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 Post subject: Assassin 378
PostPosted: Sat Jun 15, 2019 6:50 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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X-killer so 1-9 cannot repeat on either diagonal; Disjoint cage 42(7)r1c1 with r1c5 part of that cage

Assassin 378
Felt easier than the last few Assassins to me. Used two advanced steps but some 'easier' ones took some searching to find. SudokuSolver has an awful time (2.85) but JSudoku found it easy in comparison which is why I tried it.
code:
3x3:d:k:10775:10775:10775:2840:10775:4866:2307:4356:4356:10775:10775:4869:3078:2840:4866:2307:4356:2568:10775:5632:4869:3078:2840:4866:4362:2568:2568:4619:5632:4869:4869:2828:4866:4362:2829:2829:4619:5632:3847:3855:2828:2576:2576:3345:3345:4619:5632:3847:3855:3855:3855:2057:2057:10002:3604:5632:3847:3847:10002:10002:10002:10002:10002:3604:3604:2561:2561:3606:3606:5651:5651:10002:3598:3598:3598:3349:3349:3606:5651:5651:10002:
solution:
Code:
+-------+-------+-------+
| 4 6 9 | 1 7 5 | 2 8 3 |
| 8 3 1 | 9 4 2 | 7 6 5 |
| 5 2 7 | 3 6 8 | 9 4 1 |
+-------+-------+-------+
| 7 1 5 | 6 3 4 | 8 2 9 |
| 2 4 3 | 5 8 9 | 1 7 6 |
| 9 8 6 | 7 2 1 | 3 5 4 |
+-------+-------+-------+
| 6 7 2 | 4 9 3 | 5 1 8 |
| 3 5 8 | 2 1 6 | 4 9 7 |
| 1 9 4 | 8 5 7 | 6 3 2 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 378
PostPosted: Wed Jun 19, 2019 10:16 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thanks Ed. Nice :)
I found a move quite quickly (my step 3) which opened it up for me.
Assassin 378 WT:
1. Innies n3 -> r3c7 = 9
-> r4c7 = 8
-> 8 in n3 in 17(3)
-> 1 in n3 in 10(3)

2. 42(7) has no (12)
-> (12) in n1 in r2c3,r3c2,r3c3
-> 1 in r1 in n2 in r1c46
-> 1 in c5 in r678c5

3! IOD c6789 -> r78c5 = r6c6 + 9
-> Either 1 is in c5 in r6c5 or ...
... r78c5 = {19} and r6c6 = 1
-> 1 in n5 in r6c56

Easy from here...

4. -> HS 1 in n6 -> 10(2)r5c6 = [91]
-> Innies n36 -> r6c9 = 4
-> HS 9 in n6 -> 11(2)n6 = {29}
-> 13(2)n6 = {67}
-> 8(2)n6 = {35}

6. Remaining innies n5 = r4c46 = +10(2) = {37} or {46}
IOD n2 -> r1c5 = r4c6 + 3
-> Max r4c6 = 6
-> r4c46 not [37]

7. Trying r4c46 = [73] puts r1c5 = 6 leaves no solution for 11(2)n5
-> r4c46 = {46}
-> 11(2)n5 = [38]
-> 15(4)n5 = [5{127}]

8. r6c9 = 4 -> (IOD n89) r78c4 = +6(2) = {24}
-> 12(2)n2 = [93]
Also r6c456 = [7{12}]
Also r4c46 = [64]
-> r1c5 = 7

9. Only possibility for 13(2)n8 = [85]
-> 14(3)n8 = {167}
-> r7c56 = [93]

10. NS 1 in c4 -> 11(3)n2 = [1{46}]
-> 19(4)n2 = [{258}4]
-> r6c56 = [21]
-> 14(3)n8 = [1{67}]

11. Unshaded areas in 1 = {127}
-> 19(4)r2c3 = [1756] and r3c2 = 2

12. NP in r4 r4c12 = {17}
NT in r5 r5c123 = {234}
NT in r6 r6c123 = {689}
-> 18(3)n4 cannot contain a 1
-> r4c12 = [71]

13. Remaining outies c12 = r19c3 = +13(2) = {49}
-> 15(4)r5c2 can only be [3624]
-> 10(2)r8c3 = [82]
Also 18(3)n4 = [729]
-> 22(5)r3c2 = [21487]
etc.


