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Ed
 Post subject: Assassin 269
PostPosted: Thu Sep 12, 2013 11:18 pm 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Another easier one than usual but kept me looking hard to find the 'easy' way to solve it to make some sense of the SSscore of 1.15. Hope its enough of a challenge.

Assassin 269
Image
code: paste into solver:
3x3::k:3072:4097:8706:8706:8706:3075:3075:4868:4868:3072:4097:4097:8706:8706:4357:3846:3846:4868:5127:1800:1800:8706:4357:4357:3081:3846:4868:5127:9738:4107:4107:4357:3081:3081:8460:8460:5127:9738:9738:9738:9738:9738:9738:8460:8460:5127:9738:3597:3597:5390:2575:2575:8460:8460:5127:3088:3088:6929:5390:5390:2575:5394:4115:3348:3093:3093:6929:6929:5390:5394:5394:4115:3348:3093:6929:6929:6929:2070:2070:4115:4115:
Solution: 
+-------+-------+-------+
| 9 1 6 | 5 7 8 | 4 2 3 |
| 3 7 8 | 4 9 2 | 6 1 5 |
| 4 5 2 | 3 6 1 | 7 8 9 |
+-------+-------+-------+
| 2 3 9 | 7 8 4 | 1 5 6 |
| 7 4 1 | 2 5 6 | 9 3 8 |
| 6 8 5 | 9 1 3 | 2 4 7 |
+-------+-------+-------+
| 1 9 3 | 8 4 7 | 5 6 2 |
| 5 2 4 | 6 3 9 | 8 7 1 |
| 8 6 7 | 1 2 5 | 3 9 4 |
+-------+-------+-------+
Cheerio
Ed
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Frank
 Post subject: Re: Assassin 269
PostPosted: Sat Sep 14, 2013 2:47 am 
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Joined: Mon Apr 28, 2008 10:58 pm
Posts: 47
Location: Victoria, B.C., Canada
Nice one Ed :).

I struggled for an embarrassingly long time before spotting the obvious start.

Obvious start:
The 38(8) cage is missing a 7. r5c1 sees all 8 of the 38(8) cage so r5c1 = 7. That sorts out the 13(2) and 12(2) cages in c1. Also the 16(2) cage in n45 and the 12(2) cage in n7. That just leaves the hidden 10(2) cage in n1 and the hidden 8(2) cage in n7. After that, the rest is easy.

Many thanx - Cheers - Frank
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Andrew
 Post subject: Re: Assassin 269
PostPosted: Sat Sep 28, 2013 9:44 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for Assassin 269. After the "obvious" start I found it hard work and took a long time to achieve the last part of Frank's start. If there's a "simple" way to solve this puzzle, I never found it. The SS score seems far too low to me.

Here is my walkthrough for Assassin 269:
Thanks Ed for your comments and corrections.
Prelims

a) R12C1 = {39/48/57}, no 1,2,6
b) R1C67 = {39/48/57}, no 1,2,6
c) R3C23 = {16/25/34}, no 7,8,9
d) R4C34 = {79}
e) R6C34 = {59/68}
f) R7C23 = {39/48/57}, no 1,2,6
g) R89C1 = {49/58/67}, no 1,2,3
h) R9C67 = {17/26/35}, no 4,8,9
i) 10(3) cage at R6C6 = {127/136/145/235}, no 8,9
j) 21(3) cage at R7C8 = {489/579/678}, no 1,2,3
k) 38(8) cage at R4C2 = {12345689}, no 7

1. 38(8) cage at R4C2 = {12345689}, CPE no 1,2,3,4,5,6,8,9 in R5C1 -> R5C1 = 7, R3C34 = [97], clean-up: no 5 in R12C1, no 5 in R6C4, no 3 in R7C2, no 6 in R89C1
1a. R12C1 = {39} (cannot be {48} which clashes with R89C1), locked for C1 and N1, clean-up: no 4 in R3C23, no 4 in R89C1
1b. Naked pair {58} in R89C1, locked for C1 and N7, clean-up: no 4,7 in R7C23
1c. R7C23 = [93]
1d. R1C67 = {48/57} (cannot be {39} which clashes with R1C1), no 3,9
1e. 3 in N4 only in R456C2, locked for 38(8) cage at R4C2, no 3 in R5C4567
1f. 9 in 38(8) cage only in R5C4567, locked for R5
1g. 34(6) cage at R1C3 must contain 9, locked for N2

2. 45 rule on N1 2 innies R1C3 + R3C1 = 10 = [46/64/82]
2a. Killer pair 2,6 in R1C3 + R3C1 and R3C23, locked for N1
2b. 2 in N1 only in R3C123, locked for R3
2c. 6 in N1 only in R1C3 + R3C123, CPE no 6 in R3C4

3. 45 rule on N7 2 innies R7C1 + R9C3 = 8 = [17/26/62]

4. 45 rule on N3 2 innies R13C7 = 11 = [47/56/74/83]

5. 45 rule on N9 2 innies R79C7 = 8 = {17/26}/[53], clean-up: no 3 in R9C6

6. 45 rule on C89 2 outies R28C7 = 14 = {59/68}
6a. R13C7 (step 4) = [47/74/83] (cannot be [56] which clashes with R28C7), no 5,6, clean-up: no 7 in R1C6

7. 45 rule on N6 3 innies R456C7 = 12 = {129/138/147/246} (cannot be {156} which clashes with R28C7, cannot be {237/345} which clash with R13C7), no 5

8. 12(3) cage at R3C7 = {138/147/156/237/246/345}
8a. R34C7 cannot total 11 (which would clash with R13C7 = 11, step 4, CCC) -> no 1 in R4C6
[Alternatively 45 rule on N3 2 outies R4C67 = 1 innie R1C7 + 1, IOU no 1 in R4C6]
8b. 1 of {138} must be in R4C7 -> no 8 in R4C7

9. 10(3) cage at R6C6 = {127/136/145/235}
9a. R67C7 cannot total 8 (which would clash with R79C7 = 8, step 5, CCC) -> no 2 in R6C6
[Alternatively 45 rule on N7 2 outies R6C67 = 1 innie R9C7 + 2, IOU no 2 in R6C6]

10. 45 rule on N2 2(1+1) outies R1C3 + R4C5 = 1 innie R1C6 + 6, IOU no 6 in R4C5

11. 45 rule on N2 3(2+1) outies R1C37 + R4C5 = 18
11a. Max R1C37 = 15 -> min R4C5 = 3
11b. R1C37 cannot total 11,12 (because no 6,7 in R4C5) -> no 4 in R1C3, clean-up: no 6 in R3C1 (step 2)

12. 45 rule on N8 2(1+1) outies R6C5 + R9C3 = 1 innie R9C6 + 3, IOU no 3 in R6C5

13. 45 rule on N8 3(1+2) outies R6C5 + R9C37 = 11
13a. Min R9C37 = 3 -> max R6C5 = 8
13b. R9C37 cannot total 6 -> no 5 in R6C5
13c. R6C5 + R9C3 cannot total 5 -> no 6 in R9C7, clean-up: no 2 in R7C7 (step 5), no 2 in R9C6

14. 10(3) cage at R6C6 = {127/136/145/235}
14a. 2 of {127} must be in R6C7 -> no 7 in R6C7

15. R456C7 (step 7) = {129/138/246}
15a. 8,9 of {129/138} must be in R5C7 -> no 1 in R5C7
15b. 4 of {246} must be R4C7 (because R13C7 = [83] for {246}, no 7 in R4C6 and 12(3) cage at R3C7 cannot be [336]) -> no 6 in R4C7, no 4 in R56C7

16. 10(3) cage at R6C6 = {127/136/145/235}
16a. 4 of {145} must be in R6C6, 5 of {235} must be in R7C7 -> no 5 in R6C6

17. Consider placements for R3C1 = {24}
R3C1 = 2 => no 2 in R7C1 => no 6 in R9C3 (step 3)
or R3C1 = 4 => R1C3 = 6 (step 2)
-> no 6 in R9C3, clean-up: no 2 in R7C1 (step 3)
[Ed pointed out that 45 rule on N17 4(2+2) innies R19C3 + R37C1 = 18 eliminates 6 from R9C3 because R37C1 cannot total 4. It’s rare that a 45 on separated rows/columns/nonets leads to anything useful, so one tends not to look at them.]

