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Ed
 Post subject: Assassin 256
PostPosted: Fri Mar 15, 2013 1:46 am 
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Posts: 1044
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Much easier than normal and an optimised solution cracks it very quickly but the key step is interesting enough to put this one up as an Assassin. Tried doing a HATMAN and making it into a zero killer to make the end harder but the one I tried gave an even higher SudokuSolver score but no difference to the solution.

Assassin 256

Image

code: paste into solver:
3x3::k:1280:3073:7170:4611:4611:3332:11013:11013:11013:1280:3073:7170:4611:3590:3332:11013:4359:11013:6408:6408:7170:3590:3590:3590:4359:4359:11013:6408:7170:7170:6153:6153:4359:1290:11013:11013:6408:2315:2315:6153:6153:6668:1290:3597:3597:7438:7438:2315:6415:6668:6668:6668:6668:3597:7438:6415:6415:2064:3089:6162:6162:6162:6162:7438:6415:2064:2064:3089:6162:6675:1812:1812:7438:7438:3349:3349:6675:6675:6675:2070:2070:
solution: 
+-------+-------+-------+
| 2 5 9 | 3 6 8 | 1 7 4 |
| 3 7 4 | 9 1 5 | 6 2 8 |
| 6 8 1 | 2 7 4 | 5 9 3 |
+-------+-------+-------+
| 7 6 8 | 4 3 1 | 2 5 9 |
| 4 1 5 | 8 9 2 | 3 6 7 |
| 9 2 3 | 6 5 7 | 4 8 1 |
+-------+-------+-------+
| 5 3 7 | 1 8 6 | 9 4 2 |
| 8 9 2 | 5 4 3 | 7 1 6 |
| 1 4 6 | 7 2 9 | 8 3 5 |
+-------+-------+-------+
Cheerio
Ed
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Andrew
 Post subject: Re: Assassin 256
PostPosted: Sat Mar 16, 2013 9:45 pm 
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Thanks Ed for posting a nice Assassin with several interesting steps. It probably was easier than usual; I managed to finish it in one session.

I'll be interested to see what Ed's interesting key step was. I've a feeling it wasn't step 8, the first interesting step I found, which may not be necessary for my solving path (it can probably be ignored, with this result being obtained after step 22b). Step 9 or step 11 seem more likely to be Ed's key step.

Here is my walkthrough for Assassin 256:
Prelims

a) R12C1 = {14/23}
b) R12C2 = {39/48/57}, no 1,2,6
c) R12C6 = {49/58/67}, no 1,2,3
d) R45C7 = {14/23}
e) R78C5 = {39/48/57}, no 1,2,6
f) R8C89 = {16/25/34}, no 7,8,9
g) R9C34 = {49/58/67}, no 1,2,3
h) R9C89 = {17/26/34}, no 4,8,9
i) 9(3) cage at R5C2 = {126/135/234}, no 7,8,9
j) 8(3) cage at R7C4 = {125/134}
k) 14(4) cage at R2C6 = {1238/1247/1256/1346/2345}, no 9
l) 26(4) cage at R8C7 = {2789/3689/4589/4679/5678}, no 1
m) 43(8) cage at R1C7 = {13456789}, no 2

Steps resulting from Prelims
1a. 2 in N3 only in R2C8 + R3C78, locked for 17(4) cage at R2C8, no 2 in R4C6
1b. 8(3) cage at R7C4 = {125/134}, CPE no 1 in R8C6

2. 45 rule on N14 2 innies R6C12 = 11 = {29/38/47/56}, no 1

3. 45 rule on N89 2 outies R89C3 = 8 = [17/26/35] -> R9C34 = [58/67/76]

4. 45 rule on N356 1 innie R6C4 = 6, clean-up: no 5 in R6C12 (step 2), no 7 in R9C3, no 1 in R8C3 (step 3)
4a. R6C4 = 6 -> R7C23 + R8C2 = 19 = {289/379/478}, no 1,5

5. 8(3) cage at R7C4 = {125/134}, 1 locked for C4 and N8
5a. R8C3 = {23} -> no 2,3 in R78C4

6. 9(3) cage at R5C2 = {126/135} (cannot be {234} which clashes with R6C12), no 4, 1 locked for N4