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 Post subject: Re: Assassin 378
PostPosted: Wed Jun 26, 2019 5:28 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Lovely work wellbeback!. I didn't find it as easy even though I worked in similar spots.
A378 WT:
Preliminaries courtesy of SudokuSolver
Cage 17(2) n36 - cells ={89}
Cage 8(2) n6 - cells do not use 489
Cage 12(2) n2 - cells do not use 126
Cage 13(2) n6 - cells do not use 123
Cage 13(2) n8 - cells do not use 123
Cage 9(2) n3 - cells do not use 9
Cage 10(2) n78 - cells do not use 5
Cage 10(2) n56 - cells do not use 5
Cage 11(2) n6 - cells do not use 1
Cage 11(2) n5 - cells do not use 1
Cage 10(3) n3 - cells do not use 89
Cage 11(3) n2 - cells do not use 9
Cage 42(7) n12 - cells ={3456789}
Cage 39(8) n689 - cells ={12345789}

1. "45" on n3: 1 innie r3c7 = 9, Placed for D/, r4c7 = 8
1a. no 9 in 17(3)n3 -> no 1 possible
1b. no 1 in 9(2)n3

2. 13(2)n6 = {49/67}(no 5) = 4 or 7

3. 11(2)n6: {47} blocked by 13(2) = 4 or 7
3a. = {29/56}(no 3,4,7) = 2 or 6

4. 8(2)n6: {26} blocked by 11(2) = 2 or 6
4a. = {17/35}(no 2,6)

5. "45" on n6: 2 remaining innies r5c7 + r6c9 = 5 = {14/23}(no 5,6,7,9)
5a. r5c6 = (6789)

6. "45" on c789: 3 outies r5c6 + r7c56 = 21
6a. max. r57c6 = 17 -> min. r7c5 = 4
6b. max. r5c6 + r7c5 = 18 -> min. r7c6 = 3

7. 1 in r1 only in r1c46: 1 locked for n2

8. "45" on n5: 3 innies r4c46 + r5c6 = 19 (no 1)

9. 1 in r4 only in n4: 1 locked for n4

10. "45" on n3689: 3 innies r5c7 + r78c4 = 7
10a. -> max. r78c4 = 6 (no 6,7,8,9)

This is a grouped turbot fish I think.
11. if 1 in n1 in r3c2 -> 1 in n3 in r2c9 -> 1 which must be in 39(8)r6c9 only in r7c78 -> no 1 in r7c3
OR: 1 in n1 in r23c3 -> no 1 in r7c3
11a. -> no 1 in r7c3

Took a long time to find this (and hence, a long time to realise the importance of step 11).
12. 15(4)r5c3: all combinations have 1 which must go in r7c4 or the only other combination is {2346}
12a. -> no 5 in r7c4

13. "45" on n3689: 3 innies r5c7 + r78c4 = 7
13a. 1 in c5 in r6c5 -> 1 in n6 in r5c7 -> r78c4 = 6 (step 13.)= {24} only, ie no 1
13b. or 1 in c5 in r8c5 -> no 1 in r78c4
13c. -> no 1 in r78c4
(at this point the 15(4)r5c3 = {2346} only but for some reason I haven't used that now in this optimised WT. Perhaps I missed it)

14. "45" on n3689: 3 innies r5c7 + r78c4 = 7
14a. =[1]{24}/[2]{23}
14b. r5c7 = (12), r5c6 =(89), r6c9 = (34)(h5(2)n6)
14c. must have 2 in r78c4: 2 locked for c4 and n8

15. 3 in n6 only in r6: locked for r6
15a. deleted
15b. = {17}[3]/{35}[4] = 4/7, 1/5

16. 15(4)n5: must have 1 for n5
16a. but [3]{147/156} blocked by r6c789 (step 15b)
16b. = {1239/1248/1257}(no 6)
16c. must have 2: locked for n5 and r6
16d. no 9 in r4c5

17. h19(3)n5: {568} as {56}[8] only, blocked by 11(2)n6 = {29} and r5c7 = 2; ie, two 2's in n6
17a. = {379/469/478} (no 5) = 4 or 7

18. 11(2)n5: {47} blocked by h19(3)n5
18a. = [38]/{56} = 3 or 6

Loved finding this!
19. "45" on n2: 1 innie r1c5 - 3 = 1 outie r4c6
19b. but [63] blocked by 11(2)n5
19c. = [74/96]

20. h19(3)n5 must have 4/6 for r4c6 = {469/478}(no 3)
20a. 9 in {469} must be in r5c6 -> no 9 in r4c4
20b. must have 4: 4 locked for r4 and n5

21. 15(4)n5 = {1239/1257}(no 8)
21a. but {1239} as [3]{129} -> r78c4 = {24} = 6 -> from innies n3689 = 7, -> r5c7 = 1 -> r5c67 = [91]: but this leaves no place for 9 in {1239}
21b. = {1257} only: 5 & 7 locked for n5

cracked
22. r45c5 = [38]: 8 placed for both diagonals, r5c67 = [91] -> r6c9 = 4 (h5(2)) and r78c4 = 6 (from innies n3689=7) = {24} only: 4 locked for n8 and c4
22a. r4c46 = [64] (both placed for their diagonal)

