SudokuSolver Forum

Hello everyone,


Sorry to disappoint you manu, but this puzzle is just the opposite! There are several fixed cages: a 3(2), 4(2), 24(3), and even 34(5). No doubt after a couple of simple moves, you'll find even more cages/cells with severely restricted placements.

Intuitively, one would think (or at least I would think) such a puzzle would be very simple. This one managed to put up a decent fight despite itself. And thank you manu for the challenge of finding a puzzle like this! I suppose I am contrarian by nature, so your comment became my inspiration!

Enjoy!

Ronnie

Assassin 160




Note the remote 21(4) cage @ R5C37 + R37C5

Code:
3x3::k:5632:5632:5122:5122:772:5381:5381:5895:5895:3849:5632:5122:5122:772:5381:5381:5895:6417:3849:5632:5396:5396:5398:4631:4631:5895:6417:3849:3849:5396:5396:8735:4631:4631:6417:6417:1060:1060:5398:8735:8735:8735:5398:1835:1835:6189:2606:4911:4911:8735:4658:4658:2356:3637:6189:2606:4911:4911:5398:4658:4658:2356:3637:4927:6189:4927:5698:5698:5698:5957:3637:5957:4927:4927:4927:3403:3403:3403:5957:5957:5957:



SS Score 1.24

Thanks for this fun Killer, Ronnie! This one offered lots of interesting Killer subsets. My initial walkthrough had several Hidden Killer pairs and even a Hidden Grouped Killer quad in C89 to show that 23(5) must have three of (1234), but steps 3a,3b were easier, so I replaced this move.

A160 Walkthrough:

1. R5+C5
a) 4(2) = {13} locked for R5+N4
b) 7(2) = {25} locked for R5+N6
c) 3(2) = {12} locked for C5+N2
d) 21(4) = 3{459/468/567} -> 3 locked for C5
e) 34(5) = {46789} locked for N5
f) Innies R6789 = 9(2) = [45/63]
g) Innies R1234 = 12(2) = [39/48/57/84]

2. R6789
a) Outies R9 = 10(4) = {1234} locked for R8
b) Innies R89 = 13(2) = [76/85]
c) 24(3) = {789} -> 9 locked for C1; CPE: R9C1 <> 7,8
d) Outies C12 = 4(2) = {13} locked for C3+N7
e) 10(2) <> 7,9
f) 22(3) = 9{58/67} -> 9 locked for N8
g) Outies C89 = 11(2) = [29/38/47]
h) Innies N8 = 10(3) <> 7,8 since R7C5 = (35)
i) Killer pair (56) locked in Innies N8 + 22(3) for N8 -> 13(3) = {148/238/247}

3. R6789 !
a) 23(5) <> 56{129/138/147/237} blocked by R8C8 = (56)
b) 23(5) = {12389/12479/13469/23459/23468} since 178{25/34} blocked by Killer pair (78) of 13(3)
c) ! Killer quad (1234) locked in R9C3 + 13(3) + 23(5) for R9
d) 19(5) = 13{258/267/456} <> 9 since R9C1 = (56) and R89C3 = (13)

4. C1234 !
a) 15(4) = {1248/1257/2346} <> 9 since 13{29/47/56} blocked by R5C1 = (13)
b) 9 locked in 22(4) @ C2 for N1
c) Killer pair (13) locked in 15(4) + R5C1 for C1
d) ! 19(5) can only have one of (6789) since 24(3) must have 3, 22(4) must have 2 and each of 15(4) and 10(2) must have one of (6789) @ C12 (Grouped Killer quad)
-> 19(5) = 135{28/46} -> 5 locked for R9+N7

5. R6789 !
a) 9 locked in 23(5) @ R9 = 19{238/247/346} -> 1,9 locked for N9
b) 1 locked in R7C46 @ R7 for N8
c) 13(3) = 2{38/47} -> 2 locked for R9+N8
d) Innies N8 = 10(3): R7C46 <> 3,5 since R7C5 = (35)
e) ! Innies+Outies N7: -2 = R6C1 - R7C23: R6C1 = (789) -> R7C23 = {27/28/29/47} <> 6 since
{46} blocked by R7C46 = (146)
f) 6 locked in 19(5) @ N7 = {13456} -> R8C1 = 4; 6 locked for R9
g) 10(2) = {28} locked for C2
h) R8C2 = 7

