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Ed
 Post subject: Assassin 275
PostPosted: Fri Nov 08, 2013 12:26 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Don't know why but I love them this hard. Get great satisfaction when it all unravels. Took me a long time to find the key. Just do all normal stuff: nothing real tricky, just a lot of steps. JSudoku gets it out in a blink which is why I tried it. SudokuSolver muffs it up.

Assassin 275

Image

code:paste into solver:
3x3::k:5120:4865:4865:3074:8963:2564:2564:1797:1797:5120:4865:3074:3074:8963:8963:8963:8963:8963:5120:1030:9991:9991:9991:9991:9991:1800:1800:5120:1030:9991:4617:4617:3850:9991:2059:6668:2317:2317:2318:2318:4617:3850:7951:2059:6668:3600:3600:4369:2318:4617:7951:7951:6668:6668:8978:4371:4369:3604:3604:7951:7951:6668:3349:8978:4371:4369:4369:1302:1302:7951:5399:3349:8978:8978:8978:8978:8978:5399:5399:5399:5399:
solution: 
+-------+-------+-------+
| 1 4 8 | 9 6 3 | 7 2 5 |
| 6 7 2 | 1 4 5 | 9 8 3 |
| 5 3 9 | 7 2 8 | 4 6 1 |
+-------+-------+-------+
| 8 1 6 | 4 5 9 | 3 7 2 |
| 7 2 4 | 3 8 6 | 5 1 9 |
| 9 5 3 | 2 1 7 | 6 4 8 |
+-------+-------+-------+
| 2 8 7 | 5 9 4 | 1 3 6 |
| 4 9 1 | 6 3 2 | 8 5 7 |
| 3 6 5 | 8 7 1 | 2 9 4 |
+-------+-------+-------+
Cheerio
Ed
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Andrew
 Post subject: Re: Assassin 275
PostPosted: Sun Nov 10, 2013 10:56 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Ed wrote:
Just do all normal stuff: nothing real tricky, just a lot of steps.
That's a good description of how I solved this Assassin.

Here is my walkthrough for Assassin 275:
Prelims

a) R1C67 = {19/28/37/46}, no 5
b) R1C89 = {16/25/34}, no 7,8,9
c) R34C2 = {13}
d) R3C89 = {16/25/34}, no 7,8,9
e) R45C6 = {69/78}
f) R45C8 = {17/26/35}, no 4,8,9
g) R5C12 = {18/27/36/45}, no 9
h) R6C12 = {59/68}
i) R78C2 = {89}
j) R7C45 = {59/68}
k) R78C9 = {49/58/67}, no 1,2,3
l) R8C56 = {14/23}
m) 19(3) cage at R1C2 = {289/379/469/478/568}, no 1
n) 9(3) cage at R5C3 = {126/135/234}, no 7,8,9

Steps resulting from Prelims
1a. Naked pair {13} in R34C2, locked for C2, clean-up: no 6,8 in R5C1
1b. Naked pair {89} in R78C2, locked for C2 and N7, clean-up: no 1 in R5C1, no 5,6 in R6C1
1c. Killer pair 8,9 in R7C2 and R7C45, locked for R7, clean-up: no 4,5 in R8C9

2. 19(3) cage at R1C2 = {469/478} (cannot be {289/379} because 3,8,9 only in R1C3, cannot be {568} which clashes with R6C2), no 2,3,5
2a. 8,9 only in R1C3 -> R1C3 = {89}
2b. R12C2 = {46/47}, 4 locked for C2 and N1, clean-up: no 5 in R5C1

3. 45 rule on R12 2 innies R12C1 = 7 = {16/25}
3a. Hidden killer pair 8,9 in R34C1 and R6C1 for C1, R6C1 = {89} -> R34C1 must contain one of 8,9
3b. 45 rule on R12 2 outies R34C1 = 13 = {58}/[94] (cannot be {67} because R34C1 must contain one of 8,9)
3c. R34C1 = [58/94] (cannot be [85] which clashes with R6C12 = [95])
3d. 8 in C1 only in R46C1, locked for N4

