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Ed
 Post subject: Assassin 282
PostPosted: Thu Jan 16, 2014 9:50 pm 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Finally found a clean way to solve this one with a very early placement possible. But, very resistant to the very end. Used one advanced step. Some of Andrew's favourite technique available. It gets a SudokuSolver score of 1.60.

Assassin 282

Image
code: copy and paste into solver:
3x3::k:5376:5376:5376:5376:2305:2305:9218:9218:6659:6148:6148:1541:1541:5382:5382:9218:6659:6659:6148:6148:1541:8967:5382:6408:9218:9218:6659:3081:3081:8967:8967:6408:6408:6408:9218:778:3081:7179:8967:8967:2572:2572:9218:9218:778:2829:7179:11022:8967:11022:11022:11022:1295:4112:2829:7179:11022:11022:11022:7697:11022:1295:4112:2829:7179:7179:4626:7697:7697:1299:1299:4112:1300:1300:4626:4626:4626:7697:7697:4117:4117:
solution: 
+-------+-------+-------+
| 9 6 2 | 4 8 1 | 3 5 7 |
| 4 8 3 | 2 5 7 | 1 9 6 |
| 7 5 1 | 3 9 6 | 2 8 4 |
+-------+-------+-------+
| 6 1 8 | 5 7 3 | 9 4 2 |
| 5 3 4 | 9 2 8 | 7 6 1 |
| 2 7 9 | 6 1 4 | 5 3 8 |
+-------+-------+-------+
| 1 4 7 | 8 3 9 | 6 2 5 |
| 8 9 5 | 7 6 2 | 4 1 3 |
| 3 2 6 | 1 4 5 | 8 7 9 |
+-------+-------+-------+
Cheers
Ed
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Afmob
 Post subject:
PostPosted: Fri Jan 17, 2014 10:10 pm 
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Thanks for the new Assassin, Ed! My original walkthrough was quite long since I made a lot of small steps before spotting step 3b even though it was in plain sight. Note that you can swap steps 1 and 2 for an early placement.

A282 Walkthrough:
1. C789
a) 1,2,3,4 locked in 36(8) + both 5(2) for C78 (Killer X-Wing)
b) Innies C789 = 28(4) = {5689} locked for C7
c) 3(2) = {12} locked for C9+N6
d) 16(2) = {79} locked for R9+N9
e) Outies C9 = 16(2) = {79} locked for C8

2. C123+N2 !
a) Outies N1 = 6(2) = [42/51]
b) Killer triple (123) locked in 21(4)+6(3) for N1
c) 24(4) = 45{69/78} -> 4,5 locked for N1
d) 6(3) = {123} -> 3 locked for C3+N1
e) Innies+Outies C12: -10 = R8C3 - R1C12 -> R1C12 <> 1; R8C3 <> 8,9
f) 1 locked in R123C3 @ N1 for C3
g) ! Innies+Outies C12: -10 = R8C3 - R1C12: R8C3 = 5 since R1C12 <> 3,4,5 and (68,79,89) are Killer pairs of 24(4)
h) Outies C12 = 6(2) = [15/24]
i) Innies N12 = 9(2) <> 9
j) 9 locked in 21(3) @ N2 = 9{48/57}
k) Killer pair (45) locked in 21(3) + R1C4 for N2

3. R6789+N4 !
a) Innies+Outies R9: -6 = R8C4 - R9C67 -> R9C7 <> 6 (IOU @ N8); R8C4 <> 9 since R9C67 <= 14
b) ! 9 locked in 35(6) + 43(8) @ C34 for 43(8)
c) Hidden Single: R4C7 = 9 @ C7
d) 35(6) must have 9 -> CPE: R5C56 <> 9
e) 9 locked in R56C4 @ N5 for 35(6) + C4
f) Innies+Outies R6789: -3 = R5C2 - R6C4 -> R5C2 <> 7,8,9; R6C4 <> 1,2,3,8
g) 2 locked in R6C12 @ R6 for N4
h) 12(3) <> 9
i) Hidden Single: R5C4 = 9 @ R4
j) Innies+Outies R6789: -3 = R5C2 - R6C4 = [14/36/47] <> 5; R5C2 <> 6
k) 11(3): R6C1 <> 5 since 5{24} blocked by Killer pair (24) of 5(2) @ N7

