Assassin 48

[Para]

Hi all

Ok this is probably the ugliest walk-through i have made in a while. Really just jotted down everything i did and in which order. I think i might clean it up a little later, so everyone can follow it. But anyway, this is how i solved it.

Walkthrough Assassin 48

This first bit is just from left to right top to bottom. You could this much more practical of course.
1. R1C34 = {39/48/57}: no 1,2,6
2. R12C5 = {12} -->> locked for C5 and N2
3. R1C56 = {36/45}/[72/81]: R1C5: no 9, R1C6: no 7,8,9
4. R234C1 = {124} -->> locked for C1
5. R23C4 = {59/68}
6. R23C6 = {34} -->> locked for C6 and N2
6a. Clean up: R1C3: no 8,9; R1C7: no 5,6
7. 34(5) in R3C5 = {46789} -->> locked for C5
7a. Naked Pair {35} in R89C5 -->> locked for N8
8. 3 in C4 locked in 19(4) cage in R4C4 -->> R5C3: no 3
8a. 19(4) in R4C4 = {1369/1378/2359/2368/3457}
9. R5C12 = {36}/[54/72/81]: R5C1: no 9; R5C2: no 5,7,8,9
10. R5C89 = {18/27/36/45}: no 9
11. R678C1 = {389/569/578}
12. 19(5) in R7C3 = {12349/12358/12367/12457/13456}: 1 locked in 19(5) cage for N7
13. R78C4 = {19/28/46}: no 7
14. R78C6 = {67} -->> locked for C6 and N8
14a. Clean up: R78C4: no 4; R1C7: no 2, 3
14b. Killer Pair {58} in R1C6 + R23C4 -->> locked for N2
14c Clean up: R1C3: no 4,7
15. 35(5) in R7C7 = {56789} -->> locked for N9
16. R9C34 = {28}/[64/91]: R9C3: no 3,4,5,7; R9C4: no 9
17. R9C67 = {12} -->> locked for R9
17a. R9C34 = [64]
18. 9 locked in C6 for N5
18a. 9 in C6 locked in 20(4) cage in R4C6-->> R5C7: no 9
18b. 20(4) in R4C6 = {1289/2459}: 9 locked and only place for 3, 4, 6 and 7 is R5C7: 20(4) can only have one of these digits -->> R5C7: no 3, 5, 6, 7
18c. 20(4) can’t have both {12} in R456C6 -->> R5C7: no 8
18d. 2 locked in 20(4) cage: R5C4: no 2
19. Naked Triple {124} in R159C7 -->> locked for C7
20. 12(3) in R6C9 needs 2 of {1234} in R78C9: can’t have both {12} in R78C9 because of R9C7.
20a. 12(3) = {[8]{13}/[7]{14}/[7]{23}/[6]{24}/[5]{14}: R6C9 = {5678}
Forgetting those 45-tests again.
21. 45 on C123: 2 innies: R15C3 = 14 = [59]
21a. R1C4 = 7; R1C67 = [81]; R12C5 = [21]; R9C67 = [12]; R5C7 = 4
21b. R23C4 = {59} -->> locked for C4 and N2
21c. R78C4 = {28} -->> locked for C4 and N8
21d. R3C5 = 6; R7C5 = 9
21e. Clean up: R5C189: no 5; R6C9: no 6
21f. Hidden single: R5C6 = 5
22. 45 on R5: 2 innies: R5C45 = 9 = [18]
23. 19(5) in R7C3 = {12349/12358/12457} -->> 2 locked in 19(5) cage for N7
24. 28(5) cage in R1C1 can have only one digit of {124} because of R23C1
24a. 28(5) = {13789/23689/34678} = 38{179/269/467}-->> 3 and 8 locked for N1 in 28(5) cage
25. 45-test on N9: 1 outie – 1 innie: R6C9 – R7C8 = 4
25a. 13(3) in R6C7 needs one of {134} in R7C8 -->> 13(3) = {139/148/157/238/247/346}
25b. 13(3) can’t be {157}: R7C8 = 1 -->> R6C9 = 5 -->> 2 5’s in R6, so R6C78: no 5
25c. 13(3) can’t be {148}: R7C8 = 4 -->> R6C9 = 8 -->> 2 8’s in R6
OK something more productive again.
26. 45-test on R6789: 3 innies: R6C456 = 12 = {37/46}[2] -->> R6C6 = 2; R4C6 = 9
27. 13(3) = {139/346}-->> R6C78: no 7,8
28. 15(3) can’t contain both {13},{14},{15},{34},{37} or {48} because of 12(3) in R6C9
28a. 15(3) = {168/249/258/267/456}: no 3
29. 45 on N3: 1 innie – 1 outie: R3C8 – R4C9 = 1 -->> R3C8: no 4, 5; R4C9: no 5
This looks a bit chaotic I know, it’s late. This should have come before I know.
30. 45 on N1: 1 innie – 1 outie = R3C2 – R4C1 = 5: R4C1 = {24}, R3C2 = {79}
30a. R3C1 = 1(hidden)
31. 16(3) in R3C2 = {169/178/259/349/457}: needs 7 or 9 in R3C2; {367} would clash with R4C4; 7 or 9 needs to go in R3C2, so R4C23: no 7
31a. Only place for 5 is R4C2 -->> R4C2: no 2
32. 45 on N7: 1 innie = 1 outie : R6C1 = R7C2 -->> R6C1: no 6; R7C2: no 4
33. Hidden triple {124} in R7C3 + R8C23 for N7
33a. 19(5) in R7C3 = 124{39/57} : no 8; R9C12 = {39/57}
33b. 8 in R9 locked for N9
33c. Killer Pair {35} in R9C12 + R9C5 for R9
Missing moves everywhere.
34. 13(3) in R6C7 = {139}: {36}[4] clashes with R6C4 or 9 locked in R6C78 (pick one)
34a. Clean up: R6C9: no 8
34b. 4 locked in N9 for C9
34c. 1 locked in 13(3) cage in R67C8 for C8
35. 16(3) in R3C8 = {259/268/358/367} -->> R3C8: no 7: would mean R4C78 = {36} which clashes with R4C4
35a. Clean up: R4C9: no 6
36. 8 in R6 locked for N4
37. 4 in N3 locked in 28(5) in R1C8; 28(5) = 4{2589/2679/3579/3678}
38. R6C789 = [917]/{39}[5]
38a. Killer Pair {37} in R5C89 + R6C789 for N6
38b. Clean up: R3C8: no 8
38c. R4C5 = 7(hidden); R6C5 = 4
39. 8 in C23 locked in 28(5) in R1C1 and 16(3) in R6C2
39a. 16(3) in R6C2 = {178/358}: no 6
39b. R6C4 = 6(hidden); R4C4 = 3
39c. Naked triple {124} in R478C3 locked for C3
39d. 2 in N1 locked for R2
40. 28(5) in R1C8 = 347{59/68} -->> {37} locked for N1
40a. Clean up: R4C9: no 2
40b. 15(3) in R2C9 = [681/528] -->> R2C9: no 8,9; R3C9: no 5,9
40c. 8 locked in 15(3) cage for C9
40d. R9C8 = 8(hidden)
41. 16(3) in R3C8 = [952/286] -->> R4C7: no 6; R4C8: no 5
42. 45-test on C9: 3 innies : R159C9 = 18 = [927/{36}9]: R5C9: no 7
42a. Clean up: R5C8: no 2
43.Hidden Killer Pair {56} in R4C2 + R4C78; One of {56} in R4C78, only other place for 5 or 6 is R4C2, so R4C2 = {56}
44. 45 on C1: 3 innies: R159C1 = {369}/[675] -->> R9C1: no 7
44a. Clean up: R9C2: no 5
Ok this breaks the puzzle.
45. 45 on N13: 2 innies – 2 outies: R3C28 – R4C19 = 6 = [92] – [41]/ [72] – [21]: [79] – [28] clashes with R4C78 (step 41)
45a. R3C8 = 2; R4C9 = 1
45b. Naked Singles: R23C9 = [68]; R4C78 = [86]; R4C2 = 5
45c. Hidden Singles: R6C9 = 5; R9C9 = 7; R1C9 = 9; R5C89 = [72]; R7C8 = 1; R6C2 = 1; R8C3 = 1
Really didn’t wanna collapse to singles yet.
46.R9C12 = {39} (step 33a) -->> locked for R9 + N7
And now it is all singles and basic cage sums.