18. R6C5 + R9C37 = 11 (step 13)
18a. R9C37 cannot total 7 -> no 4 in R6C5

19. R13C7 (step 6a) = [47/74/83]
19a. R1C37 + R4C5 = 18 (step 11) = [648/675/873] (cannot be [684] because R3C7 = 3, R4C7 = 4 (hidden single in C7) clashes with R4C5) -> no 8 in R1C7, no 4 in R4C5, clean-up: no 4 in R1C6, no 3 in R3C7

20. Naked pair {47} in R13C7, locked for C7 and N3, clean-up: no 1 in R79C7 (step 5), no 1,7 in R9C6
20a. Killer pair 5,6 in R28C7 and R7C7, locked for C7
20b. Naked triple {123} R469C7, 1 also locked for N6
20c. 1 in R5 only in R5C23456, locked for 38(8) cage at R4C2, no 1 in R46C2

21. R6C5 + R9C37 = 11 (step 13)
21a. Min R9C37 = 5 -> max R6C5 = 6

22. 12(3) cage at R3C7 (step 8) = {147/237/246/345} (cannot be {138/156} because R3C7 only contains 4,7), no 8

23. 10(3) cage at R6C6 = {136/145/235}
23a. R7C7 = {56} -> no 6 in R6C6

24. 34(6) cage at R1C3 = {136789/345679} (cannot be {145789/235789/245689} which clash with R1C6), no 2, 3,7 locked for N2, 7 also locked for C5

25. R2C6 = 2 (hidden single in N2)
25a. 17(4) cage at R2C6 = {1268/2348/2456}
25b. 5 of {2456} must be in R4C5 -> no 5 in R3C56

26. 27(6) cage at R7C4 = {123489/123579/123678/124578} (cannot be {124569/134568/234567} which clash with R9C6), 1 locked for N8

27. 7 in N8 only in 21(4) cage at R6C5 = {1479/1578/2478/3567} (cannot be {2379} because 3,9 only in R8C6)
27a. R6C5 = {126} -> no 2,6 in R7C56 + R8C6

28. 2 in N8 only in R789C4 + R89C5, locked for 27(6) cage at R7C4 -> R9C3 = 7, R7C1 = 1 (step 3)
28a. 6 in C1 only in R46C1, locked for N4, clean-up: no 8 in R6C4
28b. 6 in 38(8) cage at R4C2 only in R5C456, locked for R5 and N5 -> R6C4 = 9, R6C3 = 5, clean-up: no 2 in R3C2
28c. 5 in 38(8) cage only in R5C456, locked for R5 and N5

29. R5C7 = 9 (hidden single in R5), clean-up: no 5 in R28C7 (step 6)
29a. Naked pair {68} in R28C7, locked for C7 -> R7C7 = 5, R9C7 = 3 (step 5), R9C6 = 5, R1C6 = 8, R1C7 = 4, R1C3 = 6, R4C5 = 8 (step 11), R3C1 = 4 (step 2), R8C56 = [47], R89C1 = [58]
29b. Naked pair {16} in R3C56, locked for R3 and N2 -> R3C23 = [52], R8C3 = 4
29c. Naked pair {68} in R7C8 + R8C7, locked for N9 -> R7C9 = 2
29d. R7C8 + R8C7 = {68}, R8C8 = 7 (cage sum)

30. R8C6 = 9 (hidden single in C6), R6C5 = 1 (cage sum), R6C7 = 2, R6C6 = 3 (cage sum), R46C1 = [26], R4C67 = [41], R4C2 = 3, R5C6 = 6, R3C56 = [61], R89C5 = [32], R5C45 = [25], R123C4 = [543]

31. Naked pair {89} in R3C89, locked for N3 -> R2C7 = 6, R23C8 = 9 = [18]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A269 at Hard 1.25.

Ed's breakthrough step 7b (see his post below) was neat :applause: , but I wouldn't call it 'simple'! It led to a much shorter solving path.


Last edited by Andrew on Thu Oct 10, 2013 4:43 am, edited 1 time in total.

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Ed
 Post subject: Re: Assassin 269
PostPosted: Thu Oct 03, 2013 9:30 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Andrew wrote:
If there's a "simple" way to solve this puzzle
There is! :) An old style Assassin this one. Have used Andrew's lovely start then the cracker is step 7. Have attached the SS file at the correct spot - download to your computer then double-click.

