step 7), clean-up: no 3 in R9C6

13. 29(5) cage at R6C9 must contain at least one of 1,2,3
13a. Killer triple 1,2,3 in 29(5) cage at R6C9 (because no 1,2,3 in R6C9) and R79C7, locked for N9

14. Min R6C8 + R7C7 = 6 -> max R7C8 = 8

15. 45 rule on C9 3 outies R159C8 = 12
15a. Min R15C8 = 4 -> max R9C8 = 8

16. Combined cage R23C4 + R2C56 = 13 = {1237/1246/1345}, 1 locked for N2

17. 29(5) cage at R6C9 must either be {34589} or contain three of 6,7,8,9
17a. {34589} can only have one of 8,9 in N9, other combinations can only have two of 6,7,8,9 in N9 (to avoid clashes with R8C78) -> R6C9 = {6789}

18. 45 rule on C12 3 innies R234C2 = 11 = {146/236/245}
18a. 5 of {245} must be in R4C2 (R34C2 cannot be [24] because 10(3) cage at R3C2 cannot be [244]), no 5 in R2C2, clean-up: no 8 in R2C3, no 4 in R3C3 (step 5)

19. 45 rule on C89 3 innies R678C8 = 20 = {479/569/578}
19a. R7C78 cannot be 15 (CCC because R78C8 = 15) -> no 5 in R6C8
19b. 5 of {569} must be in R7C8 -> no 6 in R7C8

20. 5 in N6 locked in R56C7, locked for C7
20a. 22(3) cage at R5C6 = {589}, no 6,7, CPE no 8 in R5C89, clean-up: no 3 in R5C89
20b. Naked pair {47} in R5C89, locked for R5 and N6, clean-up: no 5 in R3C9
20c. 3 in N6 locked in R4C789, locked for R4
20d. Naked triple {123} in R479C7, locked for C7

21. 6 in N6 locked in R6C89, locked for R6, CPE no 6 in R9C8, clean-up: no 2 in R7C1
21a. R6C89 = {68/69} = 14,15 -> R9C7 = {12} (step 7), clean-up: no 4 in R9C6

22. 4 in C7 locked in R123C7, locked for N3, clean-up: no 3 in R1C89 (step 4a)
22a. Naked triple {125} in 8(3) cage, locked for N3

23. 3 in R1 locked in R1C12, locked for N1 -> R3C3 = 5, R34C2 = 5 = [14], R2C2 = 6, R2C3 = 7, clean-up: no 8,9 in R1C4, no 4 in R2C4, no 1,2 in R2C56, no 1,6 in R5C1
23a. Naked pair {25} in R5C12, locked for R5 and N4, clean-up: no 3,6 in R7C1

24. Naked pair {35} in R2C56, locked for R2 and N2, clean-up: no 2 in R23C4
24a. R23C4 = [14], R2C9 = 2, clean-up: no 7 in R3C9, no 1,4 in R8C5
24b. Naked pair {23} in R8C45, locked for R8 and N8, clean-up: no 6,7 in R78C6

25. R1C7 = 4 (hidden single in R1), R2C1 = 4 (hidden single in R2), R3C6 = 2 (hidden single in N3), R3C8 = 3 (hidden single in R3)

26. Naked pair {89} in R2C78, locked for N3 -> R3C9 = 6, R4C9 = 3, R34C7 = [71], R2C7 = 9 (cage sum), R24C8 = [82], R56C7 = [85], R5C6 = 9, R6C89 = [69], R9C7 = 2, R9C6 = 5, R2C56 = [53], R7C7 = 3, R7C8 = 5 (cage sum), R1C89 = [15], R8C7 = 6, R8C8 = 9, clean-up: no 3 in R6C1, no 4 in R78C6
26a. Naked pair {18} in R78C6, locked for C6 and N8 -> R6C6 = 4

27. R6C6 = 4 -> R4C4 + R5C5 = 6 = [51], clean-up: no 6 in R5C2

28. 21(3) cage at R3C5 = {678} (only remaining combination) -> R3C5 = 8, R4C56 = {67}, locked for R4 and N5

29. R34C1 = [98], R1C3 = 8, R1C4 = 7

30. R7C4 = 6 -> R678C3 = 7 = [124]

31. R5C4 = 3, R6C45 = [82], R7C5 = 4 (cage sum)

and the rest is naked singles.