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Assassin 343 X
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=3&t=1402
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Author:  HATMAN [ Tue Mar 28, 2017 12:52 pm ]
Post subject:  Assassin 343 X

Assassin 343 X

It is X.
A serendipity one, quite a bit of number swopping to get it to 1.5.
JS does not use any fishes so perhaps a bit easier.


Image


JS Code:
3x3:d:k:5889:5889:5889:3586:4099:4099:4099:6660:6660:5889:3077:3586:3586:4099:6662:2567:6660:6660:2568:3077:3337:3337:3082:6662:2567:2567:4107:2568:2316:2316:6925:3082:6662:6662:6662:4107:5646:2319:2319:6925:6925:3088:3088:4107:4107:5646:5646:3345:6925:6925:6925:4370:3603:3603:5646:7956:3345:3345:2069:3350:4370:3603:3863:7956:7956:7956:4376:2069:3350:2073:2073:3863:7956:7956:4376:4376:4376:3098:3098:3863:3863:

Solution:
719462385
683751249
245893176
854137692
936528417
172946853
528374961
467219538
391685724

Author:  wellbeback [ Wed Apr 05, 2017 5:06 pm ]
Post subject:  Re: Assassin 343 X

Thanks HATMAN. Here is my WT.

Assassin 343 X WT:
1. 17(2) c7 = {89}
Innies n9 = r7c78 + r9c7 = +22(3)
-> r9c7 from (57)
-> 12(2)r9 = {57}

2. Outies n478 = r3c1 + r9c7 = +9(2)
-> 10(2)c1, 12(2)r9 from [28],[57] or [46],[75]

3. Innies n1 = r2c3 + r3c13 = +10(3)
Since r3c1 from (24) -> 6 in n1 in 23(4)

4! Innies c789 = r1459c7 + r4c8 = +29(5)
Max r4c8 = 9 -> Min r1459c7 = +20 -> Max r238c7 = +8(3) (i.e., no 6,7)
-> 6 in c7 in r14c7

Whether 6 in r4c7 or 6 in r1c7 (-> 6 in r2c1) -> 10(2)c1 cannot be [46]
-> 10(2)c1 = [28]
-> 12(2)r9 = [57]

Basically cracked at this point...

5. Remaining innies n9 = r7c78 = +15(2) = [96]
-> r6c7 = 8
Also 8(2)n9 = {35} and 15(4)n9 = {1248}

Remaining Innies n8 = r789c4 + r9c5 = +19(4) and must contain (38)
-> Hidden single 9 in n8 -> 13(2)n8 = [49]
-> 9 in n7 in r9c12

6. Innies - Outies n4 -> r6c3 = r7c1 - 3
-> 9 in n4 in 22(4)
-> HS 9 in n1/c3 -> r1c3 = 9

Innies n3 = r1c7 + r3c9 = +9(2) (i.e., no 9)
-> 9 in n3 in r2c89

Remaining innies n1 = r23c3 = +8(2) must be from [17] or [35]
-> HS 9 in n2/r3 -> 12(2)c5 = [93]
-> Remaining Innies n5 = r45c6 = +15(2) = [78]
-> r5c7 = 4

7. Since r7c8 = 6 -> r6c89 = +8(2)
-> Remaining innies n36 = r14c7 + r4c8 = +18(3)
Max r14c7 = {56} = +11 -> Min r4c8 = 7
Since (78) already on r4 -> r4c8 = 9
-> r14c7 = +9(2) = [36]
-> 8(2)n9 = [53]
-> 10(2)n3 = [217]
etc.

Note - not yet used the diagonals!

Rating:
1.25. Once I found the breakthrough move (Step 4) it was quite straightforward. Was that a fish? I'm never quite sure.

Author:  Andrew [ Fri Apr 07, 2017 7:48 pm ]
Post subject:  Re: Assassin 343 X

Thanks HATMAN for your latest Assassin.

I took the suggestion that JS didn't use any fishes to try to solve it without using any forcing chains. As a result this was the hardest combination analysis that I've used for a long time, but it does come out that way.

wellbeback's nice forcing chain made the puzzle a lot easier. Probably not a 'fish'; I think it would have been called an Alternating Interference Chain (AIC) back when Mike was active on this site.