7. 45 rule on N5 2 outies R6C78 = 1 remaining innie R4C6 + 11
7a. Max R6C78 = 17 -> no 7,8,9 in R4C6
7b. Min R6C78 = 12, no 1,2 in R6C78

8. 45 rule on N3 3 outies R4C689 = 15, 17(4) cage at R2C8 contains 2 = 2 + 15(3) with overlap at R4C6. Also, because the only other cage in N3 is 43(8) cage at R1C7, the other two values in R2C8 + R3C78 must be in R4C89 -> no 2 in R3C7 (because R23C8 would clash with R4C89)
8a. 2 in N3 only in R23C8, locked for C8, clean-up: no 5 in R8C9, no 6 in R9C9

9. Hidden killer quad 4,7,8,9 in 28(5) cage at R1C3 and R7C3 for C3, 28(5) cage cannot contain all of 4,7,8,9 -> R7C3 = {4789}, R1234C3 must contain three of 4,7,8,9
9a. 28(5) cage at R1C3 = {13789/14689/24589/24679/34579/34678} (cannot be {15679/23689/25678} which only contain two of 4,7,8,9)
9b. Three of 4,7,8,9 must be in R1234C3 -> no 4,7,8,9 in R4C2

10. 45 rule on N5 4 innies R45C6 + R6C56 = 15 = {1239/1248/1257/1347}, 1 locked for N5

11. 9(3) cage at R5C2 = {126/135}, R89C3 = [26/35] -> combined cage 9(3) + R89C3 = {126}[35]/{135}[26], CPE no 2,3,5,6 in R4C3

12. R9C34 = [58/67], R9C89 = [17/26/35] -> combined cage R9C3489 = [58][17]/[58][26]/[67][35], 5 locked for R9

13. 26(4) cage at R8C7 = {2789/3689/4589/4679} (cannot be {5678} which clashes with R9C4)
13a. 26(4) cage = {2789/3689/4589} (cannot be {4679} which clashes with R9C3489)
13b. 7 of {2789} must be in R8C7, 8 of {3689} must be in R8C7 (other permutations clash with R9C3489), 5 of {4589} must be in R8C7 -> R8C7 = {578}
13c. 26(4) cage = {2789/3689/4589} = 7{289}/8{369}/5{489}, 9 locked for R9
13d. Killer pair 6,8 in R9C34 and 26(4) cage, locked for R9, clean-up: no 2 in R9C9
13e. Killer pair 5,7 in R9C34 and R9C89, locked for R9

14. R8C89 = {16/34}/[52], R9C89 = {17/35} -> combined cage R89C89 = {16}{35}/{34}{17}/[52]{17}, 1 locked for N9

15. R7C23 + R8C2 (step 4a) = {289/379/478}
15a. Killer quad 1,2,3,4 in R7C23 + R8C2, R8C3 and R9C12, locked for N7

16. 1 in N7 only in R9C12, locked for R9, clean-up: no 7 in R9C89
16a. Naked pair {35} in R9C89, locked for R9 and N9 -> R9C3 = 6, R9C4 = 7, R8C3 = 2 (step 3), R78C4 = 6 = {15}, locked for C4 and N8, clean-up: no 4 in R8C89
16b. Naked pair {16} in R8C89, locked for R8 and N9 -> R78C4 = [15]
16c. Naked pair {14} in R9C12, locked for R9 and N7
16d. Naked triple {289} in R9C567, locked for 26(4) cage at R8C7 -> R8C7 = 7

17. 3 in N7 only in 25(4) cage at R6C4 = {3679} (only remaining combination), 7,9 locked for N7, 3 locked for C2 -> R78C1 = [58], clean-up: no 9 in R12C2, no 4 in R7C5

18. 9(3) cage at R5C2 (step 6) = {135} (only remaining combination, cannot be {126} because 2,6 only in R5C2), locked for N4, 3 also locked for C3

19. R4C3 = 8 (hidden single in N4)
19a. R7C6 = 6 (hidden single in N8), clean-up: no 7 in R12C6

20. 4 in N9 only in R7C789, locked for 24(5) cage at R7C6, no 4 in R8C6
20a. R78C5 = [84] (cannot be {39} which clashes with R8C6)
[With hindsight, this is better as R8C5 = 4 (hidden single in N8), R7C5 = 8.]
20b. Naked triple {249} in R7C789, locked for R7, N9 and 24(5) cage at R7C3 -> R7C23 = [37], R8C2 = 9, R8C6 = 3, R9C7 = 8

