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Hi,

Here is a puzzle I have given up at a first time. Having a look again, it offered some (interesting) solving ways.

Assassin 168





3x3::k:3072:3072:3072:1283:1283:7173:7173:7173:7173:3593:5898:5898:5898:8461:8461:8461:8461:2577:3593:5898:2068:2068:4630:4630:4630:8461:2577:1819:5898:2589:1822:4127:4127:4630:1570:2577:1819:3621:2589:5671:1822:4127:2602:1570:3372:4909:3621:5167:5671:5671:1822:2602:5172:3372:4909:6967:5167:5167:5167:2875:2875:5172:1854:4909:6967:6967:6967:6967:5172:5172:5172:1854:5704:5704:5704:5704:2124:2124:3918:3918:3918:


solution :



SScore : 1.58

Thanks for giving us A168, manu! This one was easier than I thought since the whole solving process was pretty straightforward if you like using Killer subsets like I do.

A168 Walkthrough:

1. C19
a) 12(3) = 7{14/23} since other combos blocked by Killer pairs (56) of 14(2) and (12,13,24,34) of 5(2) @ R1
-> 7 locked for R1+N1
b) Innies C1 = 5(2) = {14/23}
c) 7(2) <> {34} since it's a Killer pair of Innies C1
d) 7 locked in 19(3) @ C1 = 7{39/48}
e) Innies C9 = 15(2) = [69/87/96]
f) 13(2) <> {67} since it's a Killer pair of Innies C9

2. N689
a) Killer pair (45) locked in 6(2) + 13(2) for N6
b) 22(3) = 9{58/67} -> 9 locked for N5
c) Outies N9 = 8(2+1) <> 6,7,8,9 (no 6 since R6C8 sees R8C6 and R7C6 >= 2)
d) Innies N6 = 16(3): R4C79 <> 1,2,3 since R6C8 <= 3
e) 10(3) = 1{27/36} since R4C9 = (67) -> 1 locked for C9+N3; R23C9 <> 6,7

3. R3456 !
a) ! Killer triple (123) locked in 8(2) + 18(4) + R3C9 for R3 -> 18(4) can only have one (123)
b) 18(4) = 4{158/167/257/356} <> 9; 4 locked for R3
c) 9 locked in R4C23 @ R4 for N4
d) 14(2) = {68} locked for C2+N4
e) 7(2) = {25} locked for C1+N4
f) Outies R23 = 16(3) = 7{18/36} since (139) only possible @ R4C2 -> R4C2 = (13); 7 locked for R4+N6
g) Hidden Single: R4C3 = 9 @ N4 -> R5C3 = 1
h) 10(2) @ N6 <> 3,6
i) Hidden Single: R6C8 = 3 @ N6

4. C123+R3
a) Innies C1 = {14} locked for C1
b) 12(3) = {147} locked for R1+N1 since R1C1 = (14)
c) R4C2 = 3, R6C1 = 7, R6C3 = 4
d) Hidden Single: R3C3 = 3 @ N1 -> R3C4 = 5
e) Outie N1 = R2C4 = 4
f) 18(4) = {1467} -> R3C7 = 4
g) Hidden Single: R3C9 = 2 @ R3, R5C6 = 3 @ N5

5. C789
a) 10(3) = {127} -> R2C9 = 1, R4C9 = 7
b) Outies N9 = 5(2) = [41] -> R7C6 = 4, R8C6 = 1
c) Cage sum: R7C7 = 7
d) 1 locked in 15(3) @ N9 for R9 -> 15(3) = 1{59/68}

6. R789
a) 8(2) = [26/35/62]
b) 7(2) = {34} -> R7C9 = 3, R8C9 = 4
c) 19(3) = {379} -> R7C1 = 9, R8C1 = 3
d) 20(4) = {2468} -> 2,6,8 locked for R7
e) R7C8 = 5
f) 20(5) = {12359} -> 2,9 locked for R8+N9

7. Rest is singles.

Rating: 1.25. I used a Killer triple.

Thanks manu! I also found A168 easier than I'd expected once I found step 17, which I think is the key to this puzzle; it seems to be the one narrow point. However Ed's walkthrough, below, shows that there's another way to break it open.

I liked the cage pattern. Very much like an onion with different layers around the centre and, to some extent, solving was unwrapping the layers.


Here is my walkthrough. Thanks Afmob for a couple of detail improvements; I also found one myself.

