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Ed
 Post subject: Assassin 266
PostPosted: Fri Aug 16, 2013 7:48 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
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Not a ripsnorter but still a ripper. Hopefully not too easy for Frank this time. :) Certainly wasn't for me and very happy with the way once it revealed itself. SudokuSolver gives it 1.40. Will sure miss Andrew. Have a great hol!!

Assassin 266
Image
code: paste into solver:
3x3::k:1792:1792:4097:4610:4610:2051:2051:2051:4100:5381:5381:4097:7430:4610:8455:8455:8455:4100:5381:4104:4097:7430:7430:1545:8455:3594:4100:5381:4104:10763:4620:7430:1545:8455:3594:3594:4104:4104:10763:4620:7430:3853:8455:7438:7438:4111:4111:10763:4620:4620:3853:8455:7438:2832:4113:4111:10763:4114:4114:4114:4627:7438:2832:4113:10763:10763:10763:4114:3604:4627:2832:2832:4113:4117:4117:4117:3604:3604:4627:2582:2582:
solution: 
+-------+-------+-------+
| 5 2 9 | 7 6 1 | 4 3 8 |
| 4 8 1 | 2 5 3 | 9 7 6 |
| 3 7 6 | 8 9 4 | 5 1 2 |
+-------+-------+-------+
| 6 3 8 | 5 7 2 | 1 4 9 |
| 2 4 5 | 1 3 9 | 6 8 7 |
| 9 1 7 | 4 8 6 | 2 5 3 |
+-------+-------+-------+
| 1 6 4 | 3 2 7 | 8 9 5 |
| 8 9 3 | 6 4 5 | 7 2 1 |
| 7 5 2 | 9 1 8 | 3 6 4 |
+-------+-------+-------+
Cheerio
Ed
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Frank
 Post subject: Re: Assassin 266
PostPosted: Mon Aug 19, 2013 4:06 pm 
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Joined: Mon Apr 28, 2008 10:58 pm
Posts: 47
Location: Victoria, B.C., Canada
This assassin and I did not get along well :(. Here is how I started.

Here is how I started:
Firstly the 6 in n9 goes either in the 18(3) cage or the 10(2). It is easy to eliminate the 18(3) cage so r9c89 = {46}.
Secondly r789c6 is either {569} or {578}. It is easy to eliminate {569} so r789c6 = {578}.

After that start it is just a matter of grinding away at the remaining candidates. About as exciting as filing a tax return :).
So not my favourite assassin. I may have another try at it - perhaps start someplace else.

Many thanx anyway Ed - Cheers - Frank
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wellbeback
 Post subject: Re: Assassin 266
PostPosted: Sun Aug 25, 2013 9:24 pm 
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Posts: 282
Location: California, out of London
Ed was kind enough to post a walkthrough for my posted Assassin - so here's mine for his. It's a little messy - but what the heck.
I used both of Frank's posted steps.

Hidden Text:
1.
11/4@r6c9 = {1235}
29/4@r5c8 = {5789}

14/3@r3c8 cannot contain both a 4 and a 6
-> At least one of (46) in n6 in r456c7
-> At least one of (46) in 10/2@r9c8
-> 10/2@r9c8 = {46}
Innies - Outies n9 -> [r6c9,r7c8] = from [17], [28], [39]

2.
Outies c789 = +4 -> r12c6 = {13}
-> r1c6 from (13)

Missing values from 33/7@r2c6 = +12/2 = (39), (48), or (57)
They cannot both go in the 18/3@r7c7 since that would also require a 6 there, which is already elsewhere in n9
-> One of the missing values from the 33/7 must be in r1c7
-> r1c7 from (345)

Innies c89 -> r12c8 = +10. Cannot be {64} (Since 6 or 4 in r9c8)
-> r12c8 from [19], [28], [37]
-> r1c8 from (123)

-> 8/3@r1c6 from [143], [341], [152]

Also -> (5789) in c8 locked in r2567c8.
-> Whatever is in r2c8 (from 789) must go in r5c9.