4. N5689 !
a) 10(2) <> {46} since it's a Killer pair of Innies+Outies R6789
b) R7C6 <> 5 since it sees all 5 of N9
c) ! 5 locked in 43(8) + 16(3) @ R67 -> 16(3) = 5{38/47} -> 5 locked for C9
d) Hidden Single: R7C7 = 6 @ N9
e) 6 locked in Outies N3 @ N6 = 17(3) = 6{38/47}; R5C7 <> 4 since R45C8 <> 7
f) 10(2) = {28} locked for R5+N5 since {37} is blocked by R5C7 = (37)
g) Hidden Single: R5C1 = 5 @ R5
h) R5C9 = 1

5. N478
a) 12(3) = {156} since {345} blocked by R5C2 = (34) -> 1,6 locked for R4+N4
b) Hidden Single: R6C4 = 6 @ R6, R9C3 = 6 @ C3
c) Outie R6789 = R5C2 = 3
d) 11(3) = 1{28/37} -> 1 locked for C1+N7
e) 5(2) = {23} -> R9C12 = [32]
f) 18(4) = 6{138/147/345} <> 2 since R9C45 <> 3,7

6. N2568
a) R5C7 = 7
b) Outies N3 = 10(2) = {46} -> R45C8 = [46]
c) R6C8 = 3 -> R7C8 = 2
d) 25(4) = 39{58/67} since R4C56 = (357) -> 3 locked for N5; R3C6 = (68)
f) Innies N2 = [18/36]
g) Hidden Single: R2C4 = 2 @ C4
h) Outie N1 = R1C4 = 4
i) 43(8) = {13456789} -> 3 locked for R7+N8
j) 18(4) = {1467} -> R9C45 = [14]; R8C4 = 7

7. Rest is singles.

Rating:
Hard 1.25. I used Killer subsets combined with Innies+Outies and some Killer X-Wings.
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Andrew
 Post subject: Re: Assassin 282
PostPosted: Sun Jan 19, 2014 4:14 am 
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Joined: Wed Apr 23, 2008 6:04 pm
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Thanks Ed for your latest Assassin!

My solving path was very different from Afmob's. After a lot of fairly routine steps, I found it hard to find the breakthrough.

Thanks to Afmob and Ed for pointing out typos in step 12 and to Afmob for pointing out omissions in other steps.
Here is my walkthrough for Assassin 282:
Prelims

a) R1C56 = {18/27/36/45}, no 9
b) R45C9 = {12}
c) R5C56 = {19/28/37/46}, no 5
d) R67C8 = {14/23}
e) R8C78 = {14/23}
f) R9C12 = {14/23}
g) R9C89 = {79}
h) 6(3) cage at R2C3 = {123}
i) 21(3) cage at R2C5 = {489/579/678}, no 1,2,3
j) 11(3) cage at R6C1 = {128/137/146/236/245}, no 9
k) 26(4) cage at R1C9 = {2789/3689/4589/4679/5678}, no 1
l) 36(8) cage at R1C7 = {12345678}, no 9
m) 43(8) cage at R6C3 = {13456789}, no 2

Steps resulting from Prelims
1a. Naked pair {12} in R45C9, locked for C9 and N6, clean-up: no 3,4 in R7C8
1b. Naked pair {79} in R9C89, locked for R9 and N9
1c. Naked triple {123} in 6(3) cage at R2C3, CPE no 1,2,3 in R2C12
1d. Killer pair 1,2 in R7C8 and R8C78, locked for N9
1e. 9 in C7 only in R46C7, locked for N6

2. 45 rule on N1 2 outies R12C4 = 6 = [42/51]
2a. 6(3) cage at R2C3 = {123}, 3 locked for C3 and N1
2b. R1C56 = {18/27/36} (cannot be {45} which clashes with R1C4), no 4,5 in R1C56

3. 21(3) cage at R2C5 = {489/579} (cannot be {678} which clashes with R1C56), no 6, 9 locked for N2
3a. Killer pair 4,5 in R1C4 and 21(3) cage, locked for N2

