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HATMAN
PostPosted: Fri Mar 13, 2015 9:26 am 
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Assassin 312 X Big sevens

I made it unique with seven cagers but it was totally impossible to solve. I broke some of the cages up and got it down to SS 1.45. JS uses three fishes so probably about right.



Image



JS Code
3x3:d:k:7169:2580:2580:5909:5909:5909:7683:7683:7683:9998:7169:2580:5909:7169:7683:4626:4626:7683:9998:8717:7169:7169:7169:7169:9483:4626:7683:9998:8717:8717:8717:8717:9483:9483:3859:7683:9998:8717:6160:6160:8717:9483:9483:3859:3859:9998:9998:9998:6160:9483:9483:9221:9221:3859:9223:3601:3601:3601:4367:4367:8:9221:9221:9223:3601:9223:9223:9478:4367:9478:9478:9221:9223:9223:9223:9478:9478:9478:9478:9221:9221:

Solution:
563849172
741265398
892371564
174658923
328914657
659723841
916482735
235197486
487536219
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wellbeback
PostPosted: Sat Mar 14, 2015 12:27 am 
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Thanks HATMAN. Love the big cages! I'll try it combining some of the smaller cages as well...

Hidden Text:
1. Innies whole puzzle! r7c7 = 7

2. In n1 neither 28(7) nor 10(3) can contain (89)
-> (89) in n1 in r2c1 + r3c12
Innies n12 = r2c1 + r3c12 (which already contain (89) + r2c6 = +29
-> Min r2c6 = 5
Whatever goes in r2c6 goes in n3 in r3c78 and -> in n1 in r1c123
-> r2c6 not (89)
7 in 28(7)r1c1 only in n2 part of 28(7) (Already in D\).
-> r2c6 not 7
Also r2c6 not 6 since that would put other innie = 6 in n1 and also 6 in r3c78
-> r2c6 = 5
-> 5 in n3 in r3c78
-> HS 5 in 28(7) -> r1c1 = 5
-> Innies of n12 in n1 are {789}
-> 10(3)n1 = {136}
-> (r2c2,r3c3) = {24}
-> 23(4)n2 = {2489}

3. 7 in r1n3 in r1c789
->30(7)n3 does not contain (69)
-> (69) also in n3 in r23c78 (along with 5 in r3c78)

4. Outies n7 = r78c4 = +5
Outies n78 = r8c78+r9c7 = +14
Outies n789 = r6c78 = +12
Whatever goes in r6c78 (= +12) must go in n9 in c78
-> They must go in n3 in c9
-> Since (59) already in c78 in n3 -> r6c78 = {48}
-> (Since 4 already in D\) -> 4 in n9 in r89c7
-> r6c78 = [84]
-> r8c8 = 8
-> r89c7 = {24}
-> 36(7)n69 = [84]{13569}

5.(48) in n3 in r123c9
7 in n3 in r1c789
(569) in n3 in r23c78
-> 18(3)n3 = {369}
-> r3c7 = 5
-> r4c9 = 3
-> 15(4)n6 = {1257}
-> r45c7 = {69}

6. -> Remaining cells of 37(7)r3c7 in n5 are {2348}
-> 24(3) = [8{79}]
-> r4c5 = 5
-> (r4c4,r5c5) = {16}
-> Remaining cells in D\ -> r6c6 = 3 and r9c9 = 9

7. HS 5 in c4n8 -> r9c4 = 5
17(3)n8 must contain 8 + one of (24) (The outies from n78)
-> 17(3)n8 = {278}
-> Outies n7 r78c4 = {14}
-> r5c5 = 1, r4c4 = 6, r3c6 = 1
etc.
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Andrew
PostPosted: Sat Mar 14, 2015 5:33 am 
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Thanks HATMAN for an enjoyable Assassin. It definitely felt like a puzzle which is designed for humans to solve, rather than software solvers.

I found some interesting steps; I may have learned some of them from wellbeback's solving style.

Here is my walkthrough for Assassin 312:
Prelims

a) 10(3) cage at R1C2 = {127/136/145/235}, no 8,9
b) 24(3) cage at R5C3 = {789}
c) 14(4) cage at R7C2 = {1238/1247/1256/1346/2345}, no 9
d) 28(7) cage at R1C1 = {1234567}, no 8,9

1. 45 rule on whole grid 1 innie R7C7 = 7, placed for D\
1a. 28(7) cage at R1C1 = {1234567}, 7 locked for N2

2. Naked triple {789} in 24(3) cage at R5C3, CPE no 7,8,9 in R5C56
2a. 8,9 in N1 only in R2C1 + R3C12, CPE no 8,9 in R6C2

3. 45 rule on N7 2 outies R78C4 = 5 = {14/23}

4. 45 rule on R789 3 outies R6C78 = 12 = {39/48}/[57], no 1,2,6, no 5 in R6C8

5. 45 rule on N12 4(3+1) innies R2C16 + R3C12 = 29
5a. Max R2C1 + R3C12 = 24 -> min R2C6 = 5
5b. 8,9 in N1 only in R2C1 + R3C12
5c. R2C6 = {5689} -> R2C1 + R3C12 = 20,21,23,24 = {389/489/689/789}, no 1,2,5

6. Hidden killer quad 1,2,3,4 in R78C4, 17(3) cage at R7C5 and 37(7) cage at R8C5 for N8, R78C4 contain two of 1,2,3,4, 17(3) cage contains one of 1,2,3,4 -> 37(7) cage must contain one of 1,2,3,4 in N8
6a. 37(7) cage contains three of 1,2,3,4, one is in N8 -> two of 1,2,3,4 must be in 37(7) in N9
6b. Hidden killer quad 1,2,3,4 in 36(7) cage at R6C7 and 37(7) cage for N9, 37(7) cage contains two of 1,2,3,4 in N9 -> 36(7) cage must contain two of 1,2,3,4 in N9
6c. 36(7) cage must contain three of 1,2,3,4, two are in N9 -> one must be in R6C78 -> R6C78 (step 4) = {39/48}, no 5,7
6d. 36(7) = {1345689} (only remaining combination), no 2, 1,5,6 locked for N9

7. 2 in N9 only in R8C78 + R9C7, locked for 37(7) cage at R8C5, no 2 in R8C5 + R9C456
7a. 37(7) cage contains 2 = {1246789/2345689}, 6 locked for N8

8. 45 rule on N6789 3 innies R45C7 + R4C9 = 18 = {279/369/468/567} (cannot be {189/378/459} which clash with R6C78, no 1 in R45C7 + R4C9
8a. 30(7) cage at R1C7 must contain 1, locked for N3

9. 45 rule on N3 2 outies R2C6 + R4C9 = 1 innie R3C7 + 3
9a. Min R2C6 + R4C9 = 7 -> min R3C7 = 4
9b. Max R2C6 + R4C9 = 12, min R2C6 = 5 -> max R4C9 = 7

10. 45 rule on N78 3 outies R8C78 + R9C7 = 14 = {239/248}
10a. Whichever of 3,9 or 4,8 is in R8C78 + R9C7 must also be in R6C78 -> grouped X-Wing for 3,9 or 4,8 in R6C78 and R8C78 + R9C7 -> either 3,9 or 4,8 must be in R123C9
10b. 30(7) cage at R1C7 must contain one of 8,9, which must be in R123C9 -> no 8,9 in R1C78 + R2C6
10c. R2C6 = {56} -> R2C1 + R3C12 (step 5c) = 23,24 = {689/789}, no 3,4 in R2C1 + R3C12

11. 28(7) cage at R1C1 = {1234567} -> whichever of 5,6 is in R2C6 must also be in R1C1 + R3C3
11a. R2C1 + R3C12 + R2C6 = {789} + 5 (cannot be {689} + 6 which clashes with R1C1 + R3C3 containing 6, maybe this can be called an unusual killer combo clash) -> R2C6 = 5, R2C1 + R3C12 = {789}, locked for N1
11b. Naked triple {789} in R2C1 + R3C12, CPE no 7 in R6C2
11c. 45 rule on N2 3 outies R1C1 + R2C2 + R3C3 = 11 containing 5 = {245}, locked for N1, 28(7) cage and D\
11d. R2C5 + R3C456 = {1367}, locked for N2
11e. 2 in N9 only in R89C7, locked for C7
11f. R9C4 = 5 (hidden single in C4)

12. 37(7) cage at R3C7 = {1246789/1345789/2345689}
12a. R345C7 cannot contain more than one of 8,9 (step 10a) -> must contain at least one of 8,9 in N5
12b. Killer triple 7,8,9 in 37(7) and R56C4, locked for N5, 7 also locked for C4, N5 and 24(3) cage at R5C3, no 7 in R5C3
12c. 37(7) cage = {2345689} (only remaining combination), no 1
12d. 1 in N5 only in R4C45 + R5C5, locked for 34(7) cage at R3C2, no 1 in R4C23 + R5C2

13. 1 in N4 only in 39(7) cage at R2C1 = {1356789}, no 2,4
13a. 2,4 in N4 only in R4C23 + R5C2, locked for 34(7) cage at R3C2, no 2,4 in R4C5
13b. 4 in N5 only in R456C6 + R6C5, locked for 37(7) cage at R3C7, no 4 in R345C7