greetings

Para

[Andrew]

Wow! That was quick.

If you are in the Netherlands, I think that new Assassins appear at midnight. You must have been working on it pretty late.

[Para]

Hi

Had a very quiet night shift.

greetings

Para

[CathyW]

It's certainly harder than 47! Still working on it - currently up to step 49 and counting ...

Update: Oh bother! Two options in a cell, both leading to conflicts. Evidently made a wrong move somewhere so I'll have to start over tomorrow.

[Ruud]

Trying to please everyone in the audience...

A48-Lite (If you have trouble solving the V1)

3x3::k:5632:5632:4098:4098:7721797:6919:6919:4361:5632:56327726919:6919:4113:4361563274466919:4889:4113:43613603:4382:7446:5408:4889:4889:4113:4388:4388:4382:4382:7446:5408:5408209123504382:7446:5408:4403:4403:49172350:645674464412:4403:49176456:645633954412:4412:4917:6456:6456391418694412:4412:



A48-Hevvie (If you walked over the V1)

3x3::k:6656:6656307428216151:61516656:665620526151:6151:48813603:665671906151488136035406:7190284148813620:5406:5406:719031042091:41413630:5406:71904147:414741415688:825:71907996:41474141:5688:5688:8253899:7996:79965688:5688289031497996:7996:



Have a nice weekend!
Ruud

[Jean-Christophe]

