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 Post subject: Assassin 399
PostPosted: Tue Sep 01, 2020 6:29 am 
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Assassin 399

This puzzle gave me a lot of grief with two false WT attempts. SudokuSolver has a very hard time at 1.95 but JSudoku has no trouble which is why I first tried it. After looking at its solver log, seems I missed something.

This cage pattern is more-than-usually based on a Cross+A software ( here) generated killer, hence, with many more small cages than is usual for my assassins. I usually get it to do a batch of 20 puzzles, then pinch some of the cage shapes I like to get started on a messy cage structure with lots of big cages. This one though I only changed a couple of cages and then took out some cages to get the difficulty right. As always, JSudoku found the actual cage totals for me.

triple click code:
3x3::k:4352:4352:4609:4609:6146:4867:4867:4867:4867:4352:4352:4609:6146:6146:4867:4868:4868:4868:3589:3589:4358:6146:6407:6407:6407:6407:4868:0000:4358:4358:4358:6407:4361:4106:4106:4106:0000:0000:0000:0000:4361:4361:3087:3087:2576:4113:2066:3091:3091:3604:3604:3604:5141:2576:4113:2066:3606:1559:1560:1560:5141:5141:2576:4113:3606:3606:1559:5913:5913:4378:4378:3867:4113:5148:5148:5148:5913:4378:4378:3867:3867:
solution:
Code:
+-------+-------+-------+
| 1 9 7 | 6 4 2 | 5 3 8 |
| 4 3 5 | 9 8 1 | 6 2 7 |
| 8 6 2 | 3 5 7 | 9 1 4 |
+-------+-------+-------+
| 7 8 6 | 1 3 4 | 2 5 9 |
| 9 2 3 | 5 7 6 | 8 4 1 |
| 5 1 4 | 8 2 9 | 3 7 6 |
+-------+-------+-------+
| 6 7 8 | 2 1 5 | 4 9 3 |
| 3 5 1 | 4 9 8 | 7 6 2 |
| 2 4 9 | 7 6 3 | 1 8 5 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 399
PostPosted: Tue Sep 01, 2020 7:19 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
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Thanks Ed! Since I was so late last time - I thought I would do this one quickly :). Here a complete WT showing how I did it. One chain longer than I would like though. Probably there's a better way to do that bit.
Assassin 399 WT:
1. Outies r6789 = r5c9 = 1
-> Remaining innies n6 = r6c789 = +16(3)

2. 23(3)n8 = {689}
-> Innies n8 = r9c46 = +10(2) = {37}
IOD n69 -> r6c7 = r9c6
-> r6c7 from (37)

3! Consider case r9c46 = [37]
This puts 20(3)r9c2 = [{89}3]
puts 23(3)n8 = [{89}6]
puts (since neither 8 or 9 can go in r7c9) 20(3)r6c8 = [3{89}]
puts (remaining innie n9) 10(3)r5c9 = [163].
But this leaves no solution for the rest of n9 since 6 has to go in r8c78.
-> r9c46 = [73]

(I gave step 3 a "!" since it makes the rest of the puzzle much easier, but it is a longer chain than I would like).

4. Continuing
-> (IOD n69) r6c7 = 3
-> r6c89 = +13(2)
-> r6c12 = +6(2)
-> (Since 1 in r6 only in r6c12) -> r6c12 = {15}
But 8(2)r6c2 cannot be [53] since 3 already on r7
-> r6c12 = [51] and r7c2 = 7
Also -> 12(2)r6 = {48}
-> 14(3)r6 = [{29}3]
-> r6c89 = {67}
r6c89 cannot be [67] because that puts r7c789 = [{59}2] which contradicts 6(2)r7c5
-> r6c89 = [76]
-> r7c9 = 3
Also 12(2)n6 = {48}
-> 16(3)n6 = {259}

5. Outies c56789 = r23c4 = +12(2)
Given 12(2)r6 = {48} and r9c4 = 7 -> r23c4 = {39}
Outies r12 = r3c49 = +7(2)
-> r3c49 = [34] and r2c4 = 9

6! IOD n1 -> r1c4 = r3c3 + 4
-> r1c4 is min 5
-> r1c4 from {568}
-> IOD n23 -> r1c4 = r4c5 + 3
-> r4c5 from (235)
But (25) already on r4 in n6
-> r4c5 = 3
-> r1c4 = 6
-> r3c3 = 2