4. 39(7) cage = {1356789/2346789}
4a. Caged X-Wing for 3 in R34C2 and 39(7) cage for R34, no other 3 in R34, clean-up: no 4 in R3C89, no 5 in R5C8
4b. 4 in R3 only in 39(7) cage = {2346789}, no 1,5
4c 4,7,8 in R3 only in R3C34567, locked for 39(7) cage at R3C3, no 4,7,8 in R4C37

5. 45 rule on C12 4(1+3 or 2+2) outies R1C3 + R9C345 = 28
5a. R1C3 = {89} -> R9C345 = 19,20, no 1 in R9C345
5b. 2 of 19 = {289} must be in R9C3 -> no 2 in R9C45

6. 45 rule on R9 3(2+1) outies R78C1 + R8C8 = 11
6a. Min R78C1 = 3 -> max R8C8 = 8

7. 35(7) cage at R7C1 is missing two numbers which total 10
7a. 3,7 in C1 only in R5C1 and R789C1 -> 35(7) cage must contain both of 3,7 = {1235789/1345679/2345678}

8. 45 rule on C89 2 innies R2C89 = 2 outies R9C67 + 8
8a. Max R2C89 = 17 -> max R9C67 = 9, no 9 in R9C67
8b. Min R9C67 = 3 -> min R2C89 = 11, no 1 in R2C89

9. Hidden killer pair 1,5 in R3C12 and R3C89 for R3, R3C89 contains one of 1,5 -> R3C12 must contain one of 1,5
9a. Killer pair 1,5 in R12C1 and R3C12, locked for N1
9b. 5 in N1 only in R123C1, locked for C1
9c. 35(7) cage at R7C1 must contain 5, locked for R9

10. 35(6) cage at R1C5 must contain both of 8,9, CPE no 8,9 in R2C4

11. 5 in C1 only in R123C1 -> 20(4) cage at R1C1 = {16}[58]/{25}[94]
11a. 19(3) cage at R1C2 (step 2) = {478} (only remaining combination, cannot be {469} which clashes with 20(4) cage) -> R1C3 = 8, R12C2 = {47}, locked for C2 and N1, clean-up: no 2 in R1C67, no 2 in R5C1

12. 45 rule on N5 1 innie R6C6 = 1 outie R5C3 + 3, no 1,2,3 in R6C6

13. 45 rule on N14 5 innies R23456C3 = 24 = {13569/23469} (other combinations don’t contain at least three of 2,3,6,9 for R234C3), no 7, 3,6,9 locked for C3

14. R5C1 = 7 (hidden single in N4), R5C2 = 2, clean-up: no 8 in R4C6, no 1,6 in R4C8, no 5 in R6C6 (step 12)
14a. 3 in C1 only in R789C1, locked for 35(7) cage at R7C1, no 3 in R9C45
14b. 35(7) cage must contain both of 3,7 (step 7a), 7 locked for R9
14c. 6 in N7 only in R789C1 + R9C2, locked for 35(7) cage, no 6 in R9C45
14d. 35(7) cage contains 6 -> 35(7) cage (step 7a) must contain both of 4,6 (step 7) = {1345679/2345678}

15. R1C3 + R9C345 = 28
15a. R1C3 = 8 -> R9C345 = 20 = {479/578}, no 2
15b. Killer pair 8,9 in R7C45 and R9C45, locked for N8

16. Hidden killer pair 8,9 in R9C45 and R9C789 for R9, R9C45 contains one of 8,9 -> R9C789 must contain one of 8,9
16a. 21(5) cage cannot contain both of 8,9 -> no 8 in R8C8

17. 3 in N1 only in R2C3 + R3C23
17a. 45 rule on N1 using R12C1 = 7 (step 3), 4 remaining innies R3C12 + R23C3 = 19 = {1369/2359} = [91]{36}/[53]{29} -> R23C3 = {29/36}
17b. R23456C3 (step 13) = {13569/23469} = {36}9{15}/{29}{346} (cannot be {36}{249} which clashes with R46C1, ALS block), no 9 in R6C3

