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 Post subject: Assassin 359
PostPosted: Thu Sep 20, 2018 7:57 am 
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Posts: 774
Location: Sydney, Australia
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Assassin 359
I can still make a symmetrical puzzle! SudokuSolver gives it 1.35. A fun one! Quite a long solution.
code:
3x3::k:3584:5633:5378:3093:3093:3093:4630:4630:4630:3584:5633:5378:5378:5378:3845:3845:3845:6406:3584:5633:5633:10247:3348:6406:6406:6406:6406:3584:3081:3081:10247:3348:3348:4874:4874:4874:3083:3083:5132:10247:10247:10247:4874:1805:1805:5132:5132:5132:2318:2318:10247:3855:3855:4368:6417:6417:6417:6417:2318:10247:5650:5650:4368:6417:4627:4627:4627:5636:5636:5636:5650:4368:2563:2563:2563:4360:4360:4360:5636:5650:4368:
solution:
Code:
+-------+-------+-------+
| 2 4 9 | 5 6 1 | 8 3 7 |
| 5 7 1 | 3 8 9 | 2 4 6 |
| 6 3 8 | 2 7 4 | 9 5 1 |
+-------+-------+-------+
| 1 5 7 | 8 4 2 | 3 6 9 |
| 4 8 6 | 9 3 7 | 1 2 5 |
| 9 2 3 | 6 1 5 | 7 8 4 |
+-------+-------+-------+
| 3 9 4 | 1 2 6 | 5 7 8 |
| 8 6 5 | 7 9 3 | 4 1 2 |
| 7 1 2 | 4 5 8 | 6 9 3 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 359
PostPosted: Sun Sep 23, 2018 5:45 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 171
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Hey - I'm caught up! :bouncy:
Is was either this or do my UK taxes. Easy choice :)

I found this quite straightforward but found it difficult to express concisely and clearly some of the steps. I'm sure there's a term for what Step 2 Line 2 does. Is this IOD?

Assassin 359 WT:
1. Innies n6 -> r6c9 = 4
-> Remaining Innies n9 -> r89c7 = +10(2)
-> r8c56 = +12(2)
Outies n7 -> r78c4 = +8(2)
-> Remaining Innies n8 -> r7c56 = +8(2)

2. Innies r9 -> r9c789 = +18(3)
Since r89c7 = +10(2) -> 8 not in r9c89
Since 8 in n8 in r8c56 or r9c456 -> 8 not in r9c7
-> 8 in r9 in r9c456
-> 4 also in r9c456
-> 17(3)n8 = {458}
-> H+12(2)r8c56 = {39}
-> r89c7 from [82] or [46]
Since 9 cannot go in 10(3)n7 -> r9c789 = [2{79}] or [6{39}]
-> 10(3)n7 = {136} or {127}

3. Max r8c23 = +15(2) -> Min r8c4 = 3
Since (345) already in n8 -> Outies n7 = r78c4 = +8(2) = [17] or [26]
-> Since (39) and one of (48) already in r8 -> 18(3)r8c2 = [{56}7] or [{57}6]
But the latter puts 10(3)n7 = {136} and 2 in r7c4 which leaves no place for 2 in n7.
-> r78c4 = [17]
-> 18(3)n7 = [{56}7]
-> 10(3)n7 = {127}
-> r9c789 = [6{39}]
-> r8c7 = 4
Also r7c56 = {26}

4. HP r8c89 = {12}
Since r9c89 = {39} -> Only solution for 17(4)r6c9 = [4823]
-> 22(4)n9 = [{57}19]
-> 25(5)n7 = [{349}18]

5. Given:
a) r7c5 from (26)
b) r7c4 = 1
c) r6c9 = 4
-> Only solutions for 9(3)r6c4 are [612] or [216]. I.e., r6c5 = 1

5. Innies n4 -> r4c1 = 1
-> (26) in n4 only in 20(4)n4
-> One of (26) in r5c3 and the other in r6c123
-> (26) locked in r6c1234
-> 15(2)n6 = {78}
-> 20(4)n4 = {2369} with one of (26) in r5c3

