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Ed
 Post subject: Assassin 208
PostPosted: Fri Mar 18, 2011 4:52 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
One of the things I do to find interesting Assassins is try puzzles JSudoku solves (using "Deduce all moves") in a flash but SudokuSolver has a lot of trouble with. Unfortunately, I usually can't solve them so they have to get ditched. Fortunately, got to keep this one.

It takes me two key moves both similar in complexity to the last puzzle. Nothing heavy but still advanced moves. They are fairly common in walk-throughs here so am fairly hopeful that it will get a "fun" rating. It has big progress early so gets you hooked. However, it takes me about 30 steps to finally get it fully cracked so takes some patience.

Assassin 208

Image

code: select and paste into solver:
3x3::k:4865:4865:4865:7682:2307:2307:3332:3332:2053:1286:1286:7682:7682:2307:4631:4631:5656:2053:2312:2312:3593:7682:7682:4631:7434:5656:2053:11531:3593:3593:6412:6412:6412:7434:5656:5656:11531:6925:6925:6925:6412:7434:7434:7434:3598:11531:2831:6925:1808:6412:2321:2321:3598:3598:11531:2831:6925:1808:11531:2322:4115:4115:4115:11531:11531:11531:11531:7956:2322:2322:2325:4118:2567:2567:2567:7956:7956:7956:7956:2325:4118:
solution: 
+-------+-------+-------+
| 2 9 8 | 5 4 3 | 6 7 1 |
| 4 1 7 | 9 2 6 | 5 8 3 |
| 6 3 5 | 1 8 7 | 2 9 4 |
+-------+-------+-------+
| 7 8 1 | 6 5 4 | 9 3 2 |
| 9 2 3 | 7 1 8 | 4 6 5 |
| 5 4 6 | 3 9 2 | 7 1 8 |
+-------+-------+-------+
| 1 7 9 | 4 3 5 | 8 2 6 |
| 8 6 4 | 2 7 1 | 3 5 9 |
| 3 5 2 | 8 6 9 | 1 4 7 |
+-------+-------+-------+
Cheers
Ed
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Andrew
 Post subject: Re: Assassin 208
PostPosted: Sun Mar 20, 2011 1:44 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for continuing to post Assassins! :D

Ed wrote:
...so am fairly hopeful that it will get a "fun" rating.
Not sure I'll go quite that far but the eliminations in the interestingly shaped 45(9) cage seemed fun; I don't think that's giving anything away.

Rating Comment:
I'll rate my walkthrough for A208 at Easy 1.5, based on my use of locking-out cages in step 15, the not particularly obvious killer pair in step 20 and the analysis in step 20a. I also avoided any temptation to give a lower rating because I found several important steps difficult to spot, even when they weren't technically difficult.

Step 15 could alternatively have been done using a combined cage R23C12 with the restriction that it must contain 1; I saw the locking-out cages first, plus I think they are the "cleaner" way to do this step.

Here is my walkthrough for A208:
Prelims

a) R1C78 = {49/58/67}, no 1,2,3
b) R2C12 = {14/23}
c) R3C12 = {18/27/36/45}, no 9
d) R67C2 = {29/38/47/56}, no 1
e) R67C4 = {16/25/34}, no 7,8,9
f) R6C78 = {18/27/36/45}, no 9
g) R89C8 = {18/27/36/45}, no 9
h) R89C9 = {79}
i) 19(3) cage in N1 = {289/379/469/478/568}, no 1
j) 9(3) cage in N2 = {126/135/234}, no 7,8,9
k) 8(3) cage in N3 = {125/134}
l) 9(3) cage at R7C6 = {126/135/234}, no 7,8,9
m) 10(3) cage in N7 = {127/136/145/235}, no 8,9
n) 31(5) cage at R8C5 must contain 9
o) And of course 45(9) cage at R4C1 = {123456789}

Steps resulting from Prelims
1a. Naked pair {79} in R89C9, locked for C9 and N9, clean-up: no 2 in R89C8
1b. 8(3) cage in N3 = {125/134}, 1 locked for C9 and N3
1c. 9 in 31(5) cage at R8C5 only in R8C5 + R9C456, locked for N8
1d. 9 in R7 only in R7C123, locked for N7
1e. 9 in 45(9) cage at R4C1 only in R4567C1, