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 Post subject: Assassin 391
PostPosted: Sat Feb 01, 2020 8:09 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
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Killer x. 1-9 cannot repeat on either diagonal.
NOTE: disjoint 17(3)r1c6 + r2c46

Assassin 391
SudokuSolver messes this up but JSudoku goes well. Took me a good while to find the key step but pretty obvious and easy once you see it. Felt a lot easier than the last monster! Certainly looks easy in an optimised WT. Mine is cracked at step 12. Hope its still enough of a challenge for you guys.
code: triple click:
3x3:d:k:6144:3329:3329:3329:3329:4354:2307:3076:4357:6144:6144:6144:4354:5126:4354:2307:3076:4357:3079:3079:10504:5126:5126:5126:5641:2314:4357:3079:10504:10504:10504:10504:5641:5641:2314:2314:7179:4883:4883:10504:10504:5641:5641:9485:9485:7179:4883:4883:5903:5903:5903:9485:9485:9232:7179:7179:8977:8977:5903:9485:9485:9232:9232:7179:8977:8977:2066:2062:3852:9232:9232:9232:7179:8977:8977:2066:2062:3852:3852:9232:9232:
solution:
Code:
+-------+-------+-------+
| 3 4 1 | 2 6 5 | 7 8 9 |
| 7 8 6 | 3 1 9 | 2 4 5 |
| 9 2 5 | 4 7 8 | 6 1 3 |
+-------+-------+-------+
| 1 7 8 | 9 4 3 | 5 2 6 |
| 4 5 3 | 6 2 7 | 1 9 8 |
| 6 9 2 | 5 8 1 | 3 7 4 |
+-------+-------+-------+
| 2 3 7 | 8 9 6 | 4 5 1 |
| 5 1 9 | 7 3 4 | 8 6 2 |
| 8 6 4 | 1 5 2 | 9 3 7 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 391
PostPosted: Sun Feb 09, 2020 8:26 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Another fine puzzle - thanks Ed. Certainly easier than the previous one as you say, but still provides opportunities for some cool moves! Love the big cages :)
Assassin 391 WT:
1. 36(8)r6c9 has no 9
-> 9 in n9 in r79c7
-> 9 in n6 in 37(6)
-> r9c7 = 9
-> r6c9 = r7c7

2. IOD n8 -> r7c456 = {689} with r7c6 from (68)
-> The two 8(2)s in n8 are {17} and {35}
-> r89c6 = {24}

3! Innies n2 = r1c45 = +8(2)
This cannot be the same as either of the two 8(2)s in n8
-> r1c45 = {26}
-> 13(4)r1 = [{14}{26}]

4. Remaining outies c789 = r457c6 = +16(3)
Since r7c6 from (68) and 2 already in c6 -> 6 not in r45c6
IOD c6789 -> r2c4 + 6 = r3c6 + r7c6
-> (Since r2c4 and r3c6 see each other) r7c6 cannot be 6
-> HS 6 in c6 -> r7c6 = 6
-> r45c6 = +10(2) = {19} or {37}

5! 1 not in 37(6)
-> 1 in n6 in r4c789 or r5c7
-> r4c6 cannot be 1

41(7)r3c3 = {2456789}
-> Trying r4c6 = 9 puts r3c3 = 9 which leaves no solution for 12(3)r3c1
-> r45c6 = {37}

Also trying r4c6 = 7 puts r3c3 = 7 which also leaves no solution for 12(3)r3c1
-> r45c6 = [37]

6. 3 in n6 only in 37(6) or r6c9
If the latter -> r7c7 = 3
-> 37(6) = {346789}
-> r4c789 + r5c7 = {1256}

7. 1 in n5 only in r6c456
-> 23(4)r6c4 = {1589} with r7c5 from (89)
-> 41(8) = {57(9|8)} in n14 and {246(8|9} in n5

8. Remaining outies r1234 = r5c457 = +9(3)
This can only be [{26}1]
-> r4c789 = {256}
-> r3c3 = 5
-> r4c1 = 1
-> r34c7 = +11(2) can only be [65]
-> 9(3)r3c8 = [1{26}]

9. Also 9(2)n3 = [72]
-> 12(3)n1 = [{29}1]
Also 5 in c6 only in r12c6
-> 1 in n2 only in r2c5
-> 8(2)r8c5 = {35} and 8(2)r8c4 = {17}
-> 20(4)n2 = [1478]

10. Also HS 3 in n2 -> r2c4 = 3 and r12c6 = {59}
-> 24(4)n1 = [3{678}]
-> r3c9 = 3
-> 12(2)n3 = [84]
Also r6c4 = 5 and r6c6 = 1
-> 17(3)n3 = [953]
Also (HS 9 in D\) -> r4c4 = 9
-> r67c5 = [89]
-> 41(7) = [5{78}9462]
-> 19(4)n4 = [5{239}]
-> r56c1 = [46]
etc.