6. R6789
a) 22(3) = {589} locked for R8+N8
b) R7C5 = 3, R8C8 = 6
c) Innie R6789 = R6C5 = 6
d) 13(3) = {247} locked for R9+N8
e) 23(5) = {12389} locked for N9
f) 9(2) = {45} -> R6C8 = 4, R7C8 = 5
g) 14(3) = {167} -> R7C9 = 7, R6C9 = 1
h) R7C7 = 4, R5C8 = 2, R5C9 = 5
i) 18(4) = 45{18/36} since R7C6 = (16) and R6C6 = (235) -> R6C6 = 5

7. R1234
a) 25(4) = 6{289/379/478} -> 6 locked for C9
b) 23(4) = 49{28/37} -> R1C9 = 4; 9 locked for C8+N3
c) 23(4) = {3479} -> 3,7 locked for C8+N3
d) 25(4) = {2689} -> R4C8 = 8, R4C9 = 9; 2,6 locked for C9+N3

8. C1234
a) 24(3) = {789} -> 8 locked for C1
b) R6C7 = 3 -> R7C6 = 6
c) 19(4) = {1279} -> R6C4 = 2, R7C4 = 1, R7C3 = 9, R6C3 = 7
d) R4C4 = 3, R4C6 = 1
e) 20(4) = 2{459/468/567} -> 2 locked for C3+N1

9. R1234
a) 18(4) = {1368} since R3C7 = (58) and R4C7 = (67) -> R3C7 = 8, R4C7 = 7, R3C6 = 3
b) 21(4) @ N3 = {1578} since R12C7 = (15) -> 7,8 locked for C6+N2
c) 21(4) @ N1 = {3459} -> R3C4 = 9; 4,5 locked for C3
d) 20(4) = {2468} -> R1C4 = 6, R2C4 = 4; 8 locked for C3
e) 22(4) = {1579} since R1C1 = (57) -> R1C1 = 7; 1,5 locked for C2+N1

10. Rest is singles.

Rating: Hard 1.25. I used a Grouped Killler quad.

Whew! That was tough. Please, no one upset Ronnie again!! Perfect for a round number puzzle so thanks Ronnie! Looks I missed some things based on the SSscore.

I don't have time for a full walkthrough, so here's the beginning to the first placement. Takes 2 key moves that look deceptively simple (steps 16 & 17). I haven't had time for a close look at Afmob's WT but am very disappointed I missed out on his step 4d. Love those!

Please let me know of anything incorrect or that could to be clearer. Thanks Andrew for some clarifications.

A160
18 steps

Prelims
i. 3(2)n2 = {12}
ii. 34(5)n5 = {46789}
iii. 4(2)n4 = {13}
iv. 7(2)n6: no 7,8,9
v. 24(3)n4 = {789}
vi. 10(2)n4: no 5
vii. 9(2)n6: no 9
viii. 22(3)n8: no 1,2,3,4

1. "45" c12: 2 outies r89c3 = 4 = {13}: both locked for n7 & c3
1a. no 7,9 in r6c2

2. 24(3)n4 = {789}
2a. -> no 7,8,9 in r89c1 (CPE)

3. 22(3)n8 = {589/679}: 9 locked for n8 & r8
3a. 9 in 24(3)n4 only in c1: locked for c1

4. "45" r89: 2 innies r8c28 = 13 = [85/76]
4a. naked quint {56789} in r8c24568: all locked for r8

5. "45" c89: 2 outies r89c7 = 11 (no 1) = [29/38/47]
5a. r9c7 = (789)

6. 3(2)n2 = {12}: both locked for n2 & c5

7. "45" r6789: 2 innies r67c5 = 9 = [45/63]

8. "45" n8: 3 innies r7c456 = 10 and must have 3/5 for r7c5
8a. h10(3) = {136/145/235}(no 7,8) = [5/6..]

9. Killer pair 5,6 in n8 in h10(3) (step 8a) and 22(3)n8 (step 3): both locked for n8
9a. 13(3)n8 = {148/238/247} = [7/8..]