6. Since 1 in r6c5 and in r7c4 -> 1 not in 40(5)
-> 4 not in 40(5)
-> 4 in n5 in r4c56
-> 12(2)r4c2 = {57}
-> 12(2)r5c1 = [48]
Also (15) in n6 in r5c789
-> r5c3789 = [6][125] or [2][561]
-> r5c456 = {379}
-> r6c6 = 5

7. Outies n3 = r23c6 = +13(2)
-> HS 1 in c6 -> r1c6 = 1
Remaining Outies n1 -> r2c45 = +11(2)
-> Remaining Innies n2 = r3c45 = +9(2)
*Note* that both r1c45 and r2c45 = H+11(2)

Since 4 in r4c56 -> r3c45 cannot be {45}
-> 5 in n2 in r12c45
-> 6 in n2 in r12c45
-> r23c6 = +13(2) = {49}
-> r3c45 = [27]
-> 9(3)r6c4 = [612]
-> 13(3)r3c5 = [742]
-> r4c4 = 8
-> r7c6 = 6
Also 20(4)n4 = [6{239}]
-> 7(2)n6 = [25]
-> 19(4)n6 = [{369}1]

8. 5 in c1 only in r123c1
-> 14(4)r1c1 = [{256}1]
Remaining Innies n1 = r12c3 = +10(2)
-> HS 8 in n1 -> r3c3 = 8
Also r8c23 = [65]
-> 12(2)r4c2 = [57]
-> r12c3 = [91]
Innies r1 -> r1c123 = +15(3) which can only be [249]
-> r2c1 from (56)
-> 12(3)n2 = [561]
-> r2c45 = [38]
-> r23c2 = [73]
-> Remaining Innies r2 = r2c19 = +11(2) can only be [56]
-> r3c1 = 6

9. Also 18(3)n3 = [{38}7]
-> NS 9 in c9 -> r4c9 = 9
-> r3c9 = 1
Also r4c78 = [36]
-> r1c78 = [83]
-> r6c78 = [78]
-> r7c78 = [57]
-> HS r3c8 = 5
-> NS r2c8 = 4
-> 15(3)r2 = [924]
etc.


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 Post subject: Re: Assassin 359
PostPosted: Tue Sep 25, 2018 9:35 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1602
Location: Lethbridge, Alberta, Canada
Ed wrote:
I can still make a symmetrical puzzle!
That made it easier for me to colour the cages on my Excel worksheet, with diagonally opposite cages getting the same colours. :)

My solving path was very routine. At first I wondered where to go next after step 2, but then I went back to step 1 and added steps 1t ->, after which things were straightforward.

Here is my walkthrough for Assassin 359:
Prelims

a) R4C23 = {39/48/57}, no 1,2,6
b) R5C12 = {39/48/57}, no 1,2,6
c) R5C89 = {16/25/34}, no 7,8,9
d) R6C78 = {69/78}
e) 9(3) cage at R6C4 = {126/135/234}, no 7,8,9
f) 10(3) cage a R9C1 = {127/136/145/235}, no 8,9
g) 14(4) cage at R1C1 = {1238/1247/1256/1346/2345}, no 9

1a. 45 rule on N4 1 innie R4C1 = 1
1b. 45 rule on N1 2 remaining innies R12C3 = 10 = {19/28/37/46}, no 5
1c. R12C3 = 10 -> R2C45 = 11 = {29/38/47/56}, no 1
1d. 45 rule on N6 1 innie R6C9 = 4, clean-up: no 3 in R5C89
1e. 45 rule on N9 2 remaining innies R89C7 = 10 = {19/28/37/46}, no 5
1f. R89C7 = 10 -> R8C56 = 12 = {39/48/57}, no 1,2,6
1g. 1 in R6 only in R6C456, locked for N5
1h. 45 rule on N3 2 outies R23C6 = 13 = {49/58/67}, no 1,2,3
1i. 45 rule on N7 2 outies R78C4 = 8 = {17/26/35}, no 4,8,9
1j. 45 rule on R123 2 remaining innies R3C45 = 9 = {18/27/36/45}, no 9
1k. 45 rule on R789 2 remaining innies R7C56 = 8 = [17]/{26/35}, no 4 in R7C5, no 1,4,8,9 in R7C6
1l. 40(7) cage at R3C4 must contain 9, locked for N5
1m. 4,8,9 in N8 only in R8C56 + R9C456, CPE no 4,8,9 in R9C7, clean-up: no 1,2,6 in R8C7
1n. R78C4 = {17/26/35}, R7C56 = [17]/{26/35} -> combined hidden cages R78C4 + R7C56 = {17}{26}/{17}{35}/{26}{35}
1o. R8C56 = {39/48} (cannot be {57} which clashes with R78C4 + R7C56), no 5,7
1p. 17(3) cage at R9C4 = {179/269/359/458} (cannot be {278/467} which clash with R78C4 + R7C56, cannot be {368} which clashes with R8C56)
1q. 18(3) cage at R8C2 = {279/369/468/567} (cannot be {189/378/459} which clash with R8C56}, no 1, clean-up: no 7 in R7C4
1r. 1 in R8 only in R8C89, locked for N9, clean-up: no 9 in R8C7
1s. 22(4) cage at R8C5 = {2389/3469/3478}, CPE no 3 in R8C89
1t. 45 rule on R9 3 innies R9C789 = 18 = {279/369/567} (cannot be {378} which clashes with R89C7 = {37} CCC, cannot be {459} because no 4,5,9 in R9C7, cannot be {468} which clashes with R89C7 = [46] CCC), no 4,8
1u. 17(3) cage = {458} (only remaining combination, cannot be {179/269/359} which clash with R9C789), locked for R9 and N8
1v. Naked pair {39} in R8C56, locked for R8, N8 and 22(4) cage at R8C5, clean-up: no 7 in R89C7
1w. 9 in R9 only in R9C89, locked for N9
1x. 1 in N8 only in R7C45, locked for R7, CPE no 1 in R6C4
1y. 9(3) cage at R6C4 = {126/135}, 1 locked for C5, clean-up: no 8 in R3C4
1z. 7 in N8 only in R7C6 + R8C7, CPE no 7 in R345C4, clean-up: no 2 in R3C5
1aa. R9C789 = {279/369}
1ab. R9C7 = {26} -> no 2,6 in R9C89
1ac. 18(3) cage at R8C2 = {567} (only remaining combination, cannot be {468} which clashes with R8C7), locked for R8, 5 also locked for N7, clean-up: no 6 in R7C4
1ad. Killer pair 6,7 in R8C23 and R9C123, locked for N7
1ae. 2 in N8 only in R7C456, locked for R7

2. 3 in N6 only in 19(4) cage at R4C7 = {1369/2359} (cannot be {1378} = {378}1 which clashes with R4C23, cannot be {2368} which clashes with R6C78), no 7,8
2a. 1 of {1369} must be in R5C7 -> no 6 in R5C7
2b. R6C78 = {78} (hidden pair in N6), locked for R6
2c. 2,6 in N4 only in 20(4) cage at R5C3 = {2369/2567} (cannot be {2468} because 4,8 only in R5C3), no 4,8
2d. 7 of {2567} must be in R5C3 -> no 5 in R5C3
2e. 40(7) cage at R3C4 must contain 8, locked for N5
2f. 40(7) cage must contain 7, CPE no 7 in R4C6
2g. 13(3) cage at R3C5 = {247/256/346} (cannot be {238} = 8{23} which clashes with 19(4) cage), no 8, clean-up: no 1 in R3C4 (step 1j)
2h. 1 in N2 only in 12(3) cage at R1C4, locked for R1, clean-up: no 9 in R2C3 (step 1b)
2i. 20(4) cage at R5C3 = {2369} (only remaining combination, cannot be {2567} = 7{256} which clashes with 9(3) cage at R6C4), locked for N4
2j. 5 in R6 only in R6C456, locked for N5
2k. 40(7) cage must contain 5, CPE no 5 in R3C6 + R6C4, clean-up: no 8 in R2C6 (step 1h)
2l. Naked quad {2369} in R6C1234, locked for R6, 9 also locked for N4
2m. 9(3) cage at R6C4 = [216/351/612]
2n. 13(3) cage = {247/346} (cannot be {256} = 5{26} which clashes with 9(3) cage), no 5, clean-up: no 4 in R3C4 (step 1j)
2o. 13(3) cage = {247/346}, CPE no 4 in R5C5