7. r6c34 = {48} -> r12c3 from {39} or {57}
-> 14(2)n1 = {68}

8. 9 already in n5 -> 17(3)n5 cannot contain a 1
-> (HS 1 in r4/n5) -> r4c4 = 1
-> 17(4)r3c3 = [2{68}1]
-> 12(2)r6 = [48]
-> r4c6 = 4
-> r4c1 = 7
Also -> 17(3)n5 = [4{67}]
-> r5c4 = 5
-> 6(2)r7c4 = {24} and 6(2)r7c5 = {15}
-> r7c78 = {49}
-> 6(2)r7c4 = [24]

9. 1 in n1 only in r12c1
-> (HS 1 in n7) -> r8c3 = 1
-> 14(3)n7 = [851]
-> 20(3)r9 = [497]
-> r12c3 = {57}
Also r4c23 = [86] and 14(2)n1 = [86]
-> (NS in c3) r5c3 = 3
Also r789c1 = [632]
-> r5c12 = [92]
-> r12c1 = {14} and r12c2 = [93]

10. No solution for 15(3)n9 with 1 in r9c8
-> r9c7 = 1
-> r8c78 = [76]
-> 15(3)n9 = [2{58}]
-> 23(3)n8 = [{89}6]
-> r5c56 = [76]
-> r12c5 = {48}
-> r8c56 = [98]
-> r6c56 = [29]

11. 7 in n3 in r12c9
-> (HS 7 in r3) r3c6 = 7
HS 3 in c8 -> r1c8 = 3
2 in n2 only in r12c6
-> No solution for 19(5)r1c6 if it included a 7
-> r2c9 = 7
-> r2c78 = [62]
-> (HS 1 in c8) r3c8 = 1
-> 27(5)r3c5 = [57913]
-> 6(2)r7c5 = [15]
-> r2c6 = 1
-> r1c79 = {58}
-> r12c5 = [48]
-> r12c1 = [14]

12. r7c78 = [49]
-> 16(3)n6 = [259]
-> r9c89 = [85]
-> 12(2)n6 = [84]
-> r1c79 = [58]


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 Post subject: Re: Assassin 399
PostPosted: Wed Sep 02, 2020 3:25 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks Ed!

Thanks Ed for pointing out the error in my original post, explained below!

My first key step was fairly similar but the second one, in my re-work, is completely different although in the same area.

Here is my walkthrough for Assassin 399:
Prelims

a) R3C12 = {59/68}
b) R5C78 = {39/48/57}, no 1,2,6
c) R67C2 = {17/26/35}, no 4,8,9
d) R6C34 = {39/48/57}, no 1,2,6
e) R78C4 = {15/24}
f) R7C56 = {15/24}
g) 10(3) cage at R5C9 = {127/136/145/235}, no 8,9
h) 20(3) cage at R6C8 = {389/479/569/578}, no 1,2
i) 23(3) cage at R8C5 = {689}
j) 20(3) cage at R9C2 = {389/479/569/578}, no 1,2

1a. 45 rule on R6789 1 outie R5C9 = 1
1b. 19(5) cage at R1C6 = {12349/12358/12367/12457/13456}, CPE no 1 in R1C45

2a. R9C46 = {37} (hidden pair in N8), locked for R9
2b. 20(3) cage at R9C2 = {389/479/578} (cannot be {569} which doesn’t contain 3 or 7), no 6
2c. 45 rule on N69 1 innie R6C7 = 1 outie R9C6 -> R6C7 = {37}
2d. 45 rule on N689 2(1+1) innies R6C7 + R9C4 = 10 = {37}
2e. Naked pair {37} in R6C7 + R9C4, CPE no 3,7 in R6C4, clean-up: no 5,9 in R6C3
2f. 45 rule on N6 3 remaining innies R6C456 = 16 = {349/367/457} (cannot be {259/268} because R6C7 only contains 3,7, cannot be {358} which clashes with R5C78), no 2,8
2g. R5C9 = 1 -> R67C9 = 9 = {36/45}/[72], no 7 in R7C9
2h. 2 in N6 only in 16(3) cage at R4C7 = {259/268}, 2 locked for N6
2i. R6C34 = [39/75]{48}, R6C789 = {349/367/457} -> combined cage R6C34789 = [39]{457}/{48}{367}/[75]{349}, 3,4,7 locked for R6, clean-up: no 1,5 in R7C2
[First time through, while manually deleting 3,4,7 in R6, I carelessly also deleted them from R6C9.]
2j. 14(3) cage at R6C5 = {167/239/257/356} (cannot be {158} because R6C7 only contains 3,7), no 8
2k. Overlapping combined cage 14(3) cage + R6C789 = {16}7{45}/{29}3{67}/{25}7{36} (cannot be {56}3[94] which clashes with R6C34)
-> 14(3) cage = {167/239/257}, R6C789 = {367/457}, no 9, 7 locked for R6 and N6, clean-up: no 5 in R5C78, no 5 in R6C4
2l. 20(3) cage at R6C8 = {389/479/569/578}
2m. 3 of {389} must be in R6C8 -> no 3 in R7C78