[Overlooked at step 16c]
21. Naked pair {14} in R9C12, locked for 29(6) cage at R6C1, clean-up: no 7 in R6C12 (step 2)
21a. R6C12 = [92], R4C2 = 6
21b. Naked pair {47} in R45C1, locked for C1 and 25(4) cage at R3C1, no 4,7 in R3C12
21c. R9C12 = [14]
21d. R3C1 = 6 (hidden single in C1), R45C1 = {47} = 11 -> R3C2 = 8 (cage sum)
21e. Naked pair {57} in R12C2, locked for C2 and N1 -> R5C2 = 1, clean-up: no 4 in R4C7

22. R6C78 = R4C6 + 11 (step 7)
22a. Max R6C78 = 13 -> R4C6 = 1, R6C78 = 12 = [48/57], clean-up: no 4 in R5C7
22b. Naked pair {23} in R45C7, locked for C7 and N6

23. R4C689 = 15 (step 8) = {159} (only remaining combination), 5,9 locked for R4, N6 and 43(8) cage at R1C7 -> R6C7 = 4, R6C8 = 8 (step 22a), R7C7 = 9, R7C89 = [42], R3C7 = 5

24. R6C9 = 1 (hidden single in N6), R8C89 = [16], R5C89 = [67], R45C1 = [74]

25. R23C8 = {29} (hidden pair in N3), locked for C8 -> R4C89 = [59], R9C89 = [35], R1C8 = 7, R12C2 = [57], clean-up: no 8 in R2C6

26. R4C4 = 4 (hidden single in N5), R4C5 + R5C45 = 20 = {389} (only remaining combination) -> R4C5 = 3, R5C45 = [89], R45C7 = [23], R56C3 = [53], R5C6 = 2, R9C56 = [29], clean-up: no 4 in R12C6
26a, R12C6 = [85], R6C56 = [57], R3C6 = 4, R3C9 = 3, R3C4 = 2, R3C8 = 9, R3C3 = 1, R3C5 = 7, R2C5 = 1 (cage sum)

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A256 at 1.5. This takes account of step 8; without it I would probably go slightly lower. My other hardest steps were a hidden killer quad, combined cages and clashes with combined cages.

It's interesting to note that:
step 8 seems to be a property of the cage pattern in N3. Provided that the cage totals for the cages at R1C7 and R2C8 are a valid pair (some pairs may be impossible, even if their total is at least 51) then the number missing from the 8-cell cage must be in R23C8.
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Ed
 Post subject: Re: Assassin 256
PostPosted: Thu Mar 21, 2013 7:58 am 
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Andrew wrote:
step 8, the first interesting step I found
Glad you found that one. I originally was hoping to make a puzzle which revolved around that feature but went this other way.
Andrew wrote:
step 11 seems more likely to be Ed's key step.
I wish! Loved you finding that one. My way is....see step 4 then it's cracked by step 9. [Big thank you to Andrew for finding my incorrect step 20 and other suggestions]

Assassin 256 walkthrough
24 steps:
1. "45" on n2356: 1 innie r6c4 = 6 (Andrew noticed that "45" on just n356 gets this as well; edit 2 & Pinata used this way in his WT)
1a. r6c4 = 6 -> r7c23+r8c2 = 19 (no 1)

2. 13(2)r9c3 = {49/58}[67](no 1,2,3: no 7 in r9c3)
2a. "45" on n89: 2 outies r89c3 = 8 (no 4,8,9)
2b. = [26/35]
2c. -> r9c34 = [58/67]

3. 8(2)r9c8 = {17/26/35}(no 4,8,9)
3a. Combined cage 21(4)r9c3489 = [58]{17/26}/[67]{35}
3b. must have 5 -> 5 locked for r9

The key
4. 5 in r9 only in h8(2)r89c3 = [35] or in 8(2)r9c8 = {35}
4a. must have 3 -> no 3 in common peers r9c12 nor r8c789 (Locking cages)

5. 7(2)r8c8 = {16/25}(no 4,7,8,9) = [2/6,1/5..]
5a. 8(2)r9c8: {26} blocked by 7(2):
5b. 8(2) = {17/35}(no 2,6) = [1/5..]
5c. Killer pair 1,5 in 7(2) + 8(2): both locked for n9

6. "45" on r789: 2 outies r6c12 = 11 = {29/38/47}(no 1,5)= [2/7/8..]