Here is my walkthrough for V1. Will try the Hevvie
1. Cage 3/2 in R12C5 = {12} (NP @ N2, C5)
2. Cage 7/2 in R23C6 = {34} (NP @ N2, C6)
3. Cage 8/2 in R89C5 = {35} (NP @ N8, C5)
4. Cage 13/2 in R78C6 = {67} (NP @ N8, C6)
5. Cage 3/2 in R9C67 = {12} (NP @ R9)
6. Cage 10/2 in R9C34 = [64]
7. Since R1C4 <> 3, Cage 12/2 in R1 -> R1C3 <> 9
8. Outies of C4 -> R15C3 = 14 = [59], R1C4 = 7
9. Cage 9/2 in R1C67 = [81], R12C5 = [21], R9C67 = [12]
10. Outies of C6 -> R5C7 = 4
11. Cage 14/2 in R23C4 = {59} (NP @ N2, C4)
12. Cage 10/2 in R78C4 = {28} (NP @ N8, C4)
13. R37C5 = [69]
14. Two Cages 9/2 in R5 <> {45}, R5C6 = 5
15. Innies of R5 -> R5C45 = 9 = [18]
16. Cage 7/3 in R234C1 = {124} (NT @ C1)
17. 45 on N1 -> R23C1+R3C2 = 12 = {1(29|47)} -> R3C1 = 1, R3C2 = {79}, R4C123 = 11
18. 45 on N9 -> R7C89+R8C9 = 8 = {134}, R6C789 = 17
19. 45 on N3 -> R23C9+R3C8 = 16, R4C789 = 15
20. 45 on N7 -> R7C12+R8C1 = 20 <> {12..}, R6C123 = 16
21. Innies of R4 -> R4C456 = 19 = [(37|64)9], R6C6 = 2
22. Innies of R6 -> R6C45 = 10 = [37|64]
23. Cage 12/3 in R678C9 = {138|147|345} -> R6C9 = {578}
24. 9 of R6 locked in R6C78 -> Cage 13/3 in N69 = {139}, NT -> R45C8 <> {13}
25. 17/3 in R6C789 -> R6C9 = {57}
26. 8 of R6 locked in R6C123 -> not elsewhere in N4, 16/3 in R6C123 = {8(17|35)} <> {46..}
27. R6C45 = [64] (HS), R4C45 = [37]
28. 4 of N9 locked in R78C9 -> not elsewhere in C9
29. Cage 16/3 in R34C8+R4C7 = {259|268|358} <> {47..}
30. 45 on N7 -> R7C2 = R6C1 = {3578}
31. R78C3, R8C2 = HT on {124} in N7 -> R9C12 = 12 = {39|57}
32. R478C3 = NT {124} @ C3
33. R3C6 = 4 (HS @ R3), R2C6 = 3
34. C37 & R36 = X-Wing on 3 -> not elsewhere in R36
35. 2 of R3 locked in R3C89 -> 16/3 in R23C9+R3C8 = {2(59|68)}
36. Cage 16/3 in R34C8+R4C7 = {259|268} = {2..} -> R5C8 <> 2 = {67} -> R5C9 {23}
37. Innies of C9 -> R159C9 = 18 = {9(27|36)} -> R1C9 = {69}, R9C9 = {79}
38. R9C8 = 8 (HS @ R9)
39. 9 locked in R19C9 -> not elsewhere in C9
40. 16/3 in R23C9+R3C8 = {259|268} = {(6|9)..} & R1C9 = complex naked pair on {69} -> not elsewhere in N3
41. Cage 28/5 in N1 = {368(29|47)}, 2 of N1 locked in R2C12 -> R2C2 <> 9
42. Cage 14/2 in R23C4 = [95] (HS @ R2)
43. 45 on R12 -> R3C37 = R2C19 + 2
43b. 3 of R3 locked in R3C37 = {3(7|8)} = 10|11
-> R2C19 = 8|9 = [26|45]
43c. {26} of R2 locked in R2C129
43d. Since R2C2 can't hold both {26} -> R2C19 = [26]
This unlocks the puzzle, almost
...

Edited to fix typos

[sudokuEd]

A48-Hevvie

Very. And keeping this audience member very happy: thanks Ruud.

This is all I can find. Hope others can finish it - World Cup Cricket Final all night tonight . Oi, Oi, Oi!

Cheers. Ed

edit: A condensed and simplified walk-through for Hevvie is at the end of this thread. ]

Assassin 48 Hevvie

1. 3(2)n8 = {12}:locked for c4, n8

2. 9(2)n8 = {36/45}(no 789) = [3/5..]

3. 8(2)n2 = {17/26}(no 3589) ({35} blocked by 9(2)n8 step 2)
3a. 8(2)n2 = [1/6..]

4. 7(2)n2 = {25/34}(no 16789} ({16} blocked by 8(2)n2 step 3a)
4a. 7(2)n2 = [2/3,4/5..]