3. 25(5) cage at R7C1 = {13489} (only possible combination), no 2 -> R7C4 = 1, 3 locked for R7 and N7, R8C4 = 7 (step 1i), clean-up: no 4 in R2C5 (step 1c)
3a. 10(3) cage at R9C1 = {127} (hidden triple in N7), locked for R9, R9C7 = 6 -> R8C7 = 4 (step 1e), R8C1 = 8, clean-up: no 4 in R5C2
3b. R4C1 = 1 -> 14(4) cage at R1C1 = {1256/1346} (cannot be {1247} which clashes with R9C1), no 7, 6 locked for C1 and N1, clean-up: no 4 in R12C3 (step 1b)
3c. R6C5 = 1 (hidden single in C5), R6C6 = 5, clean-up: no 4 in R3C5 (step 1j), no 8 in R3C6 (step 1h)
3d. 9(3) cage at R6C4 = [216/612], no 3, CPE no 2,6 in R45C5
3e. 40(7) cage at R3C4 = {2356789} (only remaining combination), no 4
3f. R5C1 = 4 (hidden single in R5) -> R5C2 = 8
3g. 14(4) cage = {1256} (only remaining combination), 2,5 locked for C1 and N1, clean-up: no 8 in R12C3 (step 1b)
3h. R3C3 = 8 (hidden single in N1)
3i. Naked pair {57} in R4C23, locked for R4
3j. 19(4) cage at R4C7 (step 2) = {1369/2359}
3k. 1,5 of 19(4) cage only in R5C7 -> R5C7 = {15}
3l. 3 in N6 only in R4C789, locked for R4 -> R4C5 = 4
3m. 3 in N5 only in R5C456, locked for R5 and 40(7) cage at R3C4, clean-up: no 6 in R3C5 (step 1j)
3n. Killer pair 2,6 in R5C3 and R5C89, locked for R5
3o. Naked pair {26} in R47C6, locked for C6, clean-up: no 7 in R23C6 (step 1h)
3p. Naked pair {49} in R23C6, locked for C6 and N2 -> R8C56 = [93], R5C456 = [937], 17(3) cage at R9C4 = [458], R3C5 = 7, R3C4 = 2 (step 1j), R46C4 = [86], R4C6 = 2
3q. 2 in N6 only in R5C89 = {25}, locked for R5 -> R5C3 = 6, R8C23 = [65], R4C23 = [57], clean-up: no 3 in R12C3 (step 1b)
3r. R12C3 = [91]
3s. R6C9 = 4 -> 17(4) cage at R6C9 = {2348} (only remaining combination, cannot be {1349} because 3,9 only in R9C9, cannot {1457} because 5,7 only in R7C9) -> R789C9 = [823], R5C89 = [25], R89C8 = [19]
3t. 12(3) cage at R1C4 = [381/561]
3u. 18(3) cage at R1C7 = {378/567} (cannot be {468} which clashes with R1C5), no 2,4, 7 locked for R1 and N3
3v. Naked pair {69} in R24C9, locked for C9 -> R13C9 = [71]
3w. R2C7 = 2 (hidden single in N3) -> R2C68 = 13 = [94]

and the rest is naked singles.

Rating Comment:
I'll rate my WT for A359 at Easy 1.25; the crossover clashes within N9 were my technically hardest steps.


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 Post subject: Re: Assassin 359
PostPosted: Fri Sep 28, 2018 6:48 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 774
Location: Sydney, Australia
wellbeback wrote:
I'm sure there's a term for what Step 2 Line 2 does. Is this IOD?
CCC (see Andrew's step 1t). I saw that spot differently and used IOU (my step 6). Funny how we nearly always see this differently. Brains. I used a path quite similar to wellbeback, at least in the beginning.

a359 WT:
Preliminaries courtesy of SudokuSolver
Cage 15(2) n6 - cells only uses 6789
Cage 7(2) n6 - cells do not use 789
Cage 12(2) n4 - cells do not use 126
Cage 12(2) n4 - cells do not use 126
Cage 9(3) n58 - cells do not use 789
Cage 10(3) n7 - cells do not use 89
Cage 14(4) n14 - cells do not use 9