Here is my walkthrough for Assassin 343X:
Prelims

a) R23C2 = {39/48/57}, no 1,2,6
b) R3C34 = {49/58/67}, no 1,2,3
c) R34C1 = {19/28/37/46}, no 5
d) R34C5 = {39/48/57}, no 1,2,6
e) R4C23 = {18/27/36/45}, no 9
f) R5C23 = {18/27/36/45}, no 9
g) R5C67 = {39/48/57}, no 1,2,6
h) R67C7 = {89}
i) R78C5 = {17/26/35}, no 4,8,9
j) R78C6 = {49/58/67}, no 1,2,3
k) R8C78 = {17/26/35}, no 4,8,9
l) R9C67 = {39/48/57}, no 1,2,6
m) 10(3) cage at R2C7 = {127/136/145/235}, no 8,9
n) 26(4) cage at R1C8 = {2789/3689/4589/4679/5678}, no 1

1. Naked pair {89} in R67C7, locked for C7, clean-up: no 3,4 in R5C6, no 3,4 in R9C6
1a. 45 rule on N9 3 innies R7C78 + R9C7 = 22 = {589/679}, 9 locked for R7 and N9, clean-up: no 4 in R8C6, no 8,9 in R9C6
1b. R9C7 = {57} -> no 5,7 in R7C8
1c. Naked pair {57} in R9C67, locked for R9
1d. R78C6 = [49/58/85] (cannot be {67} which clashes with R78C5 and R9C6, killer ALS block), no 6,7
1e. 4 in N9 only in 15(4) cage at R7C9 = {1248/1347/2346}, no 5
1f. Min R7C8 = 6 -> max R6C89 = 8, no 8,9 in R6C89

2. 45 rule on N478 1 innie R4C1 = 1 outie R9C7 + 1, R9C7 = {57} -> R4C1 = {68}, R3C1 = {24}
2a. 45 rule on N1 3 innies R2C3 + R3C13 = 10 = {127/145/235} (cannot be {136} because R3C1 only contains 2,4), no 6,8,9, clean-up: no 4,5,7 in R3C4
2b. R2C3 + R3C13 = {127/145/235} = [127/145/325] -> R2C3 = {13}, R3C3 = {57}, clean-up: no 9 in R3C4
2c. R23C2 = {39/48} (cannot be {57} which clashes with R3C3), no 5,7
2d. Max R2C3 = 3 -> min R12C4 = 11, no 1 in R12C4

3. 45 rule on C89 3 innies R348C8 = 19 = {379/469/478/568} (cannot be {289} because 8,9 only in R4C8), no 1,2, clean-up: no 6,7 in R8C7
3a. 8,9 only in R4C8 -> R4C8 = {89}
3b. Naked pair {89} in R4C8 + R6C7, locked for N6
3c. 9 in C9 only in R123C9, locked for N3
3d. R7C78 + R9C7 (step 1a) = {89}5/[967]
3e. {469/568} of R348C8 = [496/586] (cannot be [685] which clashes with R7C78 + R9C7), no 6 in R3C8, no 5 in R8C8, clean-up: no 3 in R7C8
3f. 5 in N9 only in R89C7, locked for C7, clean-up: no 7 in R5C6
3g. R5C6 = {589}, R78C6 = [49/58/85] -> combined half cage R578C6 = {58}[49]/9{58}, 9 locked for C6
3h. 10(3) cage at R2C7 = {127/136/145/235} -> R23C7 = {12/14/16/23}, R3C8 = {357}
3i. 45 rule on N3 2 innies R1C7 + R3C9 = 9 = [18/27/36/45/63/72], no 1,4,9 in R3C9

4. 45 rule on R12 3 innies R2C267 = 11 = {128/137/146/236/245}, no 9, clean-up: no 3 in R3C2
4a. 8 of {128} must be in R2C2 -> no 8 in R2C6