5. 1 in c6 in 12(4)n5 = 12{36/45}(no 789)
5a. 1 locked for n5 and no 1 r5c7
5b. 12(4) must have 2 -> no 2 r5c5

6. complex hidden Killer pair 2/3 r23456c6. Here's how.
6a. 12(4)n5 = {1236} ->2/3 must be in r5c7 so r456c6 won't clash with 7(2)n2 (step 4b.) -> [2/3] both locked in 7(2) and r456c6 for c6
6b. 12(4)n5 = {1245} -> 4 must be in r5c7 so r456c6 won't clash with 7(2) (step 4b) -> [2/3] both locked in 7(2) and r456c6
6c. r5c7 = {234}
6d. no 4 r456c6
6d. 2 and 3 locked for c6 in r23456

7. 11(2)n2 = [47/56/65/74/83/92]
7a. r1c7 = 2..7

8. 12(2)n8 = [48/57/75/84/73](no 1,2,6)
8a. r9c7 no 9

9. "45"c789 -> 3 innies r159c7 = 12 = h12(3)c7 = {237/[624]/345}(no 8)
9a. no 4 r9c6

10. A neat little contradiction chain eliminates [624] from h12(3)c7
10a. from step 6a, 2 in r5c7 -> r456c6 = {136} -> 7(2)n2 = {25}
10b. 6 in r1c7 -> 5 in r1c6: but 2 5's c6
10c. h12(3) = {237/345} = 3{27/45}(no 6)
10d. no 5 r1c6
10e. 3 locked c7

11. 8 and 9 in c5 only in 28(5)
11a. 28(5) {14689} blocked by 8(2)n2
11b. 28(5) = {13789/23689/24589}
11c. 1 only in r3c5 -> no 7 r3c5

12. 4 in c6 only in n2: 4 locked for n2

13. 14(2)n2 = {59/68}

14. 12(2)n1 = {39/[48]/57}(no 1,2,6, no 8 r1c3)

15. "45"n2: 3 innies = 16 = {178/259/268/349}
15a. {169/367} blocked by 8(2)
15b. {358/457} blocked by 7(2)
15c. 1 and 2 are only available in r3c5 for 3 innies -> no 5,6,8 r3c5
15d. r1c46 = [78/59/86/34/94] ([87] means 2 4's r1:[39] means 2 9's r1)
15e. r1c6 no 7, no 4 r1c7

16. 7 in c6 only in n8:7 locked for n8
16a. r9c3, no 1,4,9

17. "45"n8 -> 3 innies = 18 = h18(3)n8
17a. h18(3) = {369/378/459} ({468/567} blocked by 15(2))
17b. r9c46 = [39] blocked by [93] in r9c67 -> {369} combo must have 3 in r7c5 -> no 6 r7c5
17c. {378}: 7 only in r9c6 -> no 8 r9c6
17d. no 4 r9c7

18. "45"n9: 4 innies = 14.
18a. min. r9c6 = 3 -> max. other 3 = 11 -> no 9

19. "45"n9: r9c7 + r7c8 = r6c9.
19a. min. 2 innies = 4 -> min r6c9 = 4
19b. max. r6c9 = 9 and min r9c7 = 3 -> max. r7c8 = 6

20. 19(3)n3: no 1
20a.14(2)n4 = {59/68}
20b. 8(2)n6: no 4,8,9

Code: Select all

.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 123456789   123456789 | 34579       35789     | 1267      | 4689        2357      | 123456789   123456789 |
:-----------.           '-----------.-----------:           :-----------.-----------'           .-----------:
| 123456789 | 123456789   123456789 | 5689      | 1267      | 2345      | 12456789    123456789 | 23456789  |
|           :-----------.           |           :-----------:           |           .-----------:           |
| 123456789 | 123456789 | 123456789 | 5689      | 1239      | 2345      | 12456789  | 12345678  | 23456789  |
|           |           '-----------+-----------:           :-----------+-----------'           |           |
| 123456789 | 123456789   123456789 | 3456789   | 23456789  | 12356     | 1245678     12345678  | 23456789  |
:-----------'-----------.-----------'           |           |           '-----------.-----------'-----------:
| 5689        5689      | 123456789   3456789   | 3456789   | 12356       234       | 123567      123567    |
:-----------.-----------'-----------.           |           |           .-----------'-----------.-----------:
| 123456789 | 123456789   123456789 | 3456789   | 23456789  | 12356     | 12456789    123456789 | 456789    |
|           |           .-----------+-----------:           :-----------+-----------.           |           |
| 123456789 | 123456789 | 123456789 | 12        | 34589     | 6789      | 12456789  | 123456    | 12345678  |
|           :-----------'           |           :-----------:           |           '-----------:           |
| 123456789 | 123456789   123456789 | 12        | 3456      | 6789      | 12456789    123456789 | 12345678  |
:-----------'           .-----------'-----------:           :-----------'-----------.           '-----------:
| 123456789   123456789 | 235678      345689    | 3456      | 579         357       | 123456789   123456789 |
'-----------------------'-----------------------'-----------'-----------------------'-----------------------'

[CathyW]

Finally managed no. 48. The Lite version more enjoyable for me. Thanks Ruud!