7. "45" on r789: 4 innies r789c1+r9c2 = 18
7a. must have 1 for n7
7b. {1368} blocked by h8(2)r89c3 = [3/6]
7c. {1278} blocked by h11(2)r6c12 (step 6)
7d. h18(4) = {1269/1359/1458/1467}(note: cannot have both 2&4)

8. 26(4)r8c7 = {2789/3689/4679}(no 1)
8a. 2 & 4 in r9 only in r9c12 (can't have both: step 7d) & 26(4)r8c7 -> 26(4) must have at least one of 2 or 4 (Hidden Killer pair)
8b. ->26(4) = {2789/4679}(no 3)

Cracked now.
9. 3 in r9 only in 8(2) = {35} only: locked for r9 and n9
9a. 7(2)n9 = {16} only: locked for r8 and n9

10. r9c34 = [67]
10a. r8c3 = 2 (h8(2)r89c3)
10b. r8c3 = 2 -> r78c4 = 6 = [15] only permutation

11. 24(5)r7c6 = {23469/23478}
11a. must have 2,3,4; r7c5 sees all of 24(5) -> no 2,3,4 in r7c5 (Common Peer Elimination CPE)
11b. 3 only in r78c6: 3 locked for c6 & n8
11c. 12(2)r7c5 = [84] only permutation

12. Naked pair {29} in r9c56: locked for n8, r9 & no 9 in r8c7 (same cage)
12a. r9c56 = 11 -> r89c7 = 15 = [78] only permutation
12b. r78c6 = [63]

13. Naked pair {14} in r9c12: 4 locked for n9 and no 4 in r6c12 (same cage)
13a. r9c12 = 5 -> r78c1 = 13 (h18(4)) = [58] only
13b. r8c2 = 9
13c. h11(2)r6c12 = [92] only permutation

14. 5(2)r1c1: {14} blocked by r9c1 = (14)
14a. = {23} only: both locked for c1 and n1

15. 25(4)r3c1 = {4678} only -> r3c2 = 8
15a. 4 only in c1: 4 locked for c1
15b. r9c12 = [14]

16. "45" on c12: 3 remaining innies r457c2 = 10 = {16}[3]
[Andrew noticed a simpler way: 12(2)n1 = {57} only, locked for c2 and n1 -> r457c2 = {16}[3]]
16a. 1 & 6 locked for n4
16b. 9(3)n4 = [1]{35} only: 3 & 5 locked for c3
16c. r4c2 = 6

17. 5(2)n6 = [14]/{23}(no 5,6,9; no 4 in r4c7) = [1/3..]
17a. 6 in n6 only in 14(3) = {167/356}(no 2,4,8,9) = [1/3..]
17b. Killer pair 1,3 in 5(2) + 14(3): both locked for n6

18. 43(8)r1c7 (no 2)
18a. Hidden single 2 in c9 -> r7c9 = 2
18b. 2 in n6 only in 5(2) = {23} only: locked for c7 and n6

19. 14(3)n6 = {67}[1] only: 7 locked for r5 and n6

20. deleted incorrect step

21. 7 in r6 only in 26(5)r5c6; but {23579} blocked since 2&9 are only in r5c6 [Alternatively, 4,7, & 8 in r6 only in 26(5)r5c6 -> must be {24578} only: Thanks Andrew]
21a. = {24578} only (no 3)
21b. -> r5c6 = 2; 7 is only in n5: locked for n5
21c. r45c1 = [74]
21d. r4c3 = 8
21e. hidden single 8 in n6: r6c8 = 8

22. "45" on n3: 3 outies r4c689 = 15 = {159} only -> r4c6 = 1
22a. r4c89 = {59}: locked for n6 and for 43(8)r1c7
22b. no 5,9 in r1c789+r2c7+r23c9

23. 8 in c6 only in 13(2)n2 = {58} only: locked for c6 and n2

24. 5 & 9 in n3 only in split 16(3)r2c8+r3c78 -> other cell must be 2 (no 3,4,6,7)