Routine cage clean-up not done unless stated.
1. "45" on n6: 1 innie r6c9 = 4
1a. no 3 in 7(2)n6

2. "45" on n7: 2 outies r78c4 = 8 (no 4,8,9)

3. "45" on n6789: 2 innies r7c56 = 8 (no 4,8,9)

4. "45" on n69: 2 innies r89c7 = 10 (no 5)

5. 8 & 9 in n8 only in r8c56 + r9c456: r9c7 sees all these -> no 8,9 in r9c7 (CPE)
5a. no 1,2 in r8c7 (h10(2))
[edit: Andrew noticed that I missed the 4 in this same spot. I did! I knew the 8 was the important elimination because of step 6. Thanks Andrew!]

No doubt Andrew will see this next step differently (and he did!).
6. "45" on r9: remembering h10(2)r89c7: 1 outie r8c7 + 8 = 2 innies r9c89
6a. 1 innie and 1 outie are in the same nonet -> no 8 in r9c89 (IOU)

7. 8 in r9 only in 17(3)n8 : 8 locked for n8
7a. = {278/368/458}(no 1,9)

8. "45" on n69: 2 outies r8c56 = 12 and must have 9 for n8 = {39} only: both locked for r8, n8 and no 3 in r9c7
8a. no 5 in r7c56 nor r78c4 (two h8(2))

9. hidden triple {458} for n8 in r9c456: all locked for r9
9a. r89c7 = h10(2) = [46/82]

10. 18(3)r8c2: {468} blocked by r8c7
10a. = {567} only: all locked for r8: 5 locked for n7
10b. r7c4 = (12) (h8(2)r78c4)

11. 10(3)n7 = {127/136}: must have 1, 1 locked for r9 & n7

12. 25(5)r7c1: must have 4,8,9 for n7
12a. = {13489} only (no 2,6,7) -> r78c4 = [17]
12b. 3 locked for n7 and r7; 9 locked for r7

13. 10(3)n7 = {127} only: 2 & 7 locked for r9
13a. r89c7 = [46] (h10(2))
13b. r8c1 = 8
13c. no 4 in r5c2
13d. r6789c9 = [4823] only valid permutation
13e. r89c8 = [19]

14. 9(3)r6c4 must have 2,6 for r7c5 = {126} only
14a. r6c5 = 1

15. 40(7)r3c4 = {2356789} only (no 4)

16. "45" on n5: 4 outies = 17. r7c56 = {26} = 8
16a. -> r3c45 = 9 (no 8,9), no 2,5 in r3c5

17. 13(3)r3c5: must have 4 for n5 -> no 4 in r3c5
17a. = {247/346}(no 5,8,9)
17b. 7 in {247} must be in r3c5 -> no 7 in r4c56
17c. r3c45 = [27]/{36}
17d. no 5 in r3c4 (h9(2))
17e. 4 locked for r4
17f. no 8 in 12(2)r4c23

18. "45" on n4: 1 innie r4c1 = 1

19. 20(4)n4 must have 2 & 6 for n4: but [4]{268} blocked by r6c4
19a. = {2369/2569}(no 4,8)

20. hidden single 4 in r5 -> r5c1 = 4, r5c2 = 8

21. r4c1 = 1 -> r123c1 = 13 = {256} only: locked for c1 and n1

22. "45" on n14: 2 innies r12c3 = 10 = {19/37}(no 4,8)

23. "45" on r1: remembering the h10(2)r12c3 -> 1 outie r2c3 + 5 = 2 innies r1c12
23a. 1 outie and 1 innie are in the same nonet -> no 5 in r1c1 (IOU)

24. "45" on r1, 3 innies r1c123 = 15 = [249] only valid permutation
24a. r2c3 = 1 (h10(2)r12c3)

25. r12c3 = 10 -> r2c45 = 11: but {56} blocked by r2c1
25a. = {38}/[47] (no 2,5,6; no 4 in r2c5)
25b. 15(3)r2c6: {456} blocked by r2c1

cracked. Much easier now.
Cheers
Ed


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