23. 13(2)n6 = {67}: both locked for r5, r5c4 = 5

24. 12(2)n2 = [93], r1c5 = 7 (placed for 42(6))

25. 19(4)n2: {168}[4] blocked by r1c4 = (18)
25a. = {258}[4] only: 2,5,8 all locked for n2 and c6
25b. r16c4 = [17], 7 placed for d/; r6c56 = [21], 1 placed for d\, r9c45 = [85], r7c56 = [93] (outies c789=21)

26. 11(2)n6 = {29}, both locked for r4

27. 15(4)r5c3 = {2346} only = [3624] only permutation, 2 placed for d/, r8c34 = [82]

28. "45" on n7: 1 innie r7c2 = 7, r7c7 = 5 (placed for d\)

29. "45" on n1: 1 innie r3c2 + 3 = 1 remaining outie r4c3, but [47] blocked by r3c3 = (47) -> = [25] only permutation

easier now
Cheers
Ed


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 Post subject: Re: Assassin 378
PostPosted: Mon Jul 01, 2019 4:23 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
Loved the way wellbeback cracked this puzzle so early. It took me a lot longer because, although I'd spotted his 45 I'd overlooked one of the steps leading up to it and therefore never used that particularly 45.

I was rather surprised that wellbeback, Ed and I all solved it different ways, since we all used the same key areas.

Here is my walkthrough for Assassin 378:
Prelims

a) R12C7 = {18/27/36/45}, no 9
b) R23C4 = {39/48/57}, no 1,2,6
c) R34C7 = {89}
d) R45C5 = {29/38/47/56}, no 1
e) R4C89 = {29/38/47/56}, no 1
f) R5C67 = {19/28/37/46}, no 5
g) R5C89 = {49/58/67}, no 1,2,3
h) R6C78 = {17/26/35}, no 4,8,9
i) R8C34 = {19/28/37/46}, no 5
j) R9C45 = {49/58/67}, no 1,2,3
k) 11(3) cage at R1C4 = {128/137/146/236/245}, no 9
l) 10(3) cage at R2C9 = {127/136/145/235}, no 8,9
m) 42(7) disjoint cage at R1C1 = {3456789}, no 1,2
n) 39(8) cage at R6C9 = {12345789}, no 6

1a. 45 rule on N3 1 innie R3C7 = 9, placed for D/, R4C7 = 8, clean-up: no 3 in R2C4, no 1 in R23C7, no 2 in R4C5, no 3 in R4C89, no 3 in R5C5, no 1,2 in R5C6, no 5 in R5C89
1b. 10(3) cage at R2C9 = {127/136/145} (cannot be {235} which clashes with R12C7), 1 locked for N3
1c. R4C89 = {29/56} (cannot be {47} which clashes with R5C89), no 4,7
1d. Killer pair 6,9 in R4C89 and R5C89, locked for N6, clean-up: no 4 in R5C6, no 2 in R6C78
1e. R5C67 = {37}/[82/91] (cannot be [64] which clashes with R5C89), no 4,6
1f. 45 rule on N6 2 remaining innies R5C7 + R6C9 = 5 = [14]/{23}, clean-up: no 3 in R5C6
1g. 45 rule on N2 1 innie R1C5 = 1 outie R4C6 + 3, no 3 in R1C5, no 7 in R4C6
1h. 42(7) disjoint cage at R1C1 = {3456789}, 3 locked for N1

2a. 45 rule on N89 2 innies R78C4 = 1 outie R6C9 + 2
2b. Max R6C9 = 4 -> max R78C4 = 6, no 6,7,8,9 in R78C4, clean-up: no 1,2,3,4 in R8C3
2c. 45 rule on N9 3 outies R6C9 + R7C56 (all in same cage) = 16 = 2{59}/3{49/58}/4{39/57}, no 1,2 in R7C56
2d. 39(8) cage at R6C9 = {12345789}, 1 locked for N9

3. 45 rule on N2356 3 innies R1C5 + R4C4 + R6C9 = 17
[This may be a step which SudokuSolver isn’t programmed for.]
3a. Max R6C9 = 4 -> min R1C5 + R4C4 = 13, no 1,2,3 in R4C4

4. 45 rule on C12 3(2+1) outies R1C35 + R9C3 = 20
4a. Max R1C35 = 17 -> min R9C3 = 3