10. 23(5)n9: combos with {56} blocked by r8c8
10a. those with {78} blocked by 13(3)n8 (step 9a) since 7 & 8 can only be in r9
10b. = {12389/12479/23459/23468} = 2{..}
10c. 2 locked for n9
10d. no 7 in r6c8
10e. = two of 5,6,7,8,9 in r9

11. hidden killer quint 5,6,7,8,9 in r9 since 13(3)n8 has one of 5..9 (step 9a) and r9c789 has two of 5..9 (step 10e)
11a. -> r9c12 must have two of 5..9 = {56789}

12. split-cage 15(3)n7 in r89c1 + r9c2 must have 5/6 for r9c1 = {258/267/456}(no 9)

13. 9 in r9 only in n9: locked for n9
13a. 23(5)n9 must have 9 = 29{138/147/345}(no 6)

14. 6 in r9 only in n7: locked for n7
14a. no 4 in r6c2
14b. split-cage 15(3)n7 must have 6 = 6{27/45}(no 8)

15. split-cage 12(3) in r8c9 + r9c89 = {129/138/147/345)({237} blocked by h11(2)r89c7 (step 5)

I'm sure there must be an easier way than the following 2 steps, but just can't find it.
16. No 4 in r8c9. Like this.
16a. 9 in n9 in h11(2)r89c7 = [29] or in split-cage 12(3) = {129}(step 15)
16b. -> r8c79 = [2]/(12)
16c. -> 4 blocked from r8c9 since [24] in r8c79 would clash with r8c1

17. 4 in r8 only in r8c17 -> no 7 in r9c2. Like this.
17a. 4 in r8c7 -> r9c7 = 7 (h11(2)r89c7)
17b. 4 in r8c1 -> r9c12 = 11 = {56} (no 7) (step 14b)
17c. either way, no 7 in r9c2.

18. r9c12 = {56}: 5 locked for r9 & n7
18a. r8c1 = 4 (split-cage 15(3) sum step 12)
18b. no 6 in r6c2

Things ease up from here.

Cheers
Ed

Thanks Ronnie : despite of many early placements, it resists again and again ....

Yes, but I was not disappointed by this one !



....

Very glad to inspire others. Stop it, too much compliments guy !!!



ASSASSIN 160 WT

Thanks Ronnie for a very challenging puzzle!

I ground to a complete halt when this Assassin first appeared, which explains some of my steps which may not be part of any direct solving path; they were what I found at the time. After having another look at it recently I managed to find step 21a, not sure why I couldn't see that from step 21 before, and after that it was fairly straightforward although still long. Maybe some of my earlier steps proved to be useful after step 21a.

The walkthroughs by Afmob, Ed and manu were all interesting. I think the key breakthrough is to show that the 23(5) cage in N9 must contain three of 1,2,3,4, unless one uses manu's cloning method.


Here is my walkthrough. Thanks Afmob for pointing out my error in step 14; I've added two new steps after step 24 and edited a few other ones.

Prelims

a) R12C5 = {12}
b) R5C12 = {13}
c) R5C89 = {16/25/34}
d) R67C2 = {19/28/37/46}, no 5
e) R67C8 = {18/27/36/45}, no 9
f) 24(3) cage at R6C1 = {789}
g) R8C456 = {589/679}
h) 34(5) cage in N5 = {46789}

With so many numbers locked by the Prelims, I’ve kept these back until step 1.

1. Naked pair {12} in R12C5, locked for C5 and N2
1a. Naked pair {13} in R5C12, locked for R5 and N4, clean-up: no 4,6 in R5C89, no 7,9 in R7C2
1b. Naked pair {25} in R5C89, locked for R5 and N6, clean-up: no 4,7 in R7C8
1c. 24(3) cage at R6C1 = {789}, CPE no 7,8,9 in R89C1
1d. 34(5) cage in N5 = {46789}, locked for N5
1e. 19(5) cage in N7 must contain 1, locked for N7, clean-up: no 9 in R6C2

2. R8C456 = {589/679}, 9 locked for R8 and N8
2a. Killer pair 7,8 in R8C2 and R8C456, locked for R8
2b. 9 in 24(3) cage at R6C1 locked in R67C1, locked for C1

3. 45 rule on R89 2 innies R8C28 = 13 = [76/85]
3a. Killer pair 5,6 in R8C456 and R8C8, locked for R8
[Alternatively 45 rule on R9 4 outies R8C1379 = 10 = {1234}, locked for R8. I prefer the innies which will allow a second placement once the first cell of R8C28 has been placed.]