3.
Since 5 already in c89 -> no 5 in 14/3@r3c8 -> 14/3@r3c8 must contain one of (789) which can only go in r4c9

Where do (46) go in c8? One is in r9c8 and the other must go in r34c8.
Where do (46) go in c9? One is in r9c9 and the other must go in r123c9.

4. Whatever is in r2c6 (1 or 3) must go in c7 in r789c7.
-> 18/3@r7c7 from {189} or {378}.
-> Whichever it is must go in the 11/4@r6c9 -> r6c9 from (13)
-> r7c8 from (79)
-> r4c9 from (79)

Either r2c6 = 1 -> r1c8 = 1
-> 8/3@r1c6 = [341]

Or r2c6 = 3 -> r6c9 = 3 -> r7c8 = 9 -> r4c9 = 9
-> r34c8 = {14} (Since those 2 cells must contain one of (46))
-> r1c8 = 3
-> 8/3@r1c8 = [143]

-> 8/3@r1c6 either [143] or [341]
-> r1c7 = 4

Also (79) locked in c8 in r27c8
-> r56c8 = {58}

Also r45c9 = {79}
-> 16/3@r1c9 = {268}
-> r8c8 = 2

Also HS 4 in n6 -> r4c8 = 4.
-> 10/2@r9c8 = [64]

Also 6/2@r3c6 = [42]

5. 7/2@r1c1 = {25}
-> HS 2 in c3 -> r9c3 = 2
Outies c123 -> r89c4 = +15
Since 6 already in r9 -> 16/3@r9c2 = [529]
-> r8c4 = 6
Innies c12 -> r89c2 = +14
-> r2c8 = 9
-> 16/3@r1c3 = {169}

Also Innies c6789 -> r789c6 = +20 - Must be {578}
-> 15/2@r5c6 = {69}

Since 2 and 5 already in r9 and since r789c6 = {578}
-> 14/3@r8c6 [518]
-> 16/4@r7c4 = {2347} with 7 in r7c6.
Also r7c9 = 5.

Also r7c8 (which was from (79)) must be 9
-> r6c9 = 3
-> r8c9 = 1
-> 18/3@r7c7 = {378}
-> r2c6 = 3
-> 8/3@r1c6 = [143]
-> r2c8 = 7
-> r5c9 = 7
-> 14/3@r3c8 = [149]
-> r23c7 = {59}
-> r456c7 = {126}

6.
Since (259) already in n7 -> 16/3@r7c1 from {178} or {367}
-> HS 7 in n1 -> r3c2 = 7
-> Innies - Outies n1 -> r4c1 = 6
-> 16/3@r7c1 = [187]
-> r7c2 = 6
-> r78c3 = {34}
-> r456c3 = {578}
-> r6c12 = +10 = [91]

Rest is cleanup
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Ed
 Post subject: Re: Assassin 266
PostPosted: Wed Aug 28, 2013 8:13 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Nice start by Frank and wellbeback. They saw it more directly than I did. My step 2 saw their start indirectly but achieved other important eliminations which wellbeback used later. My middle then went on a different track because of my step 9 [edit: Andrew found an easier way to do that step, Thanks Andrew!]. Cracked it quite effectively. Only used 11 more steps to get very close to the end.

A266 WT
20 steps:
Assassin 266

Prelims courtesy of SudokuSolver
Cage 6(2) n25 - cells only uses 1245
Cage 15(2) n5 - cells only uses 6789
Cage 7(2) n1 - cells do not use 789
Cage 10(2) n9 - cells do not use 5
Cage 8(3) n23 - cells do not use 6789
Cage 11(4) n69 - cells ={1235}
Cage 29(4) n69 - cells ={5789}
Cage 42(7) n478 - cells ={3456789}

1. "45" on c89: 2 innies r12c8 = 10 = [19/28/37/46](no 5), r2c8 = (6789)