Prelims

a) R1C45 = {14/23}
b) R23C1 = {59/68}
c) R3C34 = {17/26/35}, no 4,8,9
d) R45C1 = {16/25/34}, no 7,8,9
e) R45C3 = {19/28/37/46}, no 5
f) R45C8 = {15/24}
g) R56C2 = {59/68}
h) R56C7 = {19/28/37/46}, no 5
i) R56C9 = {49/58/67}, no 1,2,3
j) R7C67 = {29/38/47/56}, no 1
k) R78C9 = {16/25/34}, no 7,8,9
l) R9C56 = {17/26/35}, no 4,8,9
m) R234C9 = {127/136/145/235}, no 8,9
n) 7(3) cage in N5 = {124}, locked for N5
o) 22(3) cage in N5 = {589/679}, 9 locked for N5
p) R678C1 = {289/379/469/478/568}, no 1
q) R1C6789 = {4789/5689}, no 1,2,3, 8,9 locked for R1
r) 33(5) cage at R2C5 = {36789/45789}, no 1,2, CPE no 7 in R2C9

1. R678C1 = {379/469/478} (cannot be {289/568} which clash with R23C1), no 2,5

2. 45 rule on C1 2 innies R19C1 = 5 = {14/23}
2a. Killer pair 3,4 in R19C1 and R678C1, locked for C1
2b. Killer pair 5,6 in R23C1 and R45C1, locked for C1
2c. Killer pair 5,6 in R45C1 and R56C2, locked for N4, clean-up: no 4 in R45C3

3. 45 rule on C9 2 innies R19C9 = 15 = {69/78}
3a. R56C9 = {49/58} (cannot be {67} which clashes with R19C9), no 6,7
3b. Killer pair 4,5 in R45C8 and R56C9, locked for N6, clean-up: no 6 in R56C7
3c. R234C9 = {127/136/235} (cannot be {145} which clashes with R56C9), no 4

4. R1C123 = {147/237} (cannot be {156} which clashes with R23C1, cannot be {246/345} which clash with R1C45), no 5,6, 7 locked for R1 and N1, clean-up: no 1 in R3C4, no 8 in R9C9 (step 3)
4a. Killer pair 3,4 in R1C123 and R1C45, locked for R1

5. 45 rule on N3 3 outies R1C6 + R2C56 = 3 innies R2C9 + R3C79 + 16
5a. Min R2C9 +R3C79 = 6 -> min R1C6 + R2C56 = 22, no 3,4, 9 locked for N2
5b. Max R1C6 + R2C56 = 24 -> max R2C9 + R3C79 = 8, no 6,7,8,9

6. R234C9 (step 3c) = {127/136/235}
6a. 6,7 of {127/136} must be in R4C9 -> no 1 in R4C9

7. 7 in N3 locked in R2C78 + R3C8, locked for 33(5) cage at R2C5, no 7 in R2C56

8. R1C6 + R2C56 = R2C9 + R3C79 + 16 (step 5)
8a. Max R1C6 + R2C56 = 23 -> max R2C9 + R3C79 = 7, no 5
8b. R1C6 + R2C56 = 22,23 = {589/689}, 8 locked for N2

9. R234C9 (step 3c) = {127/136}, 1 locked in R23C9, locked for C9 and N3, clean-up: no 6 in R78C9
9a. 6,7 only in R4C9 -> R4C9 = {67}

10. 45 rule on N1236 1 outie R4C2 = 1 innie R6C8, no 4 in R4C2, no 6 in R6C8
10a. 4 in N4 locked in R6C13, locked for R6, clean-up: no 9 in R5C9
10b. 6 in N6 locked in R4C79, locked for R4, clean-up: no 1 in R5C1

11. 45 rule on N9 3(2+1) outies R6C8 + R78C6 = 8
11a. Min R78C6 = 3 -> no 7,8,9 in R6C8, clean-up: no 7,8,9 in R4C2 (step 10)
11b. Max R78C6 = 7, no 7,8,9, no 6 in R8C6, clean-up: no 2,3,4 in R7C7

12. 6 in N6 locked in R4C79
12a. 45 rule on N6 3 innies R4C79 + R6C8 = 16 = {169/268/367}
12b. R6C8 = {123} -> no 1,2,3 in R4C7

13. 45 rule on N1 3(2+1) outies R23C4 + R4C2 = 12
13a. Max R4C2 = 3 -> min R23C4 = 9, no 1

14. 4 in N4 locked in R6C13
14a. 45 rule on N4 3 innies R4C2 + R6C13 = 14 = {149/248/347}
14b. R4C2 = {123} -> no 1,2,3 in R6C13
14c. 3 in N4 locked in R4C23 + R5C3, CPE no 3 in R2C3