3a. 45 rule on C56789 2 outies R23C4 = 12 = {39/48/57}, no 1,2,6
3b. 45 rule on C56789 2 innies R12C5 = 12 = {39/48/57}, no 1,2,6
3c. 45 rule on R12 2 outies R3C49 = 7 = [34/43/52] -> R2C4 = {789}
3d. 45 rule on R1234 2 innies R4C16 = 11 = {38/47} (cannot be {56} which clashes with 16(3) cage at R4C7)
3e. 45 rule on R123 1 outie R4C5 = 1 innie R3C3 + 1, no 1,9 in R3C3, no 1 in R4C5
3f. 45 rule on N1 1 outie R1C4 = 1 innie R3C3 + 4 -> R1C4 = {6789}, R3C3 = {2345}, R4C5 = {3456}

4. 45 rule on N7 3(2+1) outies R6C12 + R9C4 = 13 = [157/517/823/913], no 2,6 in R6C1, no 6 in R6C2, clean-up: no 2 in R7C2

5a. Hidden killer pair 1,2 in R45C4 and R78C4 for C4, R78C4 contains one of 1,2 -> R45C4 must contain one of 1,2
5b. Killer pair 1,2 in R45C4 and 14(3) cage at R6C5 in R6C56, locked for N5
5c. 17(3) cage at R4C6 = {359/368/458/467}
[My original breakthrough, which had followed from my careless deletions in R6C9, no longer works at this stage. I’ve therefore reworked from here.]
5d. R23C4 = [75/84/93] (step 3c), 14(3) cage at R6C5 = {167/239/257}, R6C789 = {367/457} (both step 2k)
5e. Consider placement for 7 in N5
7 in R45C4 => R9C4 = 3, R23C4 = [84], R6C4 = 9 => R6C3 = 3, R6C7 = 7, R6C89 = {45}, 5 locked for R6 => 14(3) cage at R6C5 = {16}7, 6 locked for N5 -> 17(3) cage = {458}
or 7 in 17(3) cage = {467}
-> 17(3) cage = {458/467}, no 3,9, 4 locked for N5, clean-up: no 8 in R6C3
5f. Also from step 5e, 6 in 17(3) cage or R6C56 = {16}, 6 locked for N5

6a. R1C4 = 6 (hidden single in C4) -> R3C3 = 2 (step 3f) -> R4C5 = 3 (step 3e), clean-up: no 9 in R12C5 (step 3b), no 5 in R3C4 (step 3c), no 8 in R4C16 (step 3d), no 7 in R2C4 (step 3a)
6b. R1C4 = 6 -> R12C3 = 12 = {39/48/57}, no 1
6c. Naked pair {34} in R3C49, 4 locked for R3
6d. Naked pair {89} in R26C4, locked for C4
6e. Naked pair {47} in R4C16, locked for R4

7a. R78C4 = {24} (cannot be {15} which clashes with R4C4), locked for C4 and N8 -> R3C4 = 3, R2C4 = 9 (step 3a), R6C4 = 8 -> R6C3 = 4, R9C46 = [73], R45C4 = [15], R4C16 = [74], R3C9 = 4
7b. Naked pair {67} in R5C56, 6 locked for R5 and N5
7c. R6C5 = 2 (hidden single in C5), R6C6 = 9 -> R6C7 = 3 (cage sum), clean-up: no 9 in R5C78, no 6 in R7C2
7d. Naked pair {48} in R5C78, 8 locked for R5 and N6
7e. R6C89 = {67} (hidden pair in R6), 6 locked for N6
7f. Naked pair {15} in R7C56, locked for R7
7g. R4C23 = {68} (hidden pair in N4)
7h. 20(3) cage at R6C8 = {479} (only remaining combination) -> R6C8 = 7, R7C67 = {49}, locked for R7 and N9 -> R78C4 = [24]
7i. 10(3) cage at R5C9 = [163], R7C2 = 7 -> R6C2 = 1
7j. R12C3 (step 6b) = {57} (cannot be [93] which clashes with R5C3), 5 locked for C3 and N1, clean-up: no 9 in R3C12
7k. Naked pair {68} in R3C12, locked for R3 and N1
7l. Naked pair {68} in R7C13, locked for N7 -> R9C34 = [97], R9C2 = 4 (cage sum), R12C2 = [93]
7m. R5C23 = [23], R8C23 = [51] -> R7C3 = 8 (cage sum)
7n. 4 in N2 only in R12C5 (step 3a) = {48}, 8 locked for C5 and N2 -> 23(3) cage at R8C5 = [986], R5C56 = [76]