Last edited by wellbeback on Sat Mar 14, 2020 8:03 pm, edited 1 time in total.

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 Post subject: Re: Assassin 391
PostPosted: Mon Feb 17, 2020 6:49 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Really pleased you like it! I generally try and get at least a couple of big cages in....just for you!

I used the identical pathway to wellbeback (but written long before!) so perhaps its a very narrow solution. Miss one key step and it could get very, very hard. The SudokuSolver score of 2.00 might feel more realistic in that case.

Many thanks to Andrew for finding some typos. Makes things clearer.

a391 WT:
Assassin 391

Preliminaries courtesy of SudokuSolver
Cage 8(2) n8 - cells do not use 489
Cage 8(2) n8 - cells do not use 489
Cage 12(2) n3 - cells do not use 126
Cage 9(2) n3 - cells do not use 9
Cage 9(3) n36 - cells do not use 789
Cage 13(4) n12 - cells do not use 89
Cage 37(6) n689 - cells do not use 1
Cage 41(7) n145 - cells ={2456789}
Cage 36(8) n69 - cells ={12345678}

1. r7c7 sees all 9s in n6 -> no 9 (Common Peer Elimination CPE)
1a. r9c7= 9 (hsingle n9)

2. "45" on n8: 3 innies r7c456 = 23 = {689} only: all locked for r7, 6 & 8 for n8
2a. no 2 in two 8(2) cages n8

3. naked quad 1,3,5,7 in r89c45: all locked for n8

4. naked pair 2,4 in r89c6: locked for c6

5. 9 in n6 only in 37(6) -> no 9 in r7c6

key step. Took quite a while to see it even though it is the type of step I like to look for.
6. "45" on n2: 2 innies r1c45 = 8
6a. since it is a h8(2), and since both 8(2) cages in n8 partially see it, they must all have different combos
6b. -> h8(2)r1c45 = {26} only: both locked for n2 and r1
6c. -> r1c23 = 5 (cage sum) = {14} only: both locked for r1 and n1

really glad the disjoint cage gets a look-in
7. "45" on c6789: 1 outie r2c4 + 6 = 2 innies r36c6.
7a. since one innie and 1 outie are in the same nonet and can't be equal -> no 6 in r6c6 (IOU)

8. "45" on c789: 3 outies r457c6 = 16 and must have 6 or 8 for r7c6: but can't have both since no 2 -> no 6,8 in r45c6
8a. -> r7c6 = 6 (hsingle c6)
8b. -> r45c6 = 10 = {19/37}(no 5)
8c. -> r345c7 = 12

9. "45" on n9: 1 outie r6c9 = 1 innie r7c7 (no 1,6,8 in r6c9)

10. r4c6 sees all 1 in n6 -> no 1 in r4c6
10a. no 9 in r5c6 (h10(2))

11. "45" on n12: 3 innies r3c123 = 16 = {259/268/358/367}
11a. but {25}[9] and {36}[7] blocked by 5 and 3 in r4c1 respectively
11b. -> no 7,9 in r3c3

Cracked

12. 41(7) must have 7 & 9. r4c6 sees all of those -> no 7,9 in r4c6
12a. r4c6 = 3 (placed for d/), r5c6 = 7 (h10(2))
12b. 7 in 41(7) only in n4: locked for n4

13. "45" on r56789: 3 remaining innies r5c457 = 9 = {26}[1] only
13a. 2 & 6 locked for 41(7), r5 and n5
13b. 4 & 9 in 41(7) only in r4: locked for r4

14. "45" on n12: 1 innie r3c3 - 4 = 1 outie r4c1 = [51] only, 5 placed for d\

15. r34c7 = 11 (cage sum) = [65] only, 6 placed for d/, r5c45 = [62], 2 placed for both D, r1c45 = [26]

16. 9(2)n3 = [72]

17. 1 innie n3: r3c8 = 1

18. r3c12 = 11 (cage sum) = {29/38}(no 7)

19. killer pair 8,9 in r3c126: both locked for r3
[edit: Andrew noticed that Steps 18 and 19 can be simpler once you see that 2 in r3 only in r3c12 so simplified to {29}]

20. "45" on r12: 1 innie r2c5 + 2 = 1 outie r3c9
20a. = [13] only

21. 12(2)n3 = [84], 4 placed for d/

22. r3c45 = {47}, 7 locked for n2
22a. -> r3c6 = 8 (cage sum)

23. naked pairs {59} in r12c69: locked for r12
23a. r1c1 = 3 (placed for d\), r2c4 = 3, r7c7 = 4, placed for d\, r6c9 = 4 (iodn9=0)

24. "45" on c1: 2 outies r37c2 + 2 = 1 innie r2c1
24a. -> r3c2 = 2, r3c1 = 9
24b. -> r2c1 - 4 = r7c2 = [73] only

25. 8(2)r8c5 = {35}: 5 locked for c5 and n8

26. naked pair {89} in r67c5: both locked for c5 and 23(4) cage
26a. -> r6c46 = [51]: 1,5 placed for their D

27. r6c8 = 7 (hsingle n6)

Lots of naked now
Cheers
Ed


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 Post subject: Re: Assassin 391
PostPosted: Tue Feb 25, 2020 2:45 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks Ed for this latest Assassin! It could be considered to be a "Human Solvable".