4. 45 rule on C9 2 outies R29C8 = 16 = {79}, locked for C8
4a. 36(8) cage at R1C7 = {12345678}, 7 locked for C7

5. 45 rule on C789 4 innies R4679C7 = 28 = {5689} (only possible combination), locked for C7

6. 45 rule on N3 3 outies R4C8 + R5C78 = 17 = {368/458/467}
6a. 3 of {368} must be in R5C7 -> no 3 in R45C8
6b. Killer pair 3,4 in R4C8 + R5C78 and R6C8, locked for N6
[Afmob pointed out that the killer pair also eliminates 3,4 from R13C8]

7. 21(4) cage at R1C1 must contain one of 1,2 (because {4567}=22)
7a. Killer pair 1,2 in 21(4) cage and 6(3) cage at R2C3, locked for N1

8. 45 rule on C12 3(2+1) outies R1C34 + R8C3 = 11
8a. Min R1C4 = 4 -> max R18C3 = 7, no 7,8,9 in R18C3
8b. R18C3 must contain one of 1,2 (because no 3 in R18C3) -> killer pair 1,2 in R18C3 and 6(3) cage at R2C3, locked for C3

9. 45 rule on N47 5 innies R45679C3 = 34 = {46789}, locked for C3

10. R1C34 + R8C3 = 11 (step 8)
10a. R1C4 = {45} -> R18C3 = [15]/{25}, no 1 in R8C3
10b. 1 in C3 only in R123C3, locked for N1

11. 35(6) cage at R3C4 = {146789/236789/345689} (cannot be {245789} which clashes with R12C4)
11a. 4 of {146789/345689} must be in R45C3 (R3456C4 cannot contain both of 1,4 which would clash with R12C4, cannot contain both of 4,5 which would clash with R1C4), no 4 in R456C4

12. 45 rule on C1234 3 innies R6C3 + R7C34 = 1 outie R9C5 + 20
12a. Max R6C3 + R7C34 = 24 -> max R9C5 = 4
12b. Min R6C3 + R7C34 = 21, no 1,3 in R7C4

13. 43(8) cage at R6C3 = {13456789}, CPE no 1,3 in R45C5, clean-up: no 7,9 in R5C6

14. 45 rule on N8 2 outies R9C37 = 2 innies R7C45 + 3
14a. Max R9C37 = 14 -> max R7C45 = 11, min R7C4 = 4 -> max R7C5 = 7

15. 18(4) cage at R8C4 = {1368/1458/1467/2358/2367/3456} (cannot be {1269/1278/2349/2457} which clash with R9C12, cannot be {1359} because R9C3 only contains 4,6,8), no 9
15a. 7 of {1467/2367} must be in R8C4, 6 of {1368/3456} must be in R9C34 (R9C345 cannot be {138/345} which clash with R9C12), no 6 in R8C4

16. 45 rule on R6789 1 innie R6C4 = 1 outie R5C2 + 3, no 1,7,8,9 in R5C2, no 1,2,3 in R6C4

[I ought to have spotted this a lot sooner …]
17. Max R1C34 = 9 -> min R1C12 = 12, no 2 in R1C12
17a. 2 in N1 only in R123C3, locked for C3 -> R8C3 = 5, clean-up: no 8 in R6C4 (step 16)

18. 11(3) cage at R6C1 = {128/137/146/236} (cannot be {245} = 5{24} which clashes with R9C12), no 5 in R6C1
18a. 7,8 of {128/137} must be in R78C1 (R78C1 cannot be {12/13} which clash with R9C12), no 7,8 in R6C1

19. 5 in R9 only in R9C467, CPE no 5 in R7C6
[Note that when R9C7 contains 5 then R7C45 must contain 5, when R9C7 doesn’t contain 5 then R7C45 doesn’t contain 5.]
19a. R9C37 = R7C45 + 3 (step 14)
19b. R9C37 = [45/46/48/65/68/86] (cannot be [85] = 13 because R7C45 cannot total 10 containing 5) = 9,10,11,12,14 -> R7C45 = 6,7,8,9,11 = [51/43/61/53/47/63/81/74/83] -> R7C4 = {45678}, R7C5 = {1347}
[Thanks Afmob for pointing out that I’d accidentally omitted R9C37 = [48]. Fortunately it doesn’t affect the result of this step, although it did make changes to steps 20 and 21 and made step 25a more complicated.]