[rcbroughton]

A48-Hevvie

Very. And keeping this audience member very happy: thanks Ruud.

This is all I can find. Hope others can finish it - World Cup Cricket Final all night tonight

A couple more moves for you Ed. - not an easy one by any means.

21. 45 rule on n9. innies total 14 with a 3, 5 or 7 from r9c7. Only possible with 7 is 7{124} - no 7 in r78c9

22. 45 rule on n9. outies total 28 with a 5, 7 or 9 at r9c6. Also r6c78 must total 10,11,12,13,14,15 to fit with 16(3) cage.
22a. r9c6=5 - r6c789=23 - so r6c67 cannot be 10,11,12,13
22b. r9c6=7 - r6c789=21 - so r6c67 cannot be 10,11
22c. r9c6=9 - r6c789=19 - so r6c67=10 only when r6c9=9 so can't have {19} in r6c78
22d. So no 1 in r6c78

23. 45 on n147 & n5 (!!) - outies r1c4 r3c5 r7c5 r5c7 r9c4 total 23
23a. r1c4&r3c5 can't be:
[72] because of 8(2)n2
[89] because of 14(2)n2
[32]/[53] because of 7(2)n2
[51]/[91] because of 8(2)&14(2) n2
[31]/[73] because of 7(2)&8(2)n2
23b. r1c4&r9c4 can't be [96]/[56]/{58}/{89} because of 14(2)n2
23c. r7c5&r9c4 can't be
{89} because of 15(2)n8
{35}/{34}/{45}/[46] because of 9(2)n8
{45}/{58} because of 9(2)&15(2)n8
23d. r37c5 can't be [35]/[34] because of 9(2)n8
23e. putting that all together there is no possible permutation with 3 at r3c5 (anyone interested I'll list out all the possibles)

24. 45 on n2 - innies total 16. {169} blocked by 8(2) - only other combo with 9 is [592] or [349] - so no 9 at r1c4
24a. cleanup - no3 at r1c3

25. 45 rule on n369 & n5 (!!!) outies r1c6 r3c5 r5c3 r7c5 r9c6 total 27
25a. r1c6 r3c5 can't be:
[61] blocked by 8(2)n2
[69]/[89] blocked by14(2)n2
[42] blocked by 7(2)n2
[91] blocked by 8(2)&14(2)
[41] blocked by 7(2)&8(2)
25b. r3c5 r7c5 can't be [24] - blocked by 7(2)n2
25c. r1c6 r9c6 can't be
[45] - blocked by 7(2)n2
[89]/[67]/[97] - blocked by 15(2)n8
25d. r7c5 r9c6 can't be:
[89]/[97] - blcked by 15(2)n8
[47]/[57]/[85] blocked by 15(2)&9(2)n8
25e. putting all that together - no combination with 9 at r5c3


Rgds
Richard

[mhparker]

A couple more moves for you Ed. - not an easy one by any means.

Richard,

I can't speak for Ed, but you answered my prayers here, because I had just worked out a way of taking 9 off r1c3 by working my way round the grid using the outies in C37 to connect N2 with N8. I was just looking for some way to cull the {39} combo from r1c34 completely by removing 9 from r1c4 when I read your post:

26a. r1c3 = 9 -> r1c7 = 7 (outies - innies, n2 = 7, only permutation possible) -> r59c7 = [23] (h12/3, c7, only permutation possible)
26b. Innie/outie difference, n8 (=-5): 3 possible permutations of [r9c7-r9c3-r7c5] with 3 in r9c7:
(i) [364] - blocked due to 9/2 at r8c5
(ii) [353] - blocked because it would require a 2 in r5c3 (outies, c4 = 16/3), already taken for r5 in r5c7 (step 26a)
(iii) [375] - blocked due to outies, c4 = 16/3 (cage sum exceeded)
Summary: No 9 in r1c3 -> no {39} in r1c34

Unfortunately, I have no time right now for the follow-up moves. Maybe someone else can take over here?

[rcbroughton]

but you answered my prayers here

happy to help

your step moves us along quite a bit - including a first placement:
27. 3 now locked in r23c6 for n2 - locked for c6
27a. 7(2)n2={34} - locked for n2 and c6
27b. 12(4)n56={125}4 or {126}3 - no 2 in r456c6
27c. cleanup 11(2)n23 - no 7 at r1c7

28. 5 now locked in r123c4 for n2 - locked for c4
28a. cleanup in 11(2)n78 - no 6 at r9c3
28a. 21(4)n45 - no 7 possible at r5c3

29. 2 now locked in r123c5 for n2 - locked for c5
29a. cleanup 28(2)c5=1{3789}/2{3689}/2{4589} - no 9 at r3c5