2. h10(2)r12c8 & 10(2)n9 must have different combinations since r9c8 sees both of r12c8 and the two cages have the same total
2a. -> can't both be {46}
2b. 16(3)r1c9 can't be {466}-> can't have both 4 & 6
2c. 14(3)r3c8 can't be {446}-> can't have both 4 & 6
2d. the only places in c89 for 4 & 6 are the two 10(2) cages, the 16(3)n3 and the 14(3)r3c8
2e. -> 16(4)n3 must have 4 or 6 = {169/268/349/367/457}
2f. -> h10(2)r12c8 cannot have both 4 and 6 or it would clash with 16(4); h10(2) = [19/28/37](no 4,6)
2g. & 14(6)r3c8 must have 4 or 6 = {149/167/248/347/356}
2h. -> 10(2)n9 must have both 4 & 6 = {46} only: both locked for r9 and n9
2i. -> Killer pair 4 & 6 in 16(3)n3 and r9c9: both locked for c9

3. "45" on c789: 2 outies r13c6 = 4 = {13} only: both locked for n2 and c6
3a. 6(2)r3c6 = {24} only: both locked for c6

4. "45" on c6789: 1 innie r7c6 - 6 = 1 outie r9c5 = [71/82/93]
4a. r7c6 = (789); r9c5 = (123)

5. "45" on c123: 2 outies r89c4 = 15 = [69]/{78}(no 1,2,3,4,5; no 9 in r8c4)

6. "45" on c12: 2 innies r89c2 = 14 = {59}/[68](no 1,2,3,4,7; no 8 in r8c2)

7. 16(3)r9c2 = {178/259/358}
7a. must have 1,2,3 -> r9c3 = (123)
7b. 5 in {259} must be in r9c2 -> no 9 in r9c2 -> no 5 in r8c2 (h14(2)r89c2)

8. 42(7)r4c3 = {3456789}: must have 3, 4, 5 which are only in c3: all locked for c3
8a. 16(3)r9c2 = {178/259} = [817/529](no 8 in r9c4 -> no 7 in r8c4 (h15(2)r89c4)
8b. 7 must be in 42(7) only in c3: 7 locked for c3

Andrew noticed an easier way to do this next step...[16(3)n1 = {169/268}, 6 locked for c3; 6 must be in 42(7) only in r8: locked for r8].
9. from step 8a. 16(3)r9c2 = [817/529]; h14(2)r89c2 & h15(2)r89c4
9a. -> r89c24 = [6887/9569]
9b. must have 6 in r8c24: 6 locked for r8 and for 42(7)
9c. no 6 in r45678c3

10. 6 in c6 only in 15(2)r5c6 = {69} only: both locked for n5 and 9 for c6
10a. no 3 in r9c5 (IODc6789 = -6)

11. Naked triple {578} in r789c6: locked for n8
11a. r89c4 = [69]
11b. r89c2 = [95](h14(2)r89c2)
11c. r9c3 = 2 (cage sum)
11d. r9c5 = 1
11e. r7c6 = 7 (IODc6789 = -6)
11f. r89c6 = [58]

12. 6 & 9 in c3 only in r123c3 in 16(3) = {169} only: all locked for n1

13. "45" on n9: 1 innie r7c8 - 6 = 1 outie r6c9= [28/39]; r6c9 = (23), r7c8 = (89)
13a. 11(4)r6c9 must have 5 -> r7c9 = 5
13b. 11(4) must have 1 which is only in r8c89: 1 locked for n9 & r8

14. Naked quad {5789} in r2567c8: all locked for c8
14a. 5 in c8 only in n6: locked for n6

15. 33(7)r2c6 must have 2 which is only in c7: 2 locked for c7
15a. 18(3)n9 = {378} only: locked for c7 and n9
15b. r7c8 = 9, r6c9 = 3 (IODn9=+6)
15e. Naked triple {578} in r5c89+r6c8: 7,8 locked for n6