A269 Alternate cracker
13 more steps:
Hidden Text:
End of Andrew's step 6. Paste into A269 in SudokuSolver
.-------------------------------.-------------------------------.-------------------------------.
| 39        14578     468       | 12345689  123456789 458       | 478       123456789 123456789 |
| 39        14578     14578     | 12345689  123456789 12345678  | 5689      123456789 123456789 |
| 246       1256      1256      | 134589    1345678   1345678   | 347       13456789  13456789  |
:-------------------------------+-------------------------------+-------------------------------:
| 1246      1234568   9         | 7         1234568   1234568   | 1234568   1234568   1234568   |
| 7         1234568   124568    | 1245689   1245689   1245689   | 1245689   1234568   1234568   |
| 1246      1234568   568       | 689       12345689  123456    | 1234567   123456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 126       9         3         | 124568    1245678   1245678   | 124567    45678     1245678   |
| 58        12467     12467     | 12345689  123456789 123456789 | 5689      456789    123456789 |
| 58        12467     267       | 12345689  123456789 12567     | 12367     123456789 123456789 |
'-------------------------------.-------------------------------.-------------------------------'
Andrew's steps 1-6 then
7. 34(6)r1c3: {145789/245689} blocked by r1c6 = (458)
7a. = {136789/235789/345679} [edit: just looked at how SS does this and realize that 7b is actually not needed. From 7a, must have 7 in r12c5 ->7 in r3 only in n3 -> no 7 in r1c7 -> 12(2)r1c6 = {48} only]
7b. but [8]{23579} blocked by 12(2)r1c6 = {48}/[57]
7c. = {136789/345679}(no 2)
7d. Must have 3,6,7,9: 3 & 7 only in n2; both locked for n2 and 7 for c5

8. Hidden single 2 in n2 -> r2c6 = 2
8a. no 6 in r9c7

9. 7 in r3 only in n3: 7 locked for n3
9a. no 5 in r1c6
9b. no 4 in r3c7 (h11(2)r13c7)

10. 12(2)r1c6 = {48}: both locked for r1
10a. r1c3 = 6, r3c1 = 4 (h10(2)n1)
10b. no 8 in r6c4

11. 7(2)n1 = {25} only: 5 locked for n1 & r3
11a. 8 in n1 only in r2, 8 locked for r2
11b. no 6 in r8c7 (h14(2)r28c7)

12. "45" on n2: 2 remaining outies r1c7+r4c5 = 12 = {48} only

13. 6 in n2 only in 17(4)r2c6 = {1268} only
13a. r4c5 = 8, r1c7 = 4 (step 12), r3c7 = 7 (h11(2)r13c7)
13b. r3c7 = 7 -> r4c67 = 5 = [41/32]
13c. r1c6 = 8
13d. Naked pair {16} in r3c56: 1 locked for n2 and r3

14. "45" on n6: 3 innies r456c7 = 12: but {156} blocked by h14(2)r28c7 = [5/6]
14a. h12(3) = {129/138}(no 5,6)
14b. Must have 8 or 9 which are only in r5c7 -> r5c7 = (89)
14c. h12(3) must have 1: 1 locked for n6 and c7

15. 8(2)r9c6 = [53/62]
15a. no 2 in r7c7 (h8(2)r79c7)

16. "45" on n8, 3 outies r6c5+r9c37 = 11 = [623/272/173]
16a. r6c5 = (126)

17. 7 in n8 only in 21(4) = {1479/2379/3567}
17a. but {2379} blocked since 3 & 9 only in r8c6
17b. = {1479/3567}(no 2)

18. 2 in n8 only in 27(6)r7c4 -> no 2 in r9c3
18a. r9c3 = 7, r7c1 = 1 (h8(2)n7)

19. 2 remaining outies n8 = 4 (step 16)
19a. r6c5 = 1, r9c7 = 3, r7c7 = 5 (h8(2)r79c7)

Rest is a few cage sums and singles.
Cheerio
Ed


Attachments:
A269 Andrew WT ALt ending from end step 6.ssv [80.33 KiB]
Downloaded 686 times
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