4. 45 rule on C12 2 outies R89C3 = 4 = {13}, locked for C3 and N7, clean-up: no 7 in R6C2

5. 45 rule on R1234 2 innies R34C5 = 12 = [39/48/57/84], no 6, no 7,9 in R3C5

6. 45 rule on R6789 2 innies R67C5 = 9 = [45/63]

7. 45 rule on C89 2 outies R89C7 = 11 = [29/38/47], no 1, R9C7 = {789}

8. 21(4) remote cage at R3C5 = {3459/3468/3567}, 3 locked in R37C5, locked for C5

9. 45 rule on N8 3 innies R7C456 = 10 = {136/145/235} (cannot be {127} because R7C5 only contains 3,5), no 7,8
9a. Killer pair 5,6 in R7C456 and R8C456, locked for N8

10. 45 rule on N7 2 outies R6C12 = 1 innie R7C3 + 8
10a. R6C12 cannot be 16 -> no 8 in R7C3

11. 45 rule on N9 2 outies R6C89 = 1 innie R7C7 + 1
11a. Min R6C89 = 4 -> min R7C7 = 3

12. Hidden killer pair 1,3 in R123C2 and R5C2 for C2 -> R123C2 must contain one of 1,3
12a. 22(4) cage in N1 cannot contain both of 1,3 -> no 1,3 in R1C1

13. Hidden killer pair 1,3 in R23C1 and R5C1 for C1 -> R23C1 must contain one of 1,3
13a. 15(4) cage at R2C1 = {1248/1257/2346} (cannot be {1239/1347/1356} which contain both of 1,3), no 9
13b. 6,8 of {1248/2346} must be in R234C1 (R234C1 cannot be {124/234} which clash with R8C1), no 6,8 in R4C2

14. 14(3) cage at R6C9 = {158/167/257/356} (cannot be {149/239/248/347} because R8C8 only contains 5,6), no 4,9
14a. Deleted

15. R6C89 = R7C7 + 1 (step 11)
15a. R6C89 cannot total 6 -> no 5 in R7C7

16. 19(5) cage in N7, max R89C13 = 14 -> min R9C2 = 5

17. 45 rule on N9 2 innies R7C78 = 1 outie R6C9 + 8
17a. R7C78 cannot be 16 -> no 8 in R6C9

18. Deleted

19. 45 rule on C6789 4(3+1) innies R5C67 + R89C6 = 22
19a. Min R5C67 + R8C6 = 15 -> max R9C6 = 7

20. 45 rule on N7 4 innies R7C123 + R8C2 = 26 = {2789/4589/4679/5678}
20a. R7C12 + R8C2 cannot be {289} because [928] clashes with R67C2 = [82], 4,5,6 of {4679/5678} must be in R7C23 -> no 7 in R7C3

21. R89C7 = 11 (step 7) -> R8C9 + R9C89 = 12 = {129/138/147/246/345}(cannot be {156} which clashes with R8C8, cannot be {237} which clashes with R89C7)
21a. Hidden killer quad 1,2,3,4 in R7C789, R8C7 and R8C9 + R9C89 for N9, R8C7 contains one of 2,3,4, R8C9 + R9C89 contains two of 1,2,3,4 -> R7C789 must contain one of 1,2,3,4
21b. Hidden killer quad 1,2,3,4 in R7C23, R7C456 and R7C789 for R7, R7C456 contains two of 1,2,3,4, R7C789 contains one of 1,2,3,4 -> R7C23 must contain one of 2,4
21c. Killer pair 2,4 in R7C23 and R8C1, locked for N7

22. 19(5) cage in N7 = {12358/12367/13456} (cannot be {12349} because 2,4 only in R8C1), no 9
22a. 9 in N7 locked in R7C13, locked for R7
22b. 9 in C2 locked in R123C2, locked for N1

23. 45 rule on N9 4 innies R7C789 + R8C8 = 22 = {1678/3568/4567} (cannot be {3478} because R8C8 only contains 5,6, cannot be {2578} which clashes with R89C7), no 2, 6 locked for N9, clean-up: no 7 in R6C8

24. 6 in R9 locked in R9C12, locked for N7, clean-up: no 4 in R6C2
24a. 19(5) cage in N7 (step 22) = {12367/13456}, no 8