18. Hidden killer pair 1,2 in R12C1 and R789C1 for C1, R12C1 contains one of 1,2 -> R789C1 must contain one of 1,2
18a. Hidden killer pair 1,2 in R789C1 and R78C3 for N7, R789C1 contains one of 1,2 -> R78C3 must contain one of 1,2
18b. 17(4) cage at R6C3 = {1367/1457/2357/2456} contains one of 1,2 which must be in R78C3 -> no 1,2 in R6C3 + R8C4
18c. R23456C3 (step 13) = {13569/23469}
18d. 1 of {13569} must be in R5C3 -> no 5 in R5C3, clean-up: no 8 in R6C6 (step 12)
18e. 5 in N4 only in R6C23, locked for R6

19. 45 rule on R123 4 outies R4C1237 = 18 = {1368/2349} (cannot be {1269} because R4C1 only contains 4,8)
19a. 2 of {2349} must be in R4C7 -> no 9 in R4C7

20. Deleted, replaced by step 25e.

21. 45 rule on N5 3 innies R56C4 + R6C6 = 12 = {129/156/237/246/345} (cannot be {147} because 9(3) cage at R5C3 cannot be 4{14})
21a. 2 of {246} must be in R6C4, 4 of {345} must be in R6C6 -> no 4 in R6C4

22. R9C345 (step 15a) = {479/578}, 17(4) cage at R6C3 (step 18b) = {1367/1457/2357/2456}
22a. Consider combinations for R7C45 = {59/68}
R7C45 = {59}, locked for N8 => R9C345 = 5{78} => 17(4) cage = {1367}
or R7C45 = {68}, locked for N8 -> R9C345 = {479}, R9C2 = 5 (hidden single in R9), R6C2 = 6, R6C3 = 5 (hidden single in R6) => 17(4) cage = {1457/2357}
-> 17(4) cage = {1367/1457/2357}, also no 5 in R8C4 + R9C45
22b. Caged X-Wing for 7 in 35(7) cage at R7C1 and 17(4) cage, no other 7 in N78
22c. 5 in R9 only in R9C23, locked for N7

23. R23456C3 (step 17b) = {13569/23469} = {36}9{15}/{29}{346}
23a. 17(4) cage at R6C3 (step 22a) = {1367/2357} (cannot be {1457} = 5{147} which clashes with R23456C3, a sort of CCC), no 4
23b. 17(4) cage at R6C3 = {1367/2357}, CPE no 3 in R6C4

24. 4 in N7 only in R789C1 + R9C3, locked for 35(7) cage at R7C1, no 4 in R9C45
24a. Killer triple 7,8,9 in R7C45 and R9C45, locked for N8, 7 also locked for R9

25. R23456C3 (step 17b) = {13569/23469} = {36}9{15}/{29}{346}
25a. 1,4 only in R5C3 -> R5C3 = {14}
25b. 9(3) cage at R5C3 = {126/234} (cannot be {135} because 3,5 only in R5C4), no 5
25c. 2 only in R6C4 -> R6C4 = 2
25d. 3,6 only in R5C4 -> R5C4 = {36}
25e. 9(3) cage = {126} = {16}2 => R5C8 = 3 or {234} = [432] -> 3 in R5C48, locked for R5
25f. Naked pair {36} in R58C4, locked for C4, clean-up: no 8 in R7C5
[Thanks Ed for pointing out that I'd overlooked clean-up: R6C6 = {47} (step 12) in step 25a.
This leads to R5C3 + R6C7 = [14/47], CPE no 4 in R5C57, which is a bit simpler than step 27a.]