16. 14(3)r3c8 = {149} only -> r4c9 = 9
16a. r34c8 = {14} only: both locked for c8
16b. r89c8 = [26], r89c9 = [14]
16c. r12c8 = [37] (h10(2)r12c8)
16d. r12c6 = [13]
16e. r1c7 = 4 (cage sum)
16f. r34c8 = [14]
16g. r1c12 = [52]
16h. r34c6 = [42]

17. Naked pair {48} in r2c12: both locked for r2 and n1 and 21(4)r2c1
17a. no 8 in r4c1
17b. r2c12 = {48} = 12 -> r34c1 = 9 (cage sum) = [36] only permutation

18. 18(4)n5 = {1458} only: 4,5,8 locked for n5

19. Naked pair {37} in r56c5 in 29(5)r2c4: both locked for c5 and 7 for 29(5)
19a. no 7 in r3c4
19b. r78c5 = [24]

20. Hidden single 7 in n2 -> r1c4 = 7
20a. r12c5 = 11 (cage sum) = [65] only


A few more cage sums and singles
Cheerio
Ed
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Andrew
 Post subject: Re: Assassin 266
PostPosted: Sun Sep 22, 2013 12:56 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Ed wrote:
Will sure miss Andrew. Have a great hol!!

Pinata, in the Pinata Killer 43 thread) wrote:
I am glad that you enjoyed the puzzle and have a nice holiday.
Thanks guys!! I had an enjoyable holiday, away from the internet and sudokus for just over 2 weeks. So much to catch up on after the holiday that I only started working on this puzzle yesterday. Ed posted this Assassin on the day before I went away, so I didn't have time to try it then.

It's good to see that there are several more for me to catch up with! :D Also some variety because they are by Ed, HATMAN and wellbeback and are both Assassins and CNCs; I hope there will be another Pinata Killer soon, or maybe another Assassin by Pinata.

I'm particularly pleased that 5 Assassins have been posted in just over a month. Archive part J, which will include Assassins 251 to 275 and all other puzzles on this forum during this period, looked like it was going to become much longer than any previous parts; if the next 5 Assassins are posted in the next couple of months it should, hopefully, only be about the same length as part G.

My solving path was rather longer because I didn't spot the first step used by Frank and wellbeback, also found in Ed's step 2. I could say that I missed it because I'm out of practice, but it can be considered to be "non obvious" so I'll congratulate the three of you. :applause:

Here is my walkthrough for Assassin 266:
Thanks Ed for your comments and corrections.

Prelims

a) R1C12 = {16/25/34}, no 7,8,9
b) R34C6 = {15/24}
c) R56C6 = {69/78}
d) R9C89 = {19/28/37/46}, no 5
e) 8(3) cage at R1C6 = {125/134}
f) 29(4) cage at R5C8 = {5789}
g) 11(4) cage at R6C9 = {1235}
h) 42(7) cage at R4C3 = {3456789}, no 1,2

Steps resulting from Prelims
1a. 8(3) cage at R1C6 = {125/134}, 1 locked for R1, clean-up: no 6 in R1C12
1b. Naked quint {12345} in R1C12 and 8(3) cage, locked for R1
1c. 29(4) cage at R5C8 = {5789}, CPE no 5,7,8,9 in R4C8
1d. 11(4) cage at R6C9 = {1235}, CPE no 1,2,3 in R9C9, clean-up: no 7,8,9 in R9C8
1e. Caged X-Wing for 5 in 29(4) cage at R5C8 and 11(4) cage at R6C9, no other 5 in C89 and N69

2. 45 rule on C12 2 innies R89C2 = 14 = {59/68}

3. 45 rule on C123 2 outies R89C4 = 15 = {69/78}
[Alternatively 45 rule on N8 2 innies R89C4 = 15 …]

4. 42(7) cage at R4C3 = {3456789}, 3,4 locked for C3

5. Hidden killer pair 1,2 in 16(3) cage at R1C3 and R9C3 for C3, 16(3) cage cannot contain both of 1,2 -> 16(3) cage must contain one of 1,2 and R9C3 = {12}

