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Hi all,
an other x-killer with small cages ! So, there are more places to search for. I had to use many little steps to make a "decent" solving path, but , with the right order .... Not difficult for SSolver, but a bit more for me !

Assassin 195




Solution :

3x3:d:k:3072:3072:3842:3075:772:3077:2822:2055:1800:2569:2569:3842:3075:772:3077:2822:1800:2055:2834:2834:2580:4373:4373:4119:4119:2585:3866:2834:3612:2580:2580:4373:5152:4119:2585:3866:3612:3612:2342:2342:5152:1321:1321:4907:4907:2093:3630:4143:5152:4401:3122:3122:4907:3125:2093:3630:4143:4143:4401:4401:3122:3125:3125:3135:2368:1857:2370:2627:2884:3397:2118:2118:2368:3135:1857:2370:2627:2884:3397:2895:2895:

Welcome back manu and congratulations on your 100th post. Thanks for a fun Assassin.

I took some time to reach the key steps; now I know where they are I expect someone to post a much shorter optimised walkthrough.


Here is my walkthrough for A195. It starts with 28 Prelims!

Prelims

a) R1C12 = {39/48/57}, no 1,2,6
b) R12C3 = {69/78}
c) R12C4 = {39/48/57}, no 1,2,6
d) R12C5 = {12}
e) R12C6 = {39/48/57}, no 1,2,6
f) R12C7 = {29/38/47/56}, no 1
g) 8(2) cage at R1C8 = {17/26/35}, no 4,8,9
h) 7(2) cage at R1C9 = {16/25/34}, no 7,8,9
i) R2C12 = {19/28/37/46}, no 5
j) R34C8 = {19/28/37/46}, no 5
k) R34C9 = {69/78}
l) R5C34 = {18/27/36/45}, no 9
m) R5C67 = {14/23}
n) R67C1 = {17/26/35}, no 4,8,9
o) R67C2 = {59/68}
p) 12(2) cage at R8C1 = {39/48/57}, no 1,2,6
q) 9(2) cage at R8C2 = {18/27/36/45}, no 9
r) R89C3 = {16/25/34}, no 7,8,9
s) R89C4 = {18/27/36/45}, no 9
t) R89C5 = {19/28/37/46}, no 5
u) R89C6 = {29/38/47/56}, no 1
v) R89C7 = {49/58/67}, no 1,2,3
w) R8C89 = {17/26/35}, no 4,8,9
x) R9C89 = {29/38/47/56}, no 1
y) 11(3) cage at R3C1 = {128/137/146/236/245}, no 9
z) 10(3) cage at R3C3 = {127/136/145/235}, no 8,9
aa) 20(3) cage at R4C6 = {389/479/569/578}, no 1,2
bb) 19(3) cage at R5C8 = {289/379/469/478/568}, no 1

Steps resulting from Prelims
1a. Naked pair {12} in R12C5, locked for C5 and N5, clean-up: no 8,9 in R89C5
1b. 6 in N2 only in R3C456, locked for R3, clean-up: no 4 in R4C8, no 9 in R4C9

2. 45 rule on N1 3 innies R3C123 = 8 = {125/134}, 1 locked for R3 and N1, clean-up: no 9 in R2C12, no 9 in R4C8

3. 1 in N3 only in 8(2) cage at R1C8 = {17} or 7(2) cage at R1C9 = {16} -> 8(2) cage at R1C8 = {17/35} (cannot be {26}, locking-out cages), no 2,6

4. 45 rule on N3 3 innies R3C789 = 19 = {289/478} (cannot be {379} which clashes with 8(2) cage at R1C8), no 3,5, 8 locked for R3 and N3, clean-up: no 3 in R12C7, no 7 in R4C8

5. Hidden killer pair 1,3 in 8(2) cage at R1C8 and 7(2) cage at R1C9 for N3, 8(2) cage contains one of 1,3 -> 7(2) cage must contain one of 1,3 -> 7(2) cage = {16/34} (cannot be {25} which doesn’t contain 1 or 3), no 2,5

6. 8 in N2 only in one of the 12(2) cages -> one of the 12(2) cages must be {48}, 4 locked for N2

7. 45 rule on N2 1 innie R3C6 = 1 outie R4C5 + 1, no 3 in R3C6, no 3,7,9 in R4C5

8. 9(2) cage at R8C2 = {18/27/45} (cannot be {36} which clashes on D/ with 7(2) cage at R1C9), no 3,6

9. 45 rule on D/ 2 innies R3C7 + R7C3 = 9 = [27/45/72/81], no 9, no 3,4,6,8 in R7C3