On from there.
Cheerio
Ed
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Pinata
 Post subject: Re: Assassin 256
PostPosted: Thu Mar 21, 2013 7:41 pm 
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Thank you Ed, I enjoyed this puzzle. Keep them coming.
Assassin 256 Walkthrough:
Prelims
A) 5(2) in R1C1 must be [14/23]
B) 12(2) in R1C2 must be [39/48/57]
C) 13(2) in R1C6 must be [49/58/67]
D) 14(4) in R2C5 must be [1247/1238/1256/1346/2345]
E) 43(8) in R1C7 must be [13456789]
F) 9(3) in R5C2 must be [126/135/234]
G) 5(2) in R4C7 must be [14/23]
H) 8(3) in R7C4 must be [125/134]
I) 12(2) in R7C5 must be [39/48/57]
J) 26(4) in R8C7 must be [2789/3689/3589/4679/5678]
K) 7(2) in R8C8 must be [16/25/34]
L) 8(2) in R9C8 must be [17/26/35]

Walkthrough
1) Innies of N356 = 6
1a) Hidden Single R6C4 = 6
1b) Clean up- No 6 in R12345789C4, R6C12356789, R45C456, R6C56
1c) CPE- No 1 or 5 in R7C23, R8C2
1d) CPE- No 7 in R9C3
1e) Combination Blocker- 24(4) in R4C4 can’t be [1689]

2) IOD in N89- R9C4 - R8C3 = 5
2a) R8C3 should contain 234
2b) R9C4 should contain 789
2c) CPE- R9C3 should contain 456

3) Locked candidates- 1 Locked to R78C4
3a) No 1 in R789C56, R1234569C4

4) Innies of N89 = 13
4a) No 2 in R78C4

5) IOD- R89C3 – R6C4 = 2
5a) R8C3 must contain 23
5b) R9C3 must contain 56
5c) CPE- No 3 in R78C4
5d) no 9 in R9C4
5) IOD- R89C3 – R6C4 = 2
I should have seen that 45 rule, but I added the 19 from the 25(4) cage in R6C4 and added the totals for nonets 1, 4 and 7.

6) Cage blocker- 26(4) in R8C7 can’t be [5678] so it must contain a 9.

7) Innies of N14 = 11- No 1, 5 in R6C12
 
8) IOD- R8C7 – R9C12 = 2
8a) no 234 in R8C7
8b) no 789 in R9C12

9) Locked Candidates- 9 Locked to R9C567
9a) no 9 in R8C7
9b) CPE- no 6 in R9C12

10) Outies of R9 = 31
10a) as R6C12 = 11, R78C1 and R8C7 = 20
10b) no 12 in R6C12
This should be R78c1, I must have gotten carried away.

11) Locked Candidates- 1 Locked to R9C12
11a) No 1 in R6C12, R78C1, R78C23, R9C3456789
11b) CPE- No 7 in R9C89
11c) CPE as R9C3 must contain 56, R9C124567 can’t contain 56.

12) Innies of N9 = 30
1a) R789C7 and R7C89 must be [15789/24789]
1b) no 36 in R789C7 and R7C89

13) IOD- R8C7 – R9C12 = 2, no 8 in R8C7
13a) CPE- as R8C7 contains 57 and the 26(4) combination can’t be [5678], 57 can be eliminated from R9C567
13a) no 3 in R9C567

14) Hidden Single- R9C4 = 7
14a) no 7 in R9C12356789, R78C456, R9C56, R12345678C4
14b) no 2 in R1C5

15) Hidden Single- R9C3 = 6
15a) no 6 in R9C12456789, R78C123, R12345678C3

16) Hidden Single- R8C3 = 2
16a) No 2 in R7C123, R8C12456789, R9C12, R12345679C3
16b) CPE- No 46 in R5C2
16c) Killer Pair- R78C4 must contain [15]
16d) CPE- No 5 in R8C89

17) Locked Pair- [15] Locked to R78C4
17a) no [15] in R1234569C4, R789C56
17b) CPE- No 4 in R78C4
17c) no 5 in R78C5

18) Hidden Killer Pair- 8(2) in R9C8 must be [35]
18a) no 2 in R9C89
 
19) Locked Pair- [35] Locked to R89C8
19a) no 35 in R9C1234567, R78C789
19b) Hidden Single R8C7 = 7
19c) no 4 in R8C89

20) Locked Triplet- [289] locked to R9C567
20a) no 4 in R9C567

21) Locked Pair- [16] locked to R8C89
21a) No [16] in R8C1234567, R79C789

22) Hidden Single- R8C4 = 5
22a) no 5 in R8C12356789, R7C456, R89C56
22b) Hidden Single- R7C4 = 1
22c) no 1 in R7C12356789, R789C456