30. 45 on c4 - innies total 28(5) = {34579} {34678} given available digits
30a. r456c4 must total 20,19,18(no 3),17(no 4),16,15(no 6),13(no 8)
20 = {389}/{479} - r19c4=[53]
19 = {379} - r19c4=[54]
18 = {468} - r19c4=[73]
17 = {368} - r19c4=[74]
16 = {367} - r19c4=[84]
15 = {348} - r19c4=[76]
13 = {346} - r19c4=[78]
30b. no 9 at r9c4
30c. cleanup 11(2)n78 - no 2 at r9c3

31. 11(2) & 12(2) r9 must use 3 (i.e. {38}{75}/[56][93]/[74][93]) - locked for r9
31a. cleanup 9(2)n8 - no 6 at r8c5

32. 45 on n8 - innies total 18 = [369]/{38}7/[945]/[549] - {567} blocked by 15(2)
32a. no 4 at r7c5

33. 45 on c4 - outies = 16(3) = [457]/[547]/[745]/5{38}/[718]/[763]
33a. no 2at r5c3

34. 45 on r5 - innes = 23(5) - {12479}/{13478}/{23459}/{23468} - combos with 89, 56 or 69 blocked by 14(2)n3
34a. {12479} - 2 locked at c6
34b. {13478} - 1 locked at c6
34c. {23459}/{23468} - 2 locked at c6
34d. so no 5, 6 at r5c6

and now a rather convoluted 45 ...
preliminary:
35. 45 on r9 - innies = 22(5) = {12468}/{12478}/{12568}
35a. must use 4 or 5

36. 45 on n2 n8 (yes - disjoint) - innies r1c46 r37c5 r9c46 total 34(6)
36a. 8(2)n2 blocks r1c6 r3c5 with [61] and r1c4 r3c5 with [72]
36b. 14(2)n2 blocks [56]/[58]/[89] at r1c46 and [56]/[58] at r19c4
36c. 15(2)n8 blocks [97]/[89] at r7c5 r9c6 and [86] att r7c5 r9c4 and [67] r9c46 and [67]/[89] r19c6
36d. 9(2)n8 blocks [35] r7c5 r9c6
36e. 22(5) from step 35 blocks [45] at r9c46
putting that all back together . . .
36f. no placement of 5 at r1c4
36g. no placement of 9 at r1c6 or r7c5
36h. no placement of 5 at r9c6

37. (Cleanups)
37a. 12(2)n12 no 7 at r1c3
37b. 11(2)n23 no 2 at r1c7
37c. 12(2)n89 no 7 r9c7

38. 5,9 now locked in 14(2) for n2 = {59} locked for c4
38a. 21(4)n45 - no 9, so cannot have 1 at r5c3

39. 8 locked in r1c46 for n2 - locked for r1

40. 5 locked in r789c5 for n5 - locked for c5

first placement:

41. naked pair {35} at r19c7
41a. r5c7=4
41b. 12(4)n56 = {125}4 - no 6


I can see a few more things flowing from there, but need to get on with some other stuff.

Rgds
Richard

[rcbroughton]

A few more ...


42. 5,8 locked in 12(2)/11(2) for r1 - no 5 in rest of r1

43. 21(4) n45 must use 3 - eliminates 3 at r5c5

44. innies in n1 = 19(4) - examining combos with 1
44a. {1459} - either 4 or 5 at r1c3 locks 1 in r23c1
r1c3=4 - r23c1 = {51}/{91} - {59} exceeds cage sum for 13(3)
r1c3=5 - r23c1 = {14}/{91} = {49} exceeds cage sum for 13(3)
44b. {1468} - r1c3=4 - 1 locked in r23c1={16}/{18}
44c. {1567} - r1c3=5 - 1 locked in r23c1={16}/{17}
44d. no 1 at r3c2

45. revisit outies from c4 - r159c3=16(3)
45a. =[457]/5{38} - no 6 at r5c3, no 5 at r9c3
45b. cleanup 11(2)n78 -no 6 r9c4
45c. 5 locked in r159c3 for c3

46. 6 locked in n5 for c4 - nowhere else in n5

47. innies of r5 = 23(5)
47a. 23(5)=[369]14/{378}14/[53924]/[36824] {14567} blocked by 14(2)n4
47b. must use 3 - locked for r5
47c. cleanup - no 5 in 8(2)n6

48. 5 locked in n4 for r5 - nowhere else in n4

49. from 47b. 3 locked in r5 is actually locked in c34 - eliminate from r46c4 for 21(4) cage
49a. 21(4) now = {3468}/53{67} - no 7 at r5c4

50. 12(2) & 9(2) r9 must use 7 - locked for r9

51. innies on c1 = 16(3)={169}/{1[8]7}/{259}/{268}/[394]/{358}/[754]
51a. no 4 at r1c1

52. 45 rule on n1. r1c3+r3c2 = r4c1+6
52a. max innies is 9+5=14 - no 9 at r4c1

53. innies on n9 = 14(4)
53a. {1238} - 3 at r9c6, 8,1 locked in r78c9
53b. {1256} - 5 at r9c6,
r78c9={12}/{26} - blocked by 16(3) cage sum
r78c9={16} - blocked by 19(3) & 14(3) c9 if 16(3)={167} then 19(3)={289} that breaks r5c9
53c. {1346} - 3 at r9c6,
r78c9={14} ok
r78c9={16} as 53b.
r78c9={56} blocked by 16(3) cage sum
53d. {2345} - no 6 used
53e. no 6 at r78c9
53f. 3 locked in these innies - no 3 at r8c8