It took me even longer to find the key step; therefore my solving path was rather different because I did more work before I found it.

Here is my walkthrough for Assassin 391:
Prelims

a) R12C7 = {18/27/36/45}, no 9
b) R12C8 = {39/48/57}, no 1,2,6
c) R89C4 = {17/26/35}, no 4,8,9
d) R89C5 = {17/26/35}, no 4,8,9
e) 9(3) cage at R3C8 = {126/135/234}, no 7,8,9
f) 13(4) cage at R1C2 = {1237/1246/1345}, no 8,9
g) 37(6) cage at R5C8 = {256789/346789}, no 1
h) 41(7) cage at R3C3 = {2456789}, no 1,3
i) 36(8) cage at R6C9 = {12345678}, no 9

1a. 13(4) cage at R1C2 = {1237/1246/1345}, 1 locked for R1, clean-up: no 8 in R2C7
1b. 45 rule on N2 2 outies R1C23 = 5 = {14/23}
1c. R1C23 = 5 -> R1C45 = 8 = {17/26/35}, no 4
1d. 45 rule on N3 2 innies R3C78 = 7 = {16/25/34}, no 7,8,9
1e. 45 rule on N12 1 innie R3C3 = 1 outie R4C1 + 4, R3C3 = {56789}, R4C1 = {12345}
1f. 2,4 in 41(7) cage at R3C3 only in R4C2345 + R5C45, CPE no 2,4 in R4C6

2a. 9 in N9 only in R79C7, locked for C7
2b. 9 in N6 only in R5C89 + R6C8, locked for 37(6) cage at R5C8
2c. R9C7 = 9 (hidden single in C7) -> R89C6 = 6 = {15/24}
2d. 45 rule on N8 3 remaining innies R7C456 = 23 = {689}, locked for R7, 6 locked for N8, clean-up: no 2 in R78C45
2e. 9 in R7 only in R7C45, CPE no 9 in R6C4
2f. R78C6 = {24} (hidden pair in N8), locked for C6
2g. 45 rule on N9 1 outie R6C9 = 1 remaining innie R7C7 -> R6C9 = {23457}
2h. 37(6) cage at R5C8 = {256789/346789}, CPE no 7 in R45C7
2i. 1 in N6 only in R4C789 + R5C7, CPE no 1 in R4C6
2j. 7,9 in R4 only in R4C23456, CPE no 7,9 in R5C45

3. 45 rule on C789 3 remaining outies R457C6 = 16 = {169/178/358/367}
3a. R7C6 = {68} -> no 6,8 in R45C6
3b. R45C6 = {35/37}/[71/91], no 9 in R5C6
3c. Consider placement for 8 in N6
8 in R45C7 => R7C6 = 8 (because 37(6) cage at R5C8 contains 8) => R45C6 = 8 = {35}/[71] => R345C7 = 14 = {248} (cannot be {158} which clashes with R45C6)
or 8 in R5C89 + R6C78 => R7C6 = 6, R45C6 = 10 = {37}/[91], R345C7 = 12 = {156/246/345}
-> R345C7 = {156/246/248/345}
3d. 45 rule on R1234 4 outies R5C4567 = 16 = {1258/1267/1348/1456/2356} (cannot be {1357} because R5C45 only contain one odd number, cannot be {2347} = {24}[73] which clashes with R45C6)