15. R6C678 = {123} (hidden triple in R6), clean-up: no 1,2,3 in R5C7

16. R9C789 = {159/168/267} (cannot be {249/357/456} which clash with R78C9, cannot be {258/348} because R9C9 only contains 6,7,9), no 3,4
16a. 9 of {159} must be in R9C9 -> no 9 in R9C78
16b. R9C56 = {26/35} (cannot be {17} which clashes with R9C789), no 1,7
16c. Killer pair 5,6 in R9C56 and R9C789, locked for R9

17. 18(4) cage at R3C5 must contain at least one of 1,2,3
17a. Killer triple 1,2,3 in R3C34, R3C567 and R3C9, locked for R3
17b. Hidden killer triple 1,2,3 in R3C34, R3C567 and R3C9 -> R3C567 must contain one of 1,2,3
17c. 18(4) cage at R3C5 = {1458/1467/2457/3456} (other combinations contain more than one of 1,2,3), no 9, 4 locked in R3C567, locked for R3

18. R4C3 = 9 (hidden single in R4), R5C3 = 1, clean-up: no 7 in R3C4, no 5 in R4C8, no 6 in R5C1, no 5 in R56C2
18a. Naked pair {25} in R45C1, locked for C1 and N4 -> R4C2 = 3, R6C8 = 3 (step 10), clean-up: no 3 in R19C1 (step 2), no 9 in R23C1, no 7 in R5C7
19b. Naked pair {68} in R56C2, locked for C2 and N4
19c. Naked pair {14} in R19C1, locked for C1 -> R6C1 = 7, R6C3 = 4
19d. Naked pair {68} in R23C1, locked for C1 and N1, clean-up: no 2 in R3C4
19e. Naked pair {39} in R78C1, locked for N7

20. Killer pair 8,9 in R5C7 and R56C9, locked for N6
20a. Naked pair {67} in R4C79, locked for R4
20b. Naked pair {58} in R4C56, locked for R4 and N5 -> R45C1 = [25], clean-up: no 1 in R4C8, no 4 in R5C8, no 8 in R6C9
20c. R45C8 = [42], R4C4 = 1, R5C5 = 4, R6C6 = 2, R5C79 = [98], R6C79 = [15], R56C2 = [68], R5C46 = [73], clean-up: no 8 in R7C7, no 2 in R78C9, no 5,6 in R9C5, no 7 in R9C9 (step 3)

21. Deleted

22. Naked pair {69} in R19C9, locked for C9 -> R4C79 = [67], clean-up: no 5 in R7C6
22a. Naked pair {34} in R78C9, locked for C9 and N9
22b. Naked pair {12} in R23C9, locked for N3

23. R1C45 = {23} (cannot be [41] which clashes with R1C1), locked for R1 and N2 -> R1C3 = 7, clean-up: no 5 in R3C3
23a. Naked pair {14} in R1C12, locked for N1

24. R3C3 = 3 (hidden single in N1), R3C4 = 5, R3C2 = 9, R3C7 = 4
24a. Naked pair {17} in R3C56, locked for R3 -> R23C9 = [12]

25. Naked pair {25} in R2C23, locked for R2
25a. Naked triple {689} in R2C156, locked for R2 -> R2C478 = [437]
25b. 9 in R2 locked in R2C56, locked for N2

26. R2C6 = 9, R3C6 = 7, R8C6 = 1, then R7C6 = 4 (hidden singles in C6), R3C5 = 1, R7C7 = 7, R78C9 = [34], R78C1 = [93]

27. R9C8 = 1 (hidden single in C8), R9C1 = 4, R1C12 = [14]
27a. R7C2 = 1 (hidden single in C2)
27b. Deleted

28. R6C3 = 4 -> R7C345 = 16 = {268} (only remaining combination), locked for R7 -> R7C8 = 5

29. R9C789 (step 16) = {168} (only remaining combination) -> R9C79 = [86]

and the rest is naked singles.

This cage pattern reminds me of Bullseye 3 here. Thanks for making A168 a whole lot easier than that one manu. Nearly hit the bullseye with the first placement on this one (step 11)!

I worked in a different breakthrough area to Afmob and Andrew. I'll nick Andrew's start to his step 3 since he packs in the elims but then we start to do an oscillating divergence. Just to the breakthrough (step 7) plus a few extra steps just to make sure. Sorry I don't have time for a full WT.

A168Cheers
Ed