6. 45 rule on C789 2 outies R12C6 = 4 = {13}, locked for C6 and N2, clean-up: no 5 in R34C6
6a. Naked pair {24} in R34C6, locked for C6
6b. Min R89C6 = 11 -> max R9C5 = 3
6c. Max R89C6 = 13 -> no 9 in R89C6
6d. 14(3) cage at R8C6 = {158/257/356} (cannot be {167} which clashes with R56C6), 5 locked for N8
6e. Naked quint {56789} in R789C6 + R89C4, locked for N8
6f. Max R7C45 + R8C5 = 9 -> min R7C6 = 7
[With hindsight I ought to have used 45 rule on C6789 1 innie R7C6 = 1 outie R9C5 + 6, R7C6 = {789}, R9C5 = {123}.]

7. 45 rule on C89 2 innies R12C8 = 10 = [19/28/37/46]

8. 45 rule on N9 1 innie R7C8 = 1 outie R6C9 + 6 -> R6C9 = {123}, R7C8 = {789}

9. 45 rule on N5 3 innies R45C5 + R4C6 = 12 = {129/147/237/246/345} (cannot be {138/156} because R4C6 only contains 2,4), no 8 in R45C5
9a. Killer quad 1,2,3,4 in R45C5 and R789C5, locked for C5

10. 18(3) cage at R1C4 = {567} (only remaining combination) -> R2C5 = 5, R1C45 = {67}, locked for R1 and N2
10a. Killer pair 6,7 in R1C4 and R89C4, locked for C4
10b. 9 in N2 only in R24C4 + R3C5; locked for 29(5) cage at R2C4, no 9 in R45C5
10c. Min R1C3 = 8 -> max R23C3 = 8, no 8,9 in R23C3
10d. Min R1C9 = 8 -> max R23C9 = 8, no 8,9 in R23C9

11. R45C5 + R4C6 (step 9) = {147/237/246}
11a. Killer pair 6,7 in R45C5 and R56C6, locked for N5
11b. Killer pair 8,9 in R56C6 and R6C5, locked for N5

12. 16(3) cage at R1C9 = {169/178/268/349} (cannot be {367} because R1C9 only contains 8,9)
12a. Killer triple 1,2,3 in 16(3) cage at R1C9 and 11(4) cage at R6C9, locked for C9
12b. Hidden killer triple 1,2,3 in 16(3) cage and 11(4) cage for C9, 16(3) cage contains one of 1,2,3 -> R678C9 can only contain two of 1,2,3 -> R78C9 must contain 5, locked for C9 and N9

13. 33(7) cage at R2C6 = {1234689/1235679/1245678}, 2 locked for C7
13a. 5 of {1235679/1245678} must be in R3C7 -> no 7 in R3C7

14. Hidden killer pair 4,6 in 18(3) cage at R7C7 and R9C89 for N9, R9C89 must contain both or neither of 4,6 -> 18(3) cage must contain both or neither of 4,6 -> 18(3) cage = {189/378/468} (cannot be {369} which only contains one of 4,6), 8 locked for C7 and N9, clean-up: no 2 in R9C8, no 2 in R6C9 (step 8)
14a. 29(4) cage at R5C8 = {5789}, 8 locked for N6
14b. 8 in R4 only in R4C123, locked for N4

15. 14(3) cage at R3C8 = {149/167/239/347} (cannot be {248} which clashes with R4C6), no 8 in R3C8
15a. Consider combinations for the 14(3) cage
14(3) cage = {149/239}, CPE no 9 in R1C9 + R56C8 -> R1C9 = 8, naked pair {79} in R5C9 + R7C8, locked for 29(5) cage at R5C8 and CPE no 7,9 in R9C9
or 14(3) cage = {167/347}, caged X-Wing for 7 in 14(3) cage and 29(5) cage, no other 7 in C89
-> no 7 in R56C8 + R9C9, clean-up: no 3 in R9C8