4. 45 rule on C6789 2 innies R36C6 = 1 outie R2C4 + 6, IOU no 6 in R6C6

[Only just spotted what seems to be a key step; it proves to be the key step. With hindsight it could have been used immediately after step 2d.]
5. R89C4 and R89C5 are both {17/35}, preventing R1C45 being {17/35} -> R1C45 = {26}, locked for R1 and N2, clean-up: no 3 in R1C23 (step 1b), no 3,7 in R2C7
5a. Naked pair {14} in R1C23, locked for N1, 4 locked for R1, clean-up: no 5 in R2C7, no 8 in R2C8
5b. R7C6 = 6 (hidden single in C6) -> R45C6 (step 3) = 10 = {37}/[91], no 5
5c. 37(6) cage at R5C8 = {256789/346789}, 8 locked for N6
5d. Naked pair {89} in R7C45, CPE no 8 in R6C4
5e. Hidden killer pair 1,3 in R45C6 and 23(4) cage at R6C4 for N5, R45C6 contains one of 1,3 -> 23(4) cage must contain one of 1,3 = {1589/3479/3569/3578} (cannot be {1679} which clashes with R45C6, other combinations don’t contain 1 or 3), no 2
5f. 2 in N5 only in R45C45, locked for 41(7) cage in R3C3
5g. 12(3) cage at R3C1 = {129/138/237/246/345} (cannot be {147} because 1,4 only in R4C1, cannot be {156} which clashes with R3C3 + R4C1 = [51], step 1e)
5h. 4 of {345} must be in R4C1 -> no 5 in R4C1, clean-up: no 9 in R3C3 (step 1e)
5i. 41(7) cage at R3C3 = {2456789}, 9 locked for R4, clean-up: no 1 in R5C6 (step 5b)
5j. Naked pair {37} in R45C6, locked for C6, 7 locked for N5, 3 locked for 22(5) cage at R3C7, clean-up: no 4 in R3C8 (step 1d)
5k. R345C7 (step 3c) = {156/246}, 6 locked for C6, clean-up: no 3 in R1C7
5l. R12C7 = [72/81] (cannot be [54] which clashes with R345C7), no 4,5
5m. Killer pair 1,2 in R2C7 and R345C7, locked for C7, clean-up: no 2 in R6C9 (step 2g)
5n. 23(4) cage at R6C4 = {1589}, 1,5 locked for R6, 5 locked for N5, clean-up: no 5 in R7C7 (step 2g)
5o. Killer pair 1,5 in R6C4 and R89C4, locked for C4
5p. 41(7) cage = {2456789}, CPE no 5,7 in R56C3
5q. 4,6 in N5 only in R45C45, locked for 41(7) cage, clean-up: no 2 in R4C1 (step 1e)
5r. 17(3) disjoint cage at R1C6 = {179/359/458}
5s. 3,4,7 of {179/359/458} only in R2C4 -> R2C4 = {347}
5t. 45 rule on N1 3 remaining innies R3C123 = 16 = {259/268/358} (cannot be {367} because 12(3) cage at R3C1 cannot contain both of 3,6), no 7, clean-up: no 3 in R4C1 (step 1e)
5u. 41(7) cage = {2456789}, 7 locked for R4 and N4 -> R4C6 = 3, placed for D/, R5C6 = 7, clean-up: no 9 in R1C8

6a. 1,6 in N6 only in R4C789 + R5C7
6b. 45 rule on N69 4 remaining innies R4C789 + R5C7 = 14 = {1256}, 2,5 locked for N6
6c. R5C6 = 7 -> R5C4567 = {1267} (step 3d) -> R5C7 = 1, R5C45 = {26}, locked for R5 and N5, R2C7 = 2 -> R1C7 = 7, clean-up: no 5 in R12C8, no 5 in R3C7, no 5,6 in R3C8 (both step 1d), no 7 in R6C9 (step 2g)
6d. R45C6 = [37], R5C7 = 1 -> R34C7 = 11 = [65], 6 placed for D/, R3C8 = 1 (step 1d), R5C5 = 2, placed for both diagonals
6e. Naked quad {4789} in R4C2345, 4 locked for R4, 8 locked for 41(7) cage at R3C3 -> R4C1 = 1, R3C3 = 5, placed for D\
6f. 2 in R3 only in R3C12, R4C1 = 1 -> R3C12 = 11 = {29}, 9 locked for R3 and N1 -> R3C6 = 8
6g. 7 in R3 only in R3C45, locked for N2
6h. 17(3) disjoint cage at R1C6 (step 5r) = {359} (only remaining combination) -> R2C4 = 3, R12C6 = {59}, locked for N2, 9 locked for C6
6i. R6C6 = 1, placed for D\, R6C4 = 5, placed for D/
6j. Naked pair {17} in R89C4, locked for N8, 7 locked for C4 -> R3C45 = [47]
6k. R2C9 = 5 (hidden single in N3), R12C6 = [59], R2C8 = 4, placed for D/, R1C8 = 8, R1C9 = 9, placed for D/, R3C9 = 3, R56C9 = [84], R67C7 = [34], R56C8 = [97], R8C7 = 8
6l. R1C1 = 3, placed for D\, R8C8 = 6, R9C9 = 7, both placed for D\, R2C2 = 8, placed for D\, R89C4 = [71], R9C1 = 8, R8C2 = 1, R7C3 = 7, R1C2 = 4, R8C9 = 2, R89C6 = [42]
6m. R9C23 = [64] (hidden pair in R9)

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

Rating Comment:
I'll rate my walkthrough for A391 at Easy 1.5. Even if I'd found the key step sooner I'd still have given the same rating since the key step is a short implied forcing chain.


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