54. 45 on n3 - outies total 20(4) - r4c789=12 or 14
54a. r4c789=12(3) - {138} - others blocked by 8(2)n6 or missing digits
54b. r4c789=14(3) - {158}/{23}9/6{35} - others blocked by 8(2)n6 or missing digits
54c. no 7 r4c789
54d. no 2,6 r4c69
54e. no 5 r4c8

55. cleanup 11(3) n36 - no 3 at r3c8

56. 45 on n3 - r1c7+r3c8 = r4c9+2 =5,7,10,11
56a. no 1 at r3c8

57. n5 - r456c6=8 - remainder = 37(6)={346789}
57a. 14(2)n4 blocks {69}/{89} in r5
57b. 8(2)n6 blocks {67} in r5
57c. 57a/57b. eliminates 6 from r5c4

58. 21(4)n45 - no 8 at r46c4

59. from step 47 innies of r5 = 23(5)=[369]14/{378}14/[53924]/[36824]
59a. now 23(5)={38}[714]/[53924]

60. 45 on n9 r7c8+r9c7=r6c9=5/6/7/8/9
60a. [15] blocked by 31(5) - no 1 at r7c8
60b. no other possibility for innies=6 - so no 6 at r6c9

61. 45 rule on n6 - innies total 37 - with r5c7=4
61a. {126789} blocked by 8(2)
61b. {135789} - r6c67=[73]/[83]/[93] - any other breaks 16(3) cage sum
61c. {235689} - no 7
61d. no 7 at r6c8

62. 45 on n12 - innies total 23(5)
62a. 2 cells in n2=[62]/[81]/[82] ([61] blocked by 8(2))
62a. 3 cells in n1=15, 14, 13
62a. 15={159}/{249}/{258}/{348}/{357}/2{67}/{18}6 - {456} blocked by r1c3
62b. 14=1{49}/1{58}/1{67}/{239}/{248}/{257}/{347} - {356} blocked by 26(5)
62c. 13={139}/{148}/{157}/2{38}/2{47}/2{56} - {346} blocked by 26(5)
62d. no 6 at r2c1


Enough for now.

Richard

[Glyn]

I hope I am starting off from Richards finishing position for this highly unorthodox move which I was itching to try. I have a lot to learn about assassins.


Summation of all cages which fall in R5, c5 and N5 14(2)+21(4)+28(5)+8(2)+9(2)+12(3)+8(2) = 100.
Deficit = 35 accounted for double entries of R46C5,R5C46 and triple entry of R5C5 caused by the overlap of Rows, Columns and Nonets.
The surplus entries R4C5+R6C5+R5C4+R5C6+2*R5C5=35.
Odd parity of sum depends on the number of odd cells amongst the 4 cells entered once in this sum. Choose an odd number of odd candidates from this set.

The table gives the permissable values of R46C5,R5C46 and the implication for R5C5. Unfortunately the tables have lost alignment with their headings in the post.

R5C4 R46C5 R5C6 Sum R5C5
3 {47} 1 15 10 (Not possible)
3 {48} 2 17 9
3 {49} 1 17 9 (Conflict 2 9s)
3 {78} 1 19 8 (Conflict 2 8s)
3 {79} 2 21 7 (Conflict 2 7s)
3 {89} 1 21 7
8 {34} 2 17 9
8 {37} 1 19 8 (Conflict 2 8s)
8 {39} 1 21 7
8 {47} 2 21 7 (Conflict 2 7s)
8 {49} 2 23 6 (Already cleared)
8 {79} 1 25 5 (Already cleared)

R5C5<>8 and R46C5<>7

R456C9={{49}7{94}},{(78}9{78}},{{39}7{93}} ({349} blocked by 9(2) in N8.

Hope it makes sense.

All the best

Glyn

[mhparker]

Hope it makes sense.

Yes it does (I think!). Thanks for that.

However, I managed to find a couple of more powerful moves that made the same eliminations, but made a couple of placements as well.

Incidentally, one of your eliminations (r5c5) had in fact already been made by Richard - you must have missed that.

(Richard: seemed like your "no 1" in step 56a should be "no 1,3,5". I proceeded on this assumption. Please re-check. Thanks.)