5. 45 rule on R1234 3(2+1) innies R34C9 + R4C4 = 9
5a. Min R34C9 = 3 -> max R4C4 = 6
5b. Min R4C49 = 3 -> max R3C9 = 6, clean-up: no 1,2 in R1C7 (step 3i)
5c. Min R3C9 + R4C4 = 3 -> max R4C9 = 6
5d. 1 in N3 only in R23C7, locked for C7, clean-up: no 7 in R8C8
5e. Killer pair 5,6 in R7C78 + R9C7 and R8C78, locked for N9
5f. 6 in N9 only in R78C8, locked for C8
5g. R348C8 (step 3) = {379/568}, 5,7 only in R3C8 -> R3C8 = {57}
5h. Naked pair 5,7 in R3C38, locked for R3, clean-up: no 4 in R1C7 (step 3i), no 5,7 in R4C5
5i. 10(3) cage at R2C7 contains 1 = {127/145} (cannot be {136} because R3C8 only contains 5,7), no 3,6
5j. 45 rule on C89 1 innie R4C8 = 3 outies R238C7 + 1, R4C8 = {89} -> R238C7 = 7,8 = {124/125}, 2 locked for C7

6. 45 rule on C6789 3(2+1) innies R1C67 + R6C6 = 11
6a. Min R1C7 = 3 -> max R16C6 = 8, no 8 in R16C6

7. 45 rule on C12 4 outies R1458C3 = 26 = {2789/3689/4589/4679} (cannot be {5678} which clashes with R3C3), no 1, 9 locked for C3, clean-up: no 8 in R4C2, no 8 in R5C2

8. 16(4) cage at R1C5 = {1267/1348/1357/1456/2347/2356} (cannot be {1249/1258} because R1C7 only contains 3,6,7), no 9

9. 45 rule on R89 4 outies R7C2569 = 14 = {1238/1247/1256/1346/2345}
9a. 8 of {1238} must be in R7C6 -> no 8 in R7C29

10. 45 rule on N5 3 innies R4C56 + R5C6 = 18 = {189/369/378/459/468} (cannot be {279/567} because 2,6,7 only in R4C6), no 2
10a. 1,6,7 of {189/369/378/468} must be in R4C6 -> no 3,8 in R4C6
10b. R4C56 + R5C6 = {189/369/378/468} (cannot be {459} because [459/945] clash with R78C6), no 5, clean-up: no 7 in R5C7
10c. 6 of {468} must be in R4C6 -> no 4 in R4C6
10d. Killer pair 8,9 in R5C6 and R78C6, locked for C6

11. 26(5) cage at R2C6 = {13679/14579/14678/23579/23678/24569/24578/34568} (cannot be {12689/13589/23489} because 8,9 only in R4C8)
11a. R5C67 = [84/93], R78C6 = [49]/{58} -> combined cage R5C67 + R78C6 = [84][49]/[93]{58} -> 26(5) cage cannot contain both of 4,5 because 5 only in R2C6) -> 26(5) cage = {13679/14678/23579/23678} (cannot be {14579/24569/24578/34568} which contain both of 4,5)
11b. 26(5) cage = {13679/14678/23678} (cannot be {23579} = [52739] which clashes with R9C6), no 5
11c. R4C56 + R5C6 (step 10b) = {189/369/378/468}
11d. 26(5) cage = {13679/14678} (cannot be {23678} because {23}{67}8 and [72638] clash with R4C1 and {26}[738] clashes with R4C56 + R5C6 = [378]), no 2
11e. R16C6 + R1C7 = 11 (step 6)
11f. 2 in C6 only in R16C6 -> R16C6 + R1C7 = {23}6/{26}3, clean-up: no 2 in R3C9 (step 3i)
11g. Naked pair {36} in R1C7 + R3C9, locked for N3
11h. 5 in C6 only in R789C6, locked for N8, clean-up: no 3 in R78C5
11i. 26(5) cage = {13679} only remaining combination, as follows:-
6 of {14678} must be in R23C6 (cannot be R4C68 or R4C78 = [68] which clash with R4C1)
{14678} cannot be {16}[748] which clashes with R4C56 + R5C67 = [3784]
{14678} cannot be {46}[178] because R23C6 + R4C56 + R5C6 = {14}[918] clashes with R78C6
{14678} cannot be [76148] which clashes with R4C56 + R5C67 = [9184]
[Cracked, the rest is straightforward.]