[With hindsight, step 16b can be omitted.]
16. 16(3) cage at R9C2 = {178/259/268} (cannot be {169} which clashes with R9C89)
16a. 5 of {259} must be in R9C2 -> no 9 in R9C2, clean-up: no 5 in R8C2 (step 2)
16b. 16(3) cage = {178/259/268}, R9C89 = [19]/{46} -> combined cage 16(3) + R9C89 = {178}{46}/{259}{46}/{268}[19], 6 locked for R9

17. 16(3) cage at R1C9 (step 12) = {169/178/268/349}
17a. 14(3) cage at R3C8 = {149/167/239/347}
17b. {167} can only be {16}7 (cannot be [716] which clashes with 16(3) cage + R9C9) -> no 6 in R4C9
17c. 6 in N6 only in R456C7 + R4C8, CPE no 6 in R2C8, clean-up: no 4 in R1C8 (step 7)
[Cracked; the rest is easier.]

18. 8(3) cage at R1C6 = {125/134}
18a. 4,5 only in R1C7 -> R1C7 = {45}

19. 33(7) cage at R2C6 = {1234689/1235679} (cannot be {1245678} which clashes with R1C7)
19a. Killer pair 4,5 in R1C7 and 33(7) cage, locked for C7

20. 4 in N9 only in R9C89 = {46}, locked for R9 and N9, clean-up: no 8 in R8C2 (step 2), no 9 in R8C4 (step 3)

21. 6 in N8 only in R8C46, locked for R8 -> R8C2 = 9, R9C2 = 5 (step 2), R9C34 = 11 = [29], R8C4 = 6 (step 3), R1C45 = [76], clean-up: no 2 in R1C1

22. 6 in N5 only in R56C6 = {69}, locked for C6 and N5 -> R6C5 = 8, R3C5 = 9

23. 16(3) cage at R1C3 = {169} (hidden triple in C3) -> R1C3 = 9, R23C3 = {16}, locked for N1, R1C9 = 8, R23C9 = 8 = {17/26}, no 3,4
23a. Naked pair {79} in R27C8, locked for C8 -> R56C8 = [85]

24. 33(7) cage at R2C6 (step 19) = {1235679} (only remaining combination) -> R3C7 = 5, R1C7 = 4, clean-up: no 3 in R1C12
24a. R1C12 = [52]

25. 4 in N6 only in R4C89, locked for R4 -> R34C6 = [42]
25a. 14(3) cage at R3C8 (step 15) contains 4 = {149/347}, no 2,6
25b. Naked pair {13} in R13C8, locked for C8 and N3 -> R4C8 = 4, R8C8 = 2, R9C89 = [64]
25c. Naked pair {79} in R45C9, locked for C9 and N6
25d. Naked pair {26} in R23C9, locked for N3
25e. Naked pair {79} in R2C78, locked for R2

26. 45 rule on N1 1 innie R3C2 = 1 outie R4C1 + 1 -> R3C2 = {78}, R4C1 = {67}
26a. R3C2 + R4C1 = [76/87], CPE no 7 in R3C1+ R456C2
26b. R3C2 = 7 (hidden single in N1), R4C1 = 6
26c. R7C2 = 6 (hidden single in N7) -> R6C12 = 10 = [73/91]
26d. Naked pair {13} in R6C29, locked for R6 -> R6C34 = [74], R6C1 = 9, R6C2 = 1, R6C679 = [623]

27. 7 in C1 only in 16(3) cage at R7C1 = {178} (only remaining combination), locked for C1 and N7 -> R23C1 = [43], R2C2 = 8, R45C2 = [34], R4C7 = 1, R4C4 = 5, R5C4 = 1 (cage sum), R2C4 = 2, R7C4 = 3, R9C5 = 1, R78C5 = [24], R7C6 = 7 (cage sum)

and the rest is naked singles.

Rating Comment:
I'll rate for A266 at Easy 1.5
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