20. 18(4) cage at R8C4 (step 15) = {1368/1458/1467/2358/2367/3456}, R7C45 (step 19b) = [51/43/61/53/63/81/47/74/83]
20a. 9 in N8 only in 30(5) cage at R7C6 = {15789/24789/25689/34689/35679}
20b. Consider combinations for 30(5) cage
30(5) cage = {15789/24789/34689/35679} => R7C45 = [51/43/61/53/63/81/83] (cannot be {47})
or 30(5) cage = {25689}, 2 locked for N8 => 18(4) cage = {1458/1467/3456} (cannot be {1368} with 6,8 in R9C34, to avoid clash with R9C12, which clashes with 30(5) cage = {2689}5) => R7C45 = [51/43/61/53/63/81/83] (cannot be {47})
-> R7C45 = [51/43/61/53/63/81/83], no 7 in R7C4, no 4,7 in R7C5

21. 1 of 43(8) cage at R6C3 must be in R6C56 (R6C56 + R7C5 cannot be [3x]1 which clashes with R67C8) -> R7C5 = 3, 1 in R6C45, locked for R6 and N5, clean-up: no 6 in R1C6, no 9 in R5C5

22. 3 in R9 only in R9C12 = {23}, locked for R9 and N7

23. 11(3) cage at R6C1 (step 18) = {128/137/146} (cannot be {236} because 2,3 only in R6C1), 1 locked for C1 and N7
23a. R4C2 = 1 (hidden single in N4), R45C9 = [21]
23b. R4C2 = 1 -> R45C1 = 11 = {38/47/56/[92], no 9 in R5C1

24. 18(4) cage at R8C4 (step 15) = {1458/1467}, no 2, 1 locked for N8
24a. 5 of {1458} must be in R9C4 -> no 8 in R9C4
24b. 1 in R9 only in R9C45, locked for N8
24c. 4 in R9 only in R9C3456, CPE no 4 in R8C4
24d. R8C4 = {78} -> no 8 in R9C3

25. 18(4) cage at R8C4 (step 24) = {1458/1467}
25a. 2 in N8 only in 30(5) cage at R7C6 (step 20a) = {25689} (only remaining combination, cannot be {24789} = {279}48 which clashes with R78C4 because R9C67 = [48] would require R9C3 = 6, R9C37 = [68] -> R7C45 = [83], step 19b)

26. R8C4 = 7 (hidden single in N8) -> 18(4) cage at R8C4 (step 24) = {1467}, 6 locked for R9, clean-up: no 4 in R5C2 (step 16)
26a. Naked pair {58} in R9C67 -> R7C6 + R8C56 = {269}, locked for N8
26b. R9C3 = 6 (hidden single in R9)
26c. Killer pair 1,4 in R12C4 and R9C4, locked for C4

27. 9 in C4 only in R456C4, locked for N5 and 35(6) cage at R3C4, no 9 in R45C3

28. 9 in C3 only in R67C3, locked for 43(8) cage at R6C2, no 9 in R6C7
28a. R4C7 = 9 (hidden single in C7), clean-up: no 2 in R5C1 (step 23b)
28b. R5C4 = 9 (hidden single in R5), clean-up: no 6 in R5C2 (step 16)

29. 35(6) cage at R3C4 (step 11) = {236789/345689}
29a. R45C3 = {478} -> no 8 in R34C4

30. R7C4 = 8 (hidden single in C4)
30a. R67C7 = {56}, locked for C7 and 43(8) cage at R6C3 -> R9C67 = [58]

31. 2 in R6 only in R6C12, locked for N4 -> R5C2 = 3, R6C4 = 6 (step 16), R67C7 = [56], R9C12 = [32], clean-up: no 4,7 in R5C5, no 4 in R5C6
31a. Naked pair {28} in R5C56, locked for R5 and N5