8a. 6 in N9 only in R8C78, R9C6 = 3 -> 17(4) cage at R8C7 = [7631]
8b. R2C6 = 7 (hidden single in R2)

9a. 2 in R1 and C6 only in 19(5) cage at R1C6 -> R1C6 = 2
9b. R1C6 = 2, R1C8 = 3 (hidden single in R1) -> 19(5) cage at R1C6 = {12358} (only possible combination) -> R2C6 = 1, R1C79 = {58}, locked for R1 and N3


and the rest is naked singles.

Rating Comment:
I'll rate my WT for A399 at Easy 1.5. I used one forcing chain.


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 Post subject: Re: Assassin 399
PostPosted: Sun Sep 13, 2020 3:00 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Ooops, this one ended up harder than I intended. The JSudoku log is so innocuous I thought I must have missed something.
Jsudoku log:
Techniques used:
1 Last Digit
66 Naked Single
10 Hidden Single
1 Single Innies & Outies
7 Unique Pair
2 Naked Pair
1 Hidden Pair
3 Complex Hidden Single
1 Unique Triplet
2 Intersection
8 Odd Pairs
2 Odd Triplets
4 Double Innies & Outies
1 Double Split Cage
1 Mandatory Inclusion
1 Odd Quads
7 Triple Innies & Outies
4 Double Outies minus Innies
3 Complex Naked Pair
6 Complex Hidden Pair
3 Conflicting Pair
10 Quadruple Innies & Outies
2 Triple Outies minus Innies
1 Pointing Triplet
1 Grouped X-Wing
4 Conflicting Partial Pair
6 Multiple Innies & Outies
Here's how I did it. Very different to the other two WTs. I didn't get past the longish chains on those. Sorry guys. [Many thanks to Andrew for checking my WT. So many typos!]
a399 WT:
Preliminaries courtesy of SudokuSolver
Cage 6(2) n8 - cells only uses 1245
Cage 6(2) n8 - cells only uses 1245
Cage 14(2) n1 - cells only uses 5689
Cage 8(2) n47 - cells do not use 489
Cage 12(2) n6 - cells do not use 126
Cage 12(2) n45 - cells do not use 126
Cage 23(3) n8 - cells ={689}
Cage 10(3) n69 - cells do not use 89
Cage 20(3) n69 - cells do not use 12
Cage 20(3) n78 - cells do not use 12


No clean-up done unless stated
1. Hidden pair 3,7 in n8 -> r9c46 = {37}: both locked for r9

2. "45" on n689: 2 innies r6c7 + r9c4 = 10 = {37} only
2a. r6c4 sees both these -> no 3,7 in r6c4

3. "45" on r6789: 1 outie r5c9 = 1

4. "45" on n6: 3 remaining innies r6c789 = 16 and must have 3 or 7 for r6c7
4a. but {358} blocked by 12(2)n6 needing one of them
4b. = {349/367/457}(no 2,8)

5. 2 in n6 only in 16(3)r4c7 = {259/268}(no 3,4,7)
5a. 2 locked for r4

6. "45" in c56789: 2 innies r12c5 = 12 (no 1,2,6)
6a. -> r23c4 = 12 (cage sum) = {39/48/57}(no 1,2,6)

7. "45" on r12: 2 outies r3c49 = 7 = [52]/{34}
7a. r3c4 = (345), r3c9 = (234)
7b. r2c4 = (789)
7c. note: has {34} in r3c49 or 7 in r2c4

8. "45" on n1: 1 outie r1c4 - 4 = 1 innie r3c3 (iodn1=-4)
8a. but [73] blocked by r2c4 + r3c49 (step 7c)
8b. = [51/62/84/95], r1c4 = (5689), r3c3 = (1245)