14. R2C6 + R4C9 = R3C7 + 3 (step 9), R2C6 = 5 -> R3C7 = R4C9 + 2
14a. R3C7 = {5689} -> R4C9 = {3467}
14b. 30(7) cage at R1C7 must contain 2, locked for N3
14c. R123C9 must contain either 3,9 or 4,8 (step 10a)
14d. 18(3) cage at R2C7 = {369/468/567} (cannot be {378/459} which clash with R123C9), 6 locked for N3, clean-up: no 4 in R4C9
14e. 30(7) cage contains 4, locked for N3
14f. 18(3) cage = {369/567}, no 8

[Only just spotted …]
15. 7 in R1 only in R1C89, locked for N3 and 30(7) cage at R1C7, no 7 in R4C9
15a. 18(3) cage at R2C7 (step 14f) = {369} (only remaining combination), locked for N3
15b. 30(7) cage contains 3 -> R4C9 = 3, R3C7 = 5 (hidden single in N3), placed for D/, clean-up: no 9 in R6C78 (step 4)
15c. R1C1 = 5 (hidden single in N1)

16. Naked pair {48} in R6C78, locked for R6, N6 and 36(7) cage at R6C7
16a. Naked pair {69} in R45C7, locked for C7, N6 and 37(7) cage at R3C7 -> R2C7 = 3, R6C6 = 3, placed for D\
16b. Naked pair {69} in R23C8, locked for C8 -> R8C8 = 8
16c. Naked pair {16} in R4C4 + R5C5, locked for N5, D\ and 34(7) cage at R3C2 -> R4C5 = 5, R6C5 = 2, R45C6 = [84], 8 placed for D/, R9C9 = 9

17. 39(7) cage at R2C1 (step 13) = {1356789} -> R5C1 = 3

18. R9C4 = 5 -> 37(7) cage at R8C5 = {2345689}, no 1,7 -> R9C6 = 6, R89C5 = [93], clean-up: no 2 in R78C4 (step 3)
18a. Naked pair {14} in R78C4, locked for C4 and N8 -> R4C4 = 6, R5C5 = 1, placed for D/, R3C4 = 3

19. 34(7) cage at R3C2 contains 1,5,6 = {1245679} (only remaining combination), no 8

20. 2,4 in C1 only in R789C1, locked for N7 and 36(7) cage at R7C1 -> R8C4 = 1
20a. R7C2 = 1 (hidden single in N7), R7C4 = 4 -> R7C3 + R8C2 = 9 = {36}, locked for N7 and D/
20b. Naked pair {78} in R9C23, locked for N7 -> R8C3 = 5
20c. Naked pair {24} in R89C1, locked for C1 -> R7C1 = 9

21. R2C8 = 9, R6C4 = 7, both placed for D/, R7C5 = 8, R1C5 = 4, R1C9 = 2, placed for D/


and the rest is naked singles, without using the diagonals.

Rating Comment:
It's hard to know what rating to give for my walkthrough. I'll go with Hard 1.25 because I used hidden killer quads to get into the puzzle. I don't feel that my unusual variable grouped X-Wing or my unusual killer combo clash deserve any higher rating.

I noticed that SudokuSolver isn't capable of placing R7C7 immediately, but that probably didn't make any difference to the SSscore.
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Afmob
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PostPosted: Mon Mar 16, 2015 8:37 pm 
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Thanks for this week's Assassin, HATMAN! I used the same start as Andrew but then I took a different path where I didn't need any cloning moves.

A312X Walkthrough:
1. R789 !
a) Innie of grid = R7C7 = 7
b) Outies N7 = 5(2) = {14/23}
c) ! Hidden Killer quad (1234) in Outies N78 @ N9 = 14(3) = {149/239/248} <> 5,6 since 37(7) must have exactly 3 of (1234) and 17(3) must have exactly one of (1234) -> 37(7) must have exactly one of (1234) @ N8 and two @ N9
d) 5,6 locked in 36(7) @ N9 for 36(7)
e) Using R7C7 = 7: Outies R789 = 12(2) = {39/48}
f) 36(7) = {1345689} -> 1 locked for N9
g) Outies N78 @ N9 = 2{39/48} -> 2 locked for 37(7)
h) From step 1g: 37(7) = 24689{17/35} -> 6 locked for N8