26. 1 in N5 only in 18(4) cage at R4C4 = {1359/1458} (cannot be {1368/1467} which clash with R45C6), no 6,7
26a. 3 of {1359} must be in R6C5 -> no 9 in R6C5
26b. 7 in N5 only in R46C6, locked for C6, clean-up: no 3 in R1C7

27. 45 rule on N5 2 remaining innies R5C4 + R6C6 = 10 = [37/64]
27a. 9(3) cage at R5C3 (step 25b) = {126/234} = [16]2/[43]2 -> R5C34 + R6C6 = [16]4/[43]7, CPE no 4 in R5C57

28. 12(3) cage at R1C4 = {129/156/345} (cannot be {147} because no 1,4,7 in R2C3, cannot be {237/246} because 2,3,6 only in R2C3), no 7
28a. 2 of {129} must be in R2C3 -> no 9 in R2C3, clean-up: no 2 in R3C3 (step 17a)
28b. 9 in N1 only in R3C13, locked for R3

29. 5 in R8 only in R8C789, locked for N9, clean-up: no 8 in R8C9

30. Hidden killer pair 2,5 in R1C145 and R1C89 for R1, R1C89 must contain both or neither of 2,5 -> R1C145 must contain both or neither of 2,5
30a. 45 rule on R1 4 remaining innies R1C1245 = 20 = {1379/1469/2459/2567/3467} (cannot be {2369} which contains 2 but not 5)
30b. 4,7 of {1379/1469/2459/2567} must be in R1C2, 4,7 of {3467} must be in R1C24 -> no 4,7 in R1C5

31. 35(6) cage at R1C5 = {236789/345689} (cannot be {146789/245789} which clash with R2C2), no 1
31a. Killer pair 4,7 in R2C2 and 35(6) cage, locked for R2

32. R1C1245 (step 30a) = {1379/1469/2459/2567/3467}
32a. 12(3) cage at R1C4 (step 28a) = {129/156} (cannot be {345} = [435] because R1245 = {3467} = [6743] clashes with R23C3 = [36], step 17a), no 4 in R1C4, no 3 in R2C3, clean-up: no 6 in R3C3 (step 17a)
32b. 12(3) cage = {129/156}, 1 locked for C4 and N2, clean-up: no 9 in R1C7
32c. R1C1245 = {1379/1469/2459/2567} (cannot be {3467} because 4,7 only in R1C2)
32d. 1 in N5 only in R456C5, locked for C5, clean-up: no 4 in R8C6
32e. 9 in N3 only in R2C789, locked for 35(6) cage at R1C5, no 9 in R1C5 + R2C56

33. 3 in R2 only in R2C56789, locked for 35(6) cage at R1C5, no 3 in R1C5
33a. 3 in R1 only in R1C67 = [37] or in R1C89 = {34} -> R1C67 = [37/91] (cannot be {46}, locking-out cages)
33b. R1C67 = [37] -> R1C4 = 9 (hidden single in R1) or R1C67 = [91] -> no 1 in R1C4 (locking-out cages)
33c. R2C4 = 1 (hidden single in C4), clean-up: no 6 in R1C1 (step 3)

34. 6 in N1 only in R2C13, locked for R2
34a. 35(6) cage at R1C5 (step 31) = {236789/345689} -> R1C5 = 6, clean-up: no 1 in R1C89, no 8 in R7C4

35. Naked pair {59} in R7C45, locked for R7 and N8 -> R78C2 = [89], clean-up: no 4 in R7C9
35a. Naked pair {67} in R78C9, locked for C9 and N9, clean-up: no 1 in R3C8
35b. Naked pair {78} in R9C45, locked for R9
35c. R8C7 = 8 (hidden single in N9)
35d. 8 in R3 only in R3C456, locked for N2

36. 35(7) cage at R7C1 is missing two numbers which total 10 (step 7)
36a. No 9 in 35(7) cage -> no 1 in 35(7) cage
[Cracked. The rest is fairly straightforward.]