[From here onward clean-ups implied for 2-cell cages.]
12. 26(5) cage = {13679} -> R4C8 = 9, R6C7 = 8, R7C7 = 9, placed for D\
12a. R4C8 = R238C7 + 1 (step 5j), R4C8 = 9 -> R238C7 = 8 = {125} -> R23C7 = {12}, R3C8 = 7 (cage sum), R8C7 = 5 -> R8C8 = 3, placed for D\, R3C3 = 5, placed for D\, R3C4 = 8, R9C67 = [57]
12b. R5C7 = 4 (hidden single in C7) -> R5C6 = 8, R78C6 = [49]
12c. R9C5 = 8 (hidden single in C5) -> R7C8 + R8C9 = [68] (hidden pair in N9)
12d. 4 in N9 only in R9C89, locked for R9
12e. R23C2 = [84], R3C1 = 2 -> R4C1 = 8, R3C7 = 1, placed for D/, R2C7 = 2, R2C6 = 1 (hidden single in C6), R2C3 = 3, R34C5 = [93], R4C7 = 6, R4C6 = 7, placed for D/, R4C23 = [54]
12f. Naked pair {26} in R5C5 + R6C6, locked for N5 and D\ -> R4C4 = 1, placed for D\
12g. Naked pair {26} in R5C5 + R8C2, locked for D/
12h. R7C3 = 8 -> R6C3 + R7C4 = 5 = [23]
12i. R5C23 = [36]
12j. R8C2 + R9C1 = [63] (hidden pair on D/)
12k. R1C7 = 3, R34C9 = [62] -> R5C89 = 8 = [17]

and the rest is naked singles without using the diagonals.

Rating Comment:
I'll rate my walkthrough for A343X at least Hard 1.25 for my step 11. Some might think it should be higher, but one can do a lot of combination analysis for that rating.

Author:  Ed [ Tue Dec 05, 2017 5:48 am ]
Post subject:  Re: Assassin 343 X

Lovely puzzle! Quite different to the other two solutions. Nicely hidden key eliminations, but easy-once-you-see-them. Here's how I started. Thanks HATMAN.

Assassin 343 X
Start only:9 steps:
Prelims courtesy of SudokuSolver
Cage 17(2) n69 - cells = {89}
Cage 8(2) n9 - cells do not use 489
Cage 8(2) n8 - cells do not use 489
Cage 12(2) n89 - cells do not use 126
Cage 12(2) n25 - cells do not use 126
Cage 12(2) n56 - cells do not use 126
Cage 12(2) n1 - cells do not use 126
Cage 13(2) n8 - cells do not use 123
Cage 13(2) n12 - cells do not use 123
Cage 9(2) n4 - cells do not use 9
Cage 9(2) n4 - cells do not use 9
Cage 10(2) n14 - cells do not use 5
Cage 10(3) n3 - cells do not use 89
Cage 26(4) n3 - cells do not use 1

No routine clean-up unless stated.
1. 17(2)r6c7 = {89} only: both locked for c7

2. "45" on n9: 3 innies r7c78+r9c7 = 22 = (589/679}(no 1,2,3,4)
2a. must have 5 or 7 which must be in r9c7 -> no 5,7 in r7c8
2b. must have 9: locked for r7 and n9

3. "45" on c89: 3 innies r348c8 = 19 (no 1)
3a. must have 8 or 9 which are only in r4c8 -> r4c8 = {89}
3b. can't have both 8 & 9 since both are only in r4c8-> = {379/469/478/568}(no 2)

4. "45" on n3: 2 innies r1c7+r3c9 = 9
4a. no 1,9 in r3c9

5. 1 in n3 only in c7: locked for c7
5a. no 7 in r8c8

6. "45" on n478: 2 outies r3c1+r9c7 = 9 = [45/27]
6a. r4c1 = {68}

7. "45" on n1: 3 innies r3c1+r23c3 = 10 and must have 2,4 for r3c1 = {127/145/235}(no 6,8,9)
7a. can't have two of 2,4 -> no 2,4 in r23c3
7b. can't have two of 5,7 -> r2c3 = {13}
7c. r3c34 = [58/76] = 5 in r3c3 or 6 in r3c4

8. "45" on n1: 2 innies r23c3 = 1 outie r4c1
8a. = [15][6]/[17/35][8] = 5 in r3c3 or 8 in r4c1 (no eliminations yet)

9. h19(3)r348c8 (step 3b) must have 3,5,6 for r8c8 = {379/469/568}
9a. but [685] blocked by r3c34 (by D\, step 7c)
9b. and [586] blocked by r3c3+r4c1 (step 8a)
9c. h19(3)r348c8 = {379/469}(no 5,8)
9d. r4c8 = 9, r38c8 = [73/46]

Pretty straightforward from here. The other walkthroughs show the key areas to finish it off.

Cheers
Ed

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