32. R6C8 = 3 (hidden single in R6), R7C8 = 2, R7C6 = 9, clean-up: no 3 in R8C7
32a. R8C78 = {14}, locked for R8 and N9 -> R8C1 = 8, R8C2 = 9, R78C9 = [53], R6C9 = 8 (cage sum)
32b. R67C1 = [21] (hidden pair in C1)
32c. R45C1 = {56} (hidden pair in N4), locked for C1
32d. Naked triple {479} in R123C1, locked for N1

33. R5C1 = 5 (hidden single in R5), R4C1 = 6, R45C8 = [46], R5C7 = 7, R5C3 = 4, R6C2 = 7, R8C78 = [41]

34. R45C3 + R56C4 = [8496] = 27 -> R34C4 = 8 = [35]
34a. R4C56 = [73], R4C7 = 9, R3C6 = 6 (cage sum)

35. Deleted, unnecessary

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A282 at Hard 1.5. I used a forcing chain which I felt was complicated enough to be at the top of the 1.5 range and step 25a was fairly complicated.


Ed wrote Some of Andrew's favourite technique available:
He's now told me that he was referring to Caged X-Wings, which are certainly one of my favourite techniques along with Hidden Killers. Afmob used some Caged X-Wings for this puzzle; I didn't use any.
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Ed
 Post subject: Re: Assassin 282
PostPosted: Thu Jan 23, 2014 6:04 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Thanks both for your WTs. Afmob found his step 3b made a big difference. I checked my first solve and I never did find that one even though it was available. I have a cheaters button which highlights all instances of a number so have no excuse for missing it. I worked in the same areas as Andrew though very differently. My steps 4, 10 & 11 are why. Really enjoyed his 21. This optimised WT makes big chunks of progress which only come about after multiple solves. [Thanks to Andrew for some corrections and comments.]

A282
29 solving steps:
Preliminaries courtesy of SudokuSolver
Cage 3(2) n6 - cells ={12}
Cage 16(2) n9 - cells ={79}
Cage 5(2) n7 - cells only uses 1234
Cage 5(2) n9 - cells only uses 1234
Cage 5(2) n69 - cells only uses 1234
Cage 9(2) n2 - cells do not use 9
Cage 10(2) n5 - cells do not use 5
Cage 6(3) n12 - cells ={123}
Cage 21(3) n2 - cells do not use 123
Cage 11(3) n47 - cells do not use 9
Cage 26(4) n3 - cells do not use 1
Cage 36(8) n36 - cells ={12345678}
Cage 43(8) n456789 - cells ={13456789}

1. "45" on n47: 5 innies r45679c3 = 34 = {46789} only: all locked for c3

2. "45" on n1: 2 outies r12c4 = 6 = [51/42]

3. 6(3)r2c3 must have 3 which is only in r23c3, locked for c3 and n1

4. 21(4)r1c1 must have 4/5 for r1c4 = {1479/1569/1578/2469/2478/2568}
4a. Can't have both 4 & 5 -> no 4,5 in r1c123
4b. Can't have both 1 & 2 -> no 1,2 in r1c12
4c. Naked triple {123} in r123c3: 1,2 both locked for n1 and c3
4d. r8c3 = 5

Early placement done, now the more routine obvious stuff.
5. 3(2)r4c9 = {12}: both locked for c9 and n6
5a. no 3,4 in r7c8

6. 16(2)r9c8 = {79} only: both locked for r9 and n9

7. "45" on c9: 2 outies r29c8 = 16 = {79} only: both locked for c8

8. 36(8)r1c7 must have 7 which is only in c7: 7 locked for c7

9. "45" on c789: 4 innies r4679c7 = 28 = {5689} only combination: all locked for c7 and 9 locked for n6

10. "45" on r9: 1 outie r8c4 + 6 = 2 innies r9c67
10a. r8c4 and r9c6 cannot be equal because they are in the same nonet -> no 6 in r9c7 (IOU)