23) CCC- 5(2) in R1C1 must be [23]
23a) Locked Pair- [23] locked to R12C1
23b) no [23] in R3456789C1, R123C23
23c) Combination blocker- 25(4) in R3C1 can’t be [2689/3589/3679]
23d) Combination blocker- 12(2) in R1C2 can’t be [39]- no 9 in R12C2

24) Locked Candidates- 6 locked to R3C12
24a) no 6 in R12C123, R3C3456789, R45C1
24b) CPE- no 1, 5 in R3C12, R45C1

25) Cage Blocker, 25(4) in R3C1 must be [4678]
25a) no 9 in R3C12, R45C1

26) Hidden Single- R4C2 = 6
26a) no 6 in R12356789C2, R4C13456789, R56C123

27) Hidden Single- R3C1 = 6
27a) No 6 in R12C123, R3C23456789, R12456789C1

28) Hidden Single, R9C1= 1
28a) No 1 in R12345678C1, R789C23, R9C23456789

29) Hidden Single- R9C2 = 4
29a) No 4 in R12345678C2, R78C123, R9C13456789
29b) CPE- no 8 in R12C2

30) Locked pair- [57] locked to R12C2
30a) No [57] in R1C123, R3456789C2, R123C3
 
31) Hidden Single, R7C3 = 7
31a) No 7 in R789C12, R12345689C3, R7C12456789

32) Hidden Killer Pair- R78C1 must be [58]
32a) No [58] in R1234569C1, R678C2, R789C3

33) Hidden Single- R6C2 = 2
33a) No 2 in R45C123, R6C13456789, R12345789C2
33b) Combination blocker- 9(3) in R5C2 must be [135]
33c) CPE- no 4 in R5C23, R6C3

34) Hidden Single- R6C1 = 9
34a) No 9 in R12345789C1, R456C23, R6C2345789

35) Hidden Single- R5C2 = 1
35a) no 1 in R456C1, R12346789C2, R456C3, R5C13456789
35b) CPE- no 4 in R4C7

36) Hidden Single- R4C3 = 8
36a) no 8 in R12356789C3, R12456789C4, R56C123

37) Hidden Single- R3C2 = 8
37a) Hidden Single R12C123, R3C13456789, R12456789C2

38) Hidden Single- R8C1 = 8
38a) No 8 in R12345679, R789C23, R8C23456789
38b) CPE- no 4 in R7C5

39) Hidden Single- R7C1 = 5
39a) No 5 in R12345689C1, R789C23, R7C23456789

40) Hidden Single- R8C5 = 4
40a) no 4 in R12345679C5, R79C456, R8C12346789

41) Hidden Single- R7C5 = 8
41a) no 8 in R12345689C5, R7C12346789, R789C46

42) Hidden Single- R9C7 = 8
42a) no 8 in R9C12345689, R12345678C7, R7C789, R89C89

43) Hidden Single- R7C2 = 3
43a) no 3 in R12345689C2, R7C13456789, R89C123

44) Hidden Single- R8C2 = 9
44a) no 9 in R12345679C2, R79C123, R8C13456789

 
45) Hidden Single- R8C6 = 3
45a) R12345679C6, R79C456, R8C12345789

46) Hidden Single- R7C6 = 6
46a) no 6 in R12345689C6, R7C12345789, R789C45
46b) CPE- no 7 in R12C6

47) Combination blocker- 14(3) in R5C8 must be [167/356]
47a) no 2489 in R5C89, R6C9

48) Hidden single- R7C9 = 2
48b) no 2 in R789C78, R712345678, R12345689C9

49) Hidden Single- R6C8 = 8
49a) no 8 in R56C6, R6C4, R45C789, R6C79, R12345789C8

50) Locked Candidates- 489 locked to R1234C9
50a) no 489 in R1C78, R2C7, R4C8, R56789C9

51) Hidden Killer Pair- 5(2) in R4C7 must be [23]
51a) no 23 in R1236789C7, R456C89
51b) no 5 in R5C89, R6C9

It is all singles now.
Corrections and clarifications courtesy of Ed

Rating Comment:
I would rate this assassin 1.50, I reckon my hardest step was whittling down the candidates for step 8.
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