25. R7C123 + R8C2 (step 20) = {2789/4589}
25a. 7 of {2789} must be in R8C2 (R78C2 cannot be [28] because of CCC with R67C2), no 7 in R7C1
25b. 5 of {4589} must be in R7C3 -> no 4 in R7C3
25c. 7 in N7 locked in R89C2, locked for C2

26. 7 in R7 locked in R7C79, locked for N9
26a. R7C789 + R8C8 (step 23) = {1678/4567}, no 3, clean-up: no 6 in R6C8
26b. 6 of {1678} must be in R8C8, 4,7 of {4567} must be in R7C79 -> no 6 in R7C7, no 5,6 in R7C9

27. 14(3) cage at R6C9 (step 14) = {158/167} (cannot be {356} because no 3,5,6 in R7C9), no 3, 1 locked for C9

28. R8C3 = 1 (hidden single in R8), R9C3 = 3
28a. R9C456 = {148/247}, 4 locked for R9 and N8

29. R8C9 + R9C89 (step 21) = {129/138/147} (cannot be {345} because 3,4 only in R8C9), no 5 -> R9C8 = 1, clean-up: no 8 in R67C8, no 8 in R9C45 (step 28a)
29a. 2 of {129} must be in R8C9, no 2 in R9C9

30. R6C9 = 1 (hidden single in C9)

31. 2 in N9 locked in R8C79, locked for R8 -> R8C1 = 4, clean-up: no 6 in R6C2
31a. Naked pair {23} in R8C79, locked for N9 (original clean-up deleted because of added step 26)

32. Naked pair {28} in R67C2, locked for C2 -> R8C2 = 7, clean-up: no 6 in R8C456 (prelim g)
32a. Naked pair {89} in R67C1, locked for C1

33. Naked triple {589} in R8C456, locked for R8 -> R8C8 = 6, R7C8 = 5, R6C8 = 4, R5C89 = [25], R67C5 = [63], clean-up: no 9 in R4C5 (step 5)
33a. Killer pair 4,7 in R34C5 and R9C5, locked for C5

34. Naked triple {289} in R7C123, locked for R7 -> R7C79 = [47]

35. X-Wing for 8 in R67C1 and R67C2, no other 8 in R6

36. 9 in N5 locked in R5C456, locked for R5

37. 22(4) cage in N1 must contain one of 1,3 (step 12) and 9 = {1579/3469}, no 2
37a. 7 of {1579} must be in R1C1 -> no 5 in R1C1
37b. 6 of {3469} must be in R1C1 -> no 6 in R123C2

38. R9C2 = 6 (hidden single in C2), R9C1 = 5

39. 18(4) cage at R6C6 = {3456} (only remaining combination, cannot be {1467} because 1,6 only in R7C6, cannot be {2349/2457} because R7C6 only contains 1,6) -> R7C6 = 6, R6C67 = [53], R67C4 = [21], R4C46 = [31], R67C3 = [79], R67C2 = [82], R67C1 = [98], R67C2 = [82], R8C79 = [23]
39a. R9C6 = 2 (hidden single in R9)

40. 3 in N3 locked in R123C8 -> 23(3) cage = {3479} (only remaining combination) -> R1C9 = 4, R123C8 = {379}, locked for C8 and N3 -> R4C8 = 8, clean-up: no 4 in R3C5 (step 5)
40a. Naked pair {26} in R23C9, locked for C9 and N3 -> R4C9 = 9, R9C79 = [98]
40b. Naked pair {58} in R3C57, locked for R3

41. 18(4) cage at R3C6 = {1368} (only remaining combination, cannot be {1359} because 3,9 only in R3C6, cannot be {1458} because R4C7 only contains 6,7, cannot be {1467} because R3C7 only contains 5,8) -> R3C6 = 3, R34C7 = [86], R3C5 = 5, R4C5 = 7 (step 5), R9C45 = [74], R4C1 = 2, R5C7 = 7
41a. R5C3 = 6 (hidden single in R5), R8C4 = 5 (hidden single in R8)

42. 7 in N2 locked in 21(4) cage at R1C6 = {1578} (only remaining combination) -> R12C6 = {78}, locked for C6 and N2 -> R8C56 = [89], R5C456 = [894]

43. 8 in C3 locked in R12C3 -> 20(4) cage at R1C3 = {2468} (only remaining combination) -> R12C4 = [64]

and the rest is naked singles