63. Innies r1234: r1c5+r2c456 = 21/4 -> r4c456 = 19 or 20
63a. At least one of r4c456 must be >= 8 (else max. = {567} = 18) -> r4c5 = {89}
63b. {89} present only in r4c5 -> no {12} possible in r4c456 -> r4c6 = 5
63c. r4c4 = {67} (no 4)

64. 4 in r4 now locked in n4 -> not elsewhere in n4
64a. Cleanup: no 8 in r7c2 (due to {45} unavailable in r6c23)

65. outies - innies R1234: r567c5 - r4c4 = 12
65a. No permutation possible with r4c4 = 7 -> r4c4 = 6
65b. r567c5 = [7]{38} or [945] -> no 7,9 in r6c5
65c. Cleanup: no 4 in r3c8 (due to {456} unavailable in r4c78}

66. 7 in r4 now locked in n4 -> not elsewhere in n4
66a. Cleanup: no 1,6 in r7c2 (due to {457} unavailable in r6c23)

67. innies - outies n7: r7c2 + r9c3 = r6c1 + 7 = 8,9,10,13,15,16 -> no 4 in r7c2
(due to only {378} available in r9c3}

68. Outies n1: r1c4+r4c123 = 20/4 -> r4c123 = 12 or 13
68a. 7 already locked in r4c123 (step 66) -> no 8,9 in r4c123
68b. max. of r4c23 = 4 + 7 = 11 -> no 2 in r3c2

69. r4c789 may only contain 1 of {89} (due to r4c5), with none of {567} available
69a. r4c789 must therefore contain exactly one of {56789}
69b. r5c89 must contain exactly one of {56789} due to 8/2 cage sum
69c. 3 of {56789} unaccounted for -> must go in r6c789 -> no digit below 5 in r6c789
-> no 2 in r6c78, no 3 in r6c8
69d. Cleanup: min. of r6c7 + r7c8 = 6 + 2 = 8 -> no 9 in r6c8
69e. Cleanup: min. of r6c78 = 6 + 5 = 11 -> no 5,6 in r7c8

70. 3 in n6 now locked in r4 -> not elsewhere in r4

71. r4c123 = {(1|2)47} (see also step 68} -> r4c78 cannot have both of {12} -> no 8 in r3c8

72. 6 in n9 now locked in 31/5 at r7c7 = {(18|45)679} -> no 2

73. 2 in r9 locked in n7 -> not elsewhere in n7
74. 2 in n7 locked in 22/5 at r7c3 = {2..} (no eliminations yet)

75. Common Peer Elimination (CPE): r3c8 can see all candidate positions with digit 2 in r7
-> no 2 in r3c8
75. 11/3 at r3c8 = [r3c8-r4c8-r4c7] = [632|731] -> r4c7 = {12}, r4c8 = 3, r4c9 = {89}

[rcbroughton]

One or two more highly convoluted moves and another placement

[Edit] - aaghh! took too long in the message editor and overlapped with Mike. Ignore my moves for now - need to check what Mike put and see what still remains of my moves. Shame because I got another placement in n4


63. 45 rule on N2, N3. Excluded cells r1c3 r4c789 r4567c5 equal 44
63a. r4567c5 total 26 or 27
63b. r1c3=4/5
so 4 possibilities for r1c3 r4567c5:
r1c3=4 - r4567c5=26={4[9]8[5]} - r4c789 = 14(3)={18}5/[635]
r1c3=4 - r467c5+r5c5=27={389}+[7] - r4c789=13(3) = {139}/{238} - blocks 3 at r4c5
r1c3=5 - r4567c5=26={4[9]8[5]} - r4c789 = 13(3) = {139}/{238} - blocks 3 at r4c5
r1c3=5 - r467c5+r5c5=27={389}+[7] - r4c789=12(3) = {138} - blocks 3 at r4c5 [615]/[219] blocked by 8(2)
63c. no 3 at r4c5

64. 45 rule on n89 innies r7c58+r9c4 = r6c9+6 = 11,13,14,15
64a. r7c5+r9c4 can't be [34] or [53] - blocked by 9(2)n8
64b. r7c5+r9c4 can't be [58] or [84] - blocked by 9(2) & 15(2)n8
64c. leaves [54]/{38} = 9 or 11
64d. r7c8 = 2,4,5,6 or 2,3,4
64e. no 5 at r7c8
64f. cleanup - no 9 at r6c8 in 16(3)

65. 45 rule on n89 - innies r7c589+r8c9+r9c4 total 20
65a. r7c5+r9c4 can't be [34] or [53] - blocked by 9(2)n8
65b. r7c5+r9c4 can't be [58] or [84] blocked by 9(2)&15(2)
65c. leaves [54]/{38} = 9 or 11
65d. r7c89+r8c9 = 11 or 9
r7c89+r8c9 = 11 - 5 at r7c9 blocked by r7c5=5
r7c89+r8c9 = 9 - 6{12}/{234} - 3{15} blocked by 31(5)n9
65e. no 5 at r7c9

66. 45 on r1234 - innies r3c5+r4c456=21
66a. r4c456=20(no 1) or 19(no 2)
66b. r4c456=20(no 1) =[695]/[785]
66c. r4c456=19(no 2) =[685]
66d. r4c4=5
66e. cleanup 12(4)n56=5{12}4

67. 45 on n3 r1c7+r3c8=r4c9+2
67a. r1c7+r3c8=5,10,11
67b. r1c7=3,5
67c. no 4 at r3c8