9. 6 in c4 only in r145c4
9a. "45" on n23: 1 innie r1c4 - 3 = 1 outie r4c5
9b. but [96] blocks all 6 in c4 (Locking-out cages)
9c. = [63/85]
9d -> r3c3 = (24)(iodn1=-4)

10. killer pair 2,4 in r3 in r3c3 and h7(2)r3c49: both locked for r3

11. "45" on r123: 4 outies r4c2345 = 18 and must have 3 or 5 for r4c5
11a. = {1359/1368/1458/3456}(no 7)

12. "45" on r1234: 2 innies r4c16 = 11 and must have 7 for r4 = {47} only: 4 locked for r4

13. 14(3)r6c5 must have 3 or 7 for r6c7 = {167/239/257/347/356}(no 8)
13a. note: if it has 1 must also have 6

14. "45" on n7: 3 outies r6c12 + r9c4 = 13
14a. r9c4 = (37) -> r6c12 = 6 or 10
14b. -> a 6 in r6c12 must have 4
14c. 1 in r6 only in 14(3) (with 6, step 13a) or in r6c12 -> 6 in r6c12 must also have 1 there
14d. but this is impossible -> no 6 in r6c12 (locking-out cages)

15. 17(3)n5 must have 4 or 7 for r4c6 = {278/458/467}(no 3,9)

The grief step
16. h16(3)r6c789 cannot have both 4 & 6 (can't be {466})
16a. -> either 12(2)n6 = {48} for n6 or 14(3)r6c5 has 6 for r6
16b. -> 17(3)n5 as [7]{46} blocked
16c. -> 17(3) = [7]{28}/[4]{58/67}(no 4 in r5c56)

17. from 4b. h16(3)r6c789 = {349/367/457}
17a. if it has 7, must have 3 or 4
17b. -> {34}[7] blocked from 14(3)r6c5
17c. and {47}[3] blocked from 14(3) by r4c6 = (47)
17d. -> no 4 in r6c56

18. 2 in n2 only in r12c6: locked for c6 and 19(4)r1c6
18a. no 4 in r7c5

19. 4 in c5 only in 12(2)r12c6 = {48}: both locked for n2, 8 for c6
19a. r1c4 = 6
19b. -> r4c5 = 3 (iodn12=+3)
19c. and r3c3 = 2 (iodn1=-4)

20. r3c49 = 7 = [34], r2c4 = 9 (h12(2))
20a. r9c46 = [73]
20b. -> r6c7 = 3 (last innie n689)
20c. -> r6c89 = 13 (hcage sum) = {67} only: both locked for r6 and n6
20d. and r6c56 = 11 (cage sum) = [29]

21. 12(2)n6 = {48}: both locked for r5, 8 for n6
21a. r5c4 = 5
21b. 17(3)n5 = [4]{67}: 6 & 7 locked for r5
21c. r6c34 = [48], r4c14 = [71]
21d. r4c789 = {259}: 5 and 9 locked for r4
[Andrew noticed an alternative 21d, r4c23 = {68}(hidden pair r4)]

22. 6(2)r7c5 = {15}: both locked for r7

23. 20(3)r6c8 = [7]{49}(only permutation)
23a. 4 & 9 locked for r7 and n9

24. r6c9 = 6
24a. r7c9 = 3 (cage sum)

25. r12c3 = 12 (cage sum)
25a. but {39} blocked by r5c3 = (39)
25b. = {57} only: both locked for n1, c3

26. 14(2)n1 = {68}: both locked for n1 and r3

27. naked pair {68} in r47c3: both locked for c3
27a. r9c23 = [49](cage sum)

28. 8(2)r67c2 = [17]

29. r58c3 = [31]
29a. r7c3 + r8c2 = 13 (cage sum) = [85]

30. r12c2 = [93]

31. r1c6 = 2 (HS r1)
31a. r1c8 = 3 (HS r1)

32. 19(4)n3 must have 2 and 6 for n3 -> r2c789 = 15 (cage sum) = {267}, 7 locked for r2 and n3

33. r9c15 = [26]

34. 15(3)n9 = {258} only -> r8c9 = 2, 5 & 8 locked for n9

35. r4c9 = 9 (hsingle c9)

singles now
I have an idea for something to try. Will post on the 15th.

Cheers
Ed


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