2. R123+N6
a) 28(7) = {1234567} -> 7 locked for N2
b) 8,9 locked in Innies N12 @ N1 = 29(3+1) = {389}+9 / {489}+8 / {689}+6 / {789}+5 -> R2C6 = (5689); R23C1+R3C2 <> 1,2,5
c) Using R7C7 = 7: Innies R789+N6 = 18(3) <> 1 since {189} blocked by Killer pair (89) of Outies R789; R4C9 <> 2 since R45C7 <> 7
d) 30(7) = 12345{69/78} -> 1,2 locked for N3
e) Hidden Single: R1C7 = 1 @ C7

3. C789 !
a) Innies+Outies C89: 8 = R2C67+R6C7 - R8C8: R8C8 <> 2,3 since R2C67+R6C7 >= 12
b) 2 locked in 37(7) @ N9 for C7
c) 1,2 locked in 15(4) @ N6 = 12{39/48/57} <> 6
d) 6 locked in Innies R789+N6 = 18(3) = 6{39/48/57}: R4C9 <> 5 since R45C7 <> 7
e) 30(7) = 12345{69/78} -> CPE: R2C78 <> 5
f) ! Using Outies N78: Outies C89 = 22(4+1) = 5+{2348} -> R2C6 = 5; 2,3,4,8 locked for C7 since R2C6 = (5689) and 2 locked in R2689C7 @ C7 <> 1,5,7
g) 5,6,9 locked in R345C7 @ C7 for 37(7)
h) Innies R789+N6 = 18(3) = 6{39/57} since R45C7 = (569) -> R4C9 = (37)

4. R123
a) 23(4) = {2489} locked for N2
b) 1,3,6 locked in 28(7) @ N2 for 28(7)
c) 28(7) = {1234567} -> 2,4,5 locked for N1+D\
d) 10(3) = {136} -> R2C3 = 1; 3,6 locked for R1+N1
e) 30(7) = 12345{69/78} -> 4 locked for N3
f) 18(3) = 3{69/78} since R2C7 = (38) -> 3 locked for N3
g) 30(7) = 12345{69/78} -> R4C9 = 3
h) Innie N3 = R3C7 = 5
i) 37(7) = {2345689} since R45C7 = (69) -> 9 locked for N6; 2,3,4,8 locked for N5

5. N5689
a) Naked pair (48)locked in R6C78 for R6+N6+36(7)
b) 36(7) = {1345689} -> 3,9 locked for N9; 3 also locked for C7
c) Hidden Single: R4C5 = 5 @ N5, R9C4 = 5 @ N8
d) R8C8 = 8
e) 8 locked in 17(3) @ N8 = {278} -> R8C6 = 7; 2,8 locked for R7+N8
f) Outies N7 = 5(2) = {14} locked for C4+N8
g) 24(3) = {789} -> R5C3 = 8; 7,9 locked for C4+N5
h) R4C4 = 6, R6C6 = 3, R5C5 = 1, R9C9 = 9, R6C5 = 2, R5C6 = 4, R4C6 = 8
i) 7,8,9 locked in 36(7) @ N7 = 12789{36/45} -> R9C2 = 8; 2 locked for N7
j) Hidden Single: R7C1 = 9 @ R7, R3C2 = 9 @ N1, R6C3 = 9 @ N4, R1C5 = 4 @ C5
k) R6C4 = 7, R1C9 = 2

6. Rest is singles without considering diagonals.

Rating:
1.25. I used a Hidden Killer quad.
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Afmob
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PostPosted: Wed Mar 18, 2015 4:42 pm 
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I just went through SudokuSolver's solution path and noticed that there is a far easier way to solve this Assassin.

A312X Alternate wt start:
1. R123+N9 !
a) Innie of grid = R7C7 = 7
b) 28(7) = {1234567} -> 7 locked for N2
c) ! R2C6 <> 8,9 since it sees all 8,9 of R1
d) 8,9 locked in 23(4) @ N2 = 89{15/24}
e) Innies N12 = 29(3+1) = 5+{789} / 6+{689} -> R2C6 = (56); R23C1+R3C2 = 89{6/7}
f) 3 locked in 28(7) @ N2 for 28(7)
g) 3 locked in 10(3) @ N1 = 3{16/25}
h) 7 locked in 30(7) @ R1 = {1234578} -> R2C6 = 5

2. Killer is cracked.

Rating:
Hard 1.0?. I used CPE.
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Ed
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PostPosted: Thu Mar 19, 2015 6:39 pm 
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Joined: Wed Apr 16, 2008 1:16 am
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Afmob wrote:
I just went through SudokuSolver's solution path and noticed that there is a far easier way to solve this Assassin.
Thanks for pointing that out! Missed that but used the same start as wellbeback. Spotted that clone the first minute of starting and as a result, the puzzle came out super quick! Interesting how clone's can be easier for the human eye to spot than CPE....

Really fun puzzle, thanks HATMAN!
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