The key step
11. "45" on c1234: 1 outie r9c5 + 20 = 3 innies r67c3+r7c4 (note: these 3 innies all in the same 43(8)r6c3)
11a. max. 3 innies = {789} = 24 -> max. r9c5 = 4
11b. Min. 3 innies = 21 -> no 1,3 r8c4
11c. but innies as 22 = {589} blocked by r67c7(same cage) = two of {5689}
11d. but innies as 22 = {679} blocked by r679c7 = one of 6 or 9
11e. but innies as 23 = {689} blocked by r67c7 = two of {5689}
11f. -> 3 innies = 21/24 -> r9c5 from (14)

Fairly routine from here. Missing clean-ups
12. 5(2)r9c1: {14} blocked by r9c5 = (14) -> 5(2) = {23} only: both locked for r9 and n7

13. 18(4)r8c4: but {1269/1278/1359/2349/2358/2367/2457} all blocked by 2,3,7,9 only in r8c4
13a. = {1368/1458/1467/3456}(no 2,9)

14. 2 in n8 only in 30(5)r7c6 = {24789/25689}(no 1,3)
14a. Must have 9 -> 9 locked for n8

15. 9 in c4 only in 35(6)r3c4 -> no 9 in r45c4

16. 9 in c3 only in r67c3 in 43(8)r6c3 -> no 9 elsewhere in that cage
16a. Hidden single 9 in n6 -> r4c7 = 9

17. 6 in c7 only in r67c7 in 43(8)r6c3 -> no 6 elsewhere in that cage

18. 6 in c34 only in 35(6)r3c4 and 18(4)r8c4 -> they must both have 6
18a. -> 18(4)r8c4 (step 13a) = {1368/1467/3456}
18b. Must have 3 or 7 which are only in r8c4 -> r8c4 = (37)

Now a handy "45" that I can't remember Afmob or Andrew using.
19. "45" on r9, 4 outies r7c6+r8c456 = 24 and must have 2 & 9 for n8 = {2589/2679}(no 3)
19a. -> r8c4 = 7, r7c6+r8c56 = {269} only: 6 locked for n8
19b. -> hidden single 6 in r9 -> r9c3 = 6
19c. r9c45 = 5 (cage sum) = {14} only: both locked for n8

20. Naked triple {568} in 43(8)r6c3 in r67c7+r7c4: 5 & 8 locked for that cage
20a. -> r7c5 = 3
20b. 1 must be in 43(8)r6c3 and only in r6c56: locked for r6 and n5

21. deleted

22. r12c4 = 6 = [42/51] = 1 or 4 and r9c4 = (14) -> 1,4 locked for c4 (Killer pair)

23. 3,6,9 in c4 only in 35(6)r3c4 = {236789/345689}
23a. -> r45c3 = {78/48} only, 8 locked for n4 and 35(6) cage -> no 8 in r3456c4
23b. Hidden single 8 in c4 -> r7c4 = 8, r9c67 = [58]

24. deleted

25. 11(3)r6c1 must have two of {1478} for r78c1 = {128/137/146}(no 5)
25a. must have 1, locked for c1 and n7
[Andrew noticed that r78c1 = [18] (hidden pair in n7) -> r6c1 = 2
It might have got to step 29a quicker. Thanks Andrew. I often miss hidden singles/pairs]

26. "45" on r6789: 1 outie r5c2 + 3 = 1 innie r6c4 = [25/36/69](r5c2 = (236); r6c4 = (569))

27. Hidden single 1 in n4 -> r4c2 = 1
27a. r45c9 = [21]
27b. r4c2 = 1 -> r45c1 = 11; but {47} blocked by r45c3 = {478} -> r45c1 = {56} only combination: both locked for c1 and n4

28. deleted

29. 2 in n5 only in r5: locked for r5
29a. r5c2 = 3, r9c12 = [32]
29b. r5c2 = 3 -> r6c4 = 6 (IODr6789=+3), r67c7 = [56]

30. Hidden single 5 in n9 -> r7c9 = 5

31. 10(2)n5 = {28} only combination: both locked for r5 and n5
31a. Hidden single 8 in n4 -> r4c3 = 8

32. Naked pair {47} in r5c37: both locked for r5

On from there.
Cheers
Ed
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