10. 9 on D/ only in 20(3) cage at R4C6, locked for N5
10a. Hidden killer pair 3,6 in 7(2) cage at R1C9 and 20(3) cage at R4C6 for D/, 7(2) cage contains one of 3,6 -> 20(3) cage at R4C6 must contain one of 3,6 = {389/569} (cannot be {479} which doesn’t contain 3 or 6), no 4,7

11. R89C4 = {18/27/45} (cannot be {36} which clashes with R89C5), no 3,6
11a. R89C6 = {29/38/56} (cannot be {47} which clashes with R89C5), no 4,7

12. 45 rule on N1 1 outie R4C1 = 1 innie R3C3 + 3, no 1,2,3 in R4C1

13. 45 rule on N9 1 innie R7C7 = 1 outie R6C9 + 1, no 9 in R6C9, no 1 in R7C7

14. 45 rule on N9 3 outies R6C679 = 11 = {128/137/146/236/245}, no 9

15. 45 rule on N7 3 innies R7C123 = 17 = {179/269/278/359} (cannot be {368} because no 3,6,8 in R7C3)
15a. 8,9 only in R7C2 -> R7C2 = {89}, clean-up: no 8,9 in R6C2
15b. 3 of {359} must be in R7C1 -> no 5 in R7C1, clean-up: no 3 in R6C1

16. 45 rule on N8 1 outie R6C5 = 1 innie R7C4 + 2, no 7,8,9 in R7C4

17. 45 rule on R1234 2 innies R4C26 = 11 = [29/38/56/65/83], no 1,4,7,9 in R4C2

18. 45 rule on R6789 2 innies R6C48 = 11 = {38/56}/[92], no 4,7,9 in R6C8

19. 45 rule on N2 3 innies R3C456 = 18 = {369/567}
19a. 5 of {567} must be in R3C6 (R3C45 cannot be {56/57} because 17(3) cage at R3C4 cannot be {56}6/{57}5), no 5 in R3C45

20. 45 rule on N8 3 innies R7C456 = 15 = {159/168/258/456} (cannot be {267/348} which clash with R89C5, cannot be {249} which clashes with R7C123, cannot be {357} because 17(3) cage at R6C5 cannot be 5{57}/7{37}), no 3,7, clean-up: no 5 in R6C5 (step 16)
20a. 4 of {456} must be in R7C56 (R7C56 cannot be {56} because 17(3) cage at R6C5 cannot be 6{56}), no 4 in R7C4, clean-up: no 6 in R6C5 (step 16)

21. 45 rule on N9 3 innies R7C789 = 13 = {139/238/247/346} (cannot be {148/157/256} which clash with R7C456), no 5, clean-up: no 4 in R6C9 (step 13)
21a. R7C123 (step 15) = {179/278/359} (cannot be {269} which clashes with R7C789), no 6, clean-up: no 2 in R6C1

22. 6 in N7 only in R89C3 = {16}, locked for C3 and N7, clean-up: no 9 in R12C3, no 4 in R4C1 (step 12), no 3,8 in R5C4, no 7 in R6C1, no 8 in 9(2) cage at R8C2

23. Naked pair {78} in R12C3, locked for C3 and N1, clean-up: no 4,5 in R1C12, no 2,3 in R2C12, no 1,2 in R5C4

24. Naked pair {39} in R1C12, locked for R1 and N1, clean-up: no 3,9 in R2C4, no 3,9 in R2C6, no 2 in R2C7, no 4 in R2C8, no 5 in R2C9, no 6 in R4C1 (step 12)

25. Naked pair {46} in R2C12, locked for R2 and N1, clean-up: no 8 in R1C4, no 8 in R1C6, no 5,7 in R1C7, no 1 in R1C9, no 7 in R4C1 (step 12)

26. R1C3 = 8 (hidden single in R1), R2C3 = 7, clean-up: no 5 in R1C4, no 5 in R1C6, no 4 in R1C7, no 1 in R1C8

27. R1C5 = 1 (hidden single in R1), R2C5 = 2

28. 11(2) cage at R3C1 = {128} (only remaining combination) -> R4C1 = 8, R3C12 = {12}, locked for R3, R3C3 = 5, placed for D\, R7C3 = 2, R3C7 = 7 (step 9), placed for D/, R1C8 = 5, R2C9 = 3, R2C8 = 1, R1C9 = 6, placed for D/, R12C7 = [29], R34C9 = [87], R3C8 = 4, R4C8 = 6, clean-up: no 9 in R3C6 (step 7), no 4 in R4C5 (step 7), no 4,7 in R5C4, no 3 in R5C6, no 6 in R6C1, no 4,6 in R89C7, no 2 in R8C89, no 4 in R9C2, no 3,8 in R9C8