5. 45 rule on N5 3 innies R4C46 + R5C6 = 19 = {289/379/469/478/568}, no 1 in R4C6, clean-up: no 4 in R1C5 (step 1g)
5a. R4C46 + R5C6 = {289/379/469/478} (cannot be {568} = {56}8 because {56}+R5C67 = [82] clashes with R4C89), no 5, clean-up: no 8 in R1C5 (step 1g)
5b. Consider combinations for R4C46 + R5C6
R4C46 + R5C6 = {289/379/469}, 9 locked for N5
or R4C46 + R5C6 = {478} => R4C46 = {47}, R5C67 = [82], no 2 in R5C5
-> R45C5 = [38]/{47/56}, no 2,9
5c. Consider combinations for R45C5
R45C5 = [38]/{47} => R4C46 + R5C6 = {289/469} (cannot be {379/478} which clash with R45C5)
or R45C5 = {56} => R4C89 = {29} (cannot be {56} which clashes with R4C5), 2 locked for N6 => no 8 in R5C6 => R4C46 + R5C6 = {379/469}
-> R4C46 + R5C6 = {289/379/469}, 9 locked for N5
5d. R45C5 (step 5b) = [38]/{47/56}, R4C46 + R5C6 (step 5c) = {289/379/469}
Consider combinations for R1C5 + R4C6 (step 1g) = [52/63/74/96]
R1C5 + R4C6 = [52/63/96] => R45C5 = {38/47}
or R1C5 + R4C6 = [74], R4C46 + R5C6 = {469}, 6 locked for N5
-> R45C5 = [38]/{47}, no 5,6
5e. R4C46 + R5C6 (step 5c) = {289/469} (cannot be {379} which clashes with R45C5), no 3,7, clean-up: no 6 in R1C5 (step 1g), no 3 in R5C7, no 2 in R6C9 (step 1f)
5f. Killer pair 2,6 in R4C46 and R4C89, locked for R4
5g. 3 in N6 only in R6C789, locked for R6
5h. 42(7) disjoint cage at R1C1 = {3456789}, 4,6,8 locked for N1
5i. 39(8) cage at R6C9 = {12345789}, 2 locked for N9
5j. R4C46 + R5C6 = {289/469}, R45C5 = [38]/{47} -> combined cage R4C46 + R5C6 + R45C5 = {289}{47}/{469}[38], 4,8 locked for N5, 8 also locked for R5
5k. 15(4) cage at R5C4 = {1257} (cannot be {1356} = 3{156} which clashes with R6C78), locked for N5
[Cracked. A lot easier now.]
5l. R4C46 + R5C6 = {469} (only remaining combination) -> R4C46 = {46}, locked for R4 and N5, R5C6 = 9 -> R5C7 = 1, R6C9 = 4 (step 1f), R45C5 = [38], 8 placed for both diagonals, clean-up: no 5 in R1C5 (step 1g), no 5 in R4C89, no 7 in R6C78, no 5 in R9C4
5m. Naked pair {29} in R4C89, 9 locked for R4
5n. Naked pair {67} in R5C89, locked for R5
5o. Naked pair {35} in R6C78, 5 locked for R6
5p. Naked triple {127} in R6C456, locked for R6, 2 locked for N5 -> R5C4 = 5, clean-up: no 7 in R23C4
5q. R78C4 = R6C9 + 2 (step 2a), R9C6 = 4 -> R78C4 = 6 = {24}, locked for C4 and N8 -> R4C4 = 6, placed for D\, R4C6 = 4, placed for D/, clean-up: no 8 in R23C4, no 9 in R9C4, no 7,9 in R9C5
5r. R23C4 = [93], R1C5 = 7
5s. 42(7) disjoint cage at R1C1 = {3456789}, 5 locked for N1
5t. R6C9 + R7C56 (step 2c) = 16, R6C9 = 4 -> R7C56 = 12 = [93] (cannot be [57] which clashes with R9C56)
Further clean-up: no 2 in R2C7, no 7,9 in R8C3
5u. 4 in N2 only in R23C5 -> 11(3) cage at R1C4 = {146} (cannot be {245} because 2,5 only in R23C5) -> R1C4 = 1, R23C5 = {46}, 6 locked for C5 and N2, R6C4 = 7, placed for D/, R9C45 = [85], R68C5 = [21], R6C6 = 1, placed for D\
5v. 1 in R9 only in 14(3) cage at R9C1 = {149) (only possible combination, cannot be {167} which clashes with R9C6) -> R9C1 = 1, R9C23 = {49}, locked for R9 and N7
5w. R8C78 = [49] (hidden pair in N9), 9 placed for D\, R8C4 = 2 -> R8C3 = 8
5x. R9C78 = {36} (hidden pair in N9), 6 locked for R9 -> R89C6 = [67], R9C9 = 2, placed for D\, R3C3 = 7, placed for D\, R7C7 = 5, placed for D\, R6C78 = [35], R9C78 = [63], R12C7 = [27]
5y. R2C8 = 6 -> R1C89 = 11 = [83], 3,6 placed for D/

6a. R7C4 = 4 -> R567C3 = 11 = [362]
6b. R8C2 = 5 -> R78C1 = 9 = [63]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A378 at 1.5. I used three fairly short forcing chains.
I really don't understand the SS score; far too high.


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