37. R1C1 = 1 (hidden single in C1), R1C2 = 6 (step 3), R1C7 = 7, R1C6 = 3, R12C2 = [47], R2C3 = 2, R1C4 = 9 (cage sum), R34C2 = [31], R3C3 = 9, R3C1 = 5, R4C1 = 8 (step 3b), R6C1 = 9, R6C2 = 5, R5C3 = 4, R5C4 = 3 (cage sum), R9C23 = [65], R7C45 = [59], R45C4 = [45], R6C6 = 7, R8C4 = 6, R46C3 = [63], R4C6 = 9, R5C6 = 6, R4C789 = [372], R3C9 = 1, R3C8 = 6, R5C8 = 1, R78C9 = [67], R78C3 = [71], R8C6 = 2, R8C5 = 3, R56C5 = [81], R9C45 = [87], R2C56 = [45], R3C5 = 2, R3C7 = 4, R2C7 = 9

38. R5C7 = 5, R6C67 = [76], R8C7 = 8 total 26 -> R7C67 = 5 = [41]

and the rest is naked singles.

An interesting feature:
of the cage pattern is R45C8 and 26(5) cage at R4C9 “see” all of each other’s cells so form combined 34(7) cage, must contain 1, missing numbers must total 11. I couldn’t see any way to use this.

Rating Comment:
I'll rate my walkthrough for A275 at Hard 1.5.

The SS score which Ed didn't give, maybe he didn't want to frighten solvers, is 2.45. I've no idea why it's so high. I don't think there are any of my steps which SS won't be able to find.
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Ed
 Post subject: Re: Assassin 275
PostPosted: Sat Nov 16, 2013 10:37 pm 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Ed wrote:
Just do all normal stuff: nothing real tricky, just a lot of steps.
Andrew wrote:
That's a good description of how I solved this Assassin.
Andrew's solving has gone up a notch I feel. The last two Assassins you've been using various advanced, tricky steps with ease. In this puzzle, steps 22a, 23a, 32a. The steps that use 5 innies are also pretty good and SudokuSolver won't be able to find them either. I had to really concentrate to follow all those steps but you describe them as pretty routine. :applause:

My key move was available from Andrew's step 9 but have veered off at end of step 11. We come back and overlap on a couple of steps but generally go a different way. On the whole, my way is a bit simpler I feel but perhaps that's only because I found the rest quite quickly.

A275 Alternate crack
18 more steps:
paste grid into A275 in SudokuSolver. Alternatively, download the attached file to your computer and open with SudokuSolver: 
.-------------------------------.-------------------------------.-------------------------------.
| 1256      47        8         | 12345679  12345679  134679    | 134679    123456    123456    |
| 1256      47        2369      | 1234567   123456789 123456789 | 123456789 23456789  23456789  |
| 59        13        2369      | 2346789   2346789   2346789   | 2346789   1256      1256      |
:-------------------------------+-------------------------------+-------------------------------:
| 48        13        2369      | 12456789  12456789 6789       | 2369      12567     12456789  |
| 347       256       123456    | 123456    123456789 6789      | 123456789 12367     123456789 |
| 89        56        12345679  | 123456    123456789 123456789 | 123456789 123456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 123467    89        1234567   | 5689      5689      1234567   | 1234567   1234567   4567      |
| 123467    89        1234567   | 123456789 1234      1234      | 123456789 12345678  6789      |
| 123467    256       234567    | 3456789   3456789   1234678   | 1234678   12346789  12346789  |
'-------------------------------.-------------------------------.-------------------------------'

End of Andrew's step 11 to above (or download the attached file which is at the same spot) then this is the key step which eluded me for so long and makes everything unravel
12. 5 in c6 & 7 only in r2c67 in 35(6)r1c5 or the 31(6)r5c7
12a. -> 31(6) must have 5
12b. and 35(6)r1c5 must have 5 in r2c67 -> no 5 in r12c5 nor r2c89
12c. and 5 locked for r2
12d. 35(6)r1c5 = {245789/345689}(no 1)
12e. Must have 4 -> caged x-wing on 4 with r12c2: no other 4 in r12
12f. no 6 in 10(2)r1c6
12g. no 3 in 7(2)r1c8
12h. h7(2)r12c1 = {16}[52](no 2 in r1c1) = [5] or {6}

13. [561] in 12(3)r1c4 blocked since it clashes with h7(2)r12c1 (step 12h) (alternatively, 5 in r1 locked in r189c1 through combined half cage)
13a. no other way for 5 to be in r1c4 -> no 5
13b. Hidden single 5 in n2 -> r2c6 = 5

14. Naked quad {1256} in r13c89: all locked for n3
14a. no 9 in r1c6

15. 35(6)r1c5 = {245789/345689}
15a. 4 or 7 in {245789} must be in r1c5 to avoid clashing with r2c2 = (47)
15b. -> no 2 in r1c5

16. 12(3)r1c4 = {129/237}(no 6)
16a. must have 2 -> no 2 in r2c5 since it sees all of 12(3)

17. 35(6)r1c5 = {345689} only (no 7)

18. deleted

19. "45" on c12: 3 remaining outies r9c345 = 20 (no 2)
19a. -> r789c1+r9c2 = 15
19b. but {127}[5] blocked by h7(2)r12c1 = {16}/[52]
19c. {1347} blocked since r9c2 doesn't have any of them
19d. h15(3) = {1356/2346}(no 7)
19e. must have 3 & 6: both locked for n7, 3 for c1, and for 35(7)r7c1 -> no 3,6 in r9c345

20. Hidden single 7 in c1 -> r5c1 = 7, r5c2 = 2
20a. no 1,6 in r4c8
20b. no 8 in r4c6

21. h20(3)r9c345 = {479/578}
21a. r9c45 cannot be {58} since it would clash with 14(2)n8 = [5/8] -> 5 in {578} must be in r9c3 -> no 5 in r9c45

22. 5 in r9 only in n7: locked for n7

23. "45" on n78: 1 outie r6c3 + 2 = 2 innies r79c6
23a. r79c6 cannot be {12/24} which clash with 5(2)r8c5 = {14/23} and no other way for r79c6 to equal 6
23b. -> no 1,4 in r6c3

24. 17(4)r6c3: only permutations for r678c3 with 5 in r8c4 = [9]{12}/[3]{27}/[6]{24} but these all clash with r234c3 = three of {2369} (Almost Locked Set Block, ALS block)
24a. -> no 5 in r8c4

25. 5 in r8 only in n9: locked for n9
25a. no 8 in r8c9

26. 5 in r7,n8 only in 14(2)n8 = {59} only: 9 locked for r7 and n8
26a. r78c2 = [89]
26b. 13(2)n9 = {67} only: both locked for n9 and c9
26c. no 1 in r13c8

Cracked. No routine clean-up now.
27. h20(3)r9c345 = {578} only -> r9c3 = 5
27a. r9c45 = {78}, both locked for n8 and 8 for r9
27b. r9c2 = 6, -> r789c1 = 9 = {234} only: all locked for c1 and n7

28. Hidden pair {58} in r8 in r8c78 -> both = (58)

29. r78c3 = {17} only: 1 locked for c7
29a. r78c3 = 8 -> r6c3+r8c4 = 9 = {36} only -> no 3,6 in r6c4 since it sees both of those {36}

on from there. Mostly naked singles, doubles and a couple of cage sums
Cheerio
Ed


Attachments:
A275 Andrew WT end step 11.ssv [95.07 KiB]
Downloaded 718 times
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Andrew
 Post subject: Re: Assassin 275
PostPosted: Sun Nov 17, 2013 4:16 am 
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Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks for the compliments, Ed! :D

Your step 12 was well spotted! I loved the way it led to more Caged X-Wings!

It made your solving path quite a lot simpler than mine.

If I'd seen that step, then I wouldn't have found the 5 innies in N14, which would have been a pity.

I assume that SS would have found the 5 innies, but possibly not what I did with them. BTW I couldn't see any steps in Ed's solving path which SS wouldn't be able to find, so I don't understand its high score (it's given in the Rating Comment in my walkthrough post).
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