29. R4C5 = 5, R3C6 = 6, R4C7 = 3 (cage sum), R4C23 = [24], R4C4 = 1, R4C6 = 9, R5C34 = [36], R5C5 = 8, placed for D\, R6C4 = 3, R6C3 = 9, R7C4 = 5, R6C5 = 7 (step 16), R2C4 = 8, R1C4 = 4, R12C6 = [75], R3C45 = [93], clean-up: no 2 in R89C6

30. R7C56 = [91] (hidden pair in N8), R7C2 = 8, R6C2 = 6, R7C1 = 7 (step 21a), R6C1 = 1, R7C89 = [34], R6C9 = 5 (cage sum), R7C7 = 6, R5C12 = [57], R2C2 = 4, placed for D\, R6C6 = 2, placed for D\, R9C9 = 9, placed for D\

and the rest is naked singles without using the diagonals (I’ve a feeling it may have been down to naked singles earlier in step 30 but I continued until all placements were made on the diagonals).

Thanks Andrew for your WT showing interesting interactions between hidden cages at R7. The first part is similar to mine, but my further steps are different (whereas I also use several hidden subsets for blocking combos too).

I have an Assassin (#196 ) ready; please tell me if you are interested and allow a same puzzle poster for two consecutive weeks. It seems that many of us are in holidays ....

ASSASSIN 195 WALKTHROUGH


prelims: remove non valid candidates from cage sums.


Step A : R123

1)a) R12C5 = {12}, locked for C5 and N2.
b) R3C123= h8(3) = 1{25/34} : 1 locked for N1 and R3. Clean up : R4C8 <> 9.
2)6 locked for N2 and R3 at R3C456. Clean up : R4C9 <> 9.
3)R3C456 = h18(3) = 6{39/48/57}.
4)From step 1)+3) : 5 locked for R3 at R3C123456 since h8(3) and h18(3) contain 5 or at least one of {3/4}
5)R3C789 = h19(3) : {289/379/478}
6)8(2)+7(2) at N3 : {1257/1347/1356/2346}. But combinations {1257/2346} are blocked by all combinations of h19(3) => 8(2)+7(2)=13{47/56}
a)=> 3 locked for R3C789 3 locked for R12C7
b)=> h19(3)={29/47}8 : 8 locked for R3 and N3.
c)=> 8(2)={17/35} and 7(2)={16/34}
7)4 locked for N2 at 12(2) +12(2) => one of both 12(2) is {48} : 4 locked for N3 at 12(2)+12(2).

Step B : N3 + R4.

8)Innies-outies for N2 : R4C5=R3C6 – 1.
R4C5 <> 2 => R3C6 <> 3 .
9)From previous step, R4C5 <> R3C6, R3C5, R3C4. From step 2), R4C5 <> 6 => R3C6 <> 7.
10) Innies for R1234 : R4C26= h11(2). R4C6 <> 2 => R4C2 <> 9.
11)9 locked for R4 at R4C67 => CPE : R3C6 <> 9 and (step 8) R4C5 <> 8.

Step C : D/

12) Innies for D/ : R3C7+R7C3 = h9(2) : no 9 .
13)9 locked for D/ and N5 at 20(3).
14) 9(2) and h9(2) at D/ cannot be {36} (block combo of 7(2) : see step 6) c) ) and 7(2) contains exactly one of {36} => 20(3) contains one of {36}. 20(3)={389/569} : no 4/7

Step D : C456

15)Innies for C1234 : R36c4 = h12(2) = [39/75/93]
16)Innies for C6789 : R47C6=h10(2)=[37/64/82/91]
17)Combinations for 17(3) at N2 : [395/764/935] : R34C5 <> 7 (important)
18)7 locked for C5 at R6789C5 => CPE R7C6 <> 7. Clean up : R4C6 <> 3.
19)At N8 : 10(2)={37/46} => 11(2) <> {47}
20)At N8 : 11(2)={29/38} ({56} blocked by R3C6=5/6.
21)At C6 : 11(2) contains one of {489}, h10(2)=[64/82/91] contains one of {489}
=> 12(2) contain at most one of {48}. Since one of both 12(2) at N2 is {48} (step 7) , we deduce R12C4={48} locked for N2 and C4.
22)At N8 : 9(2) <> {36} (blocks combinations of 10(2), see step 19) ) => 9(2)={27} locked for C4 and N8.
The puzzle is cracked, and the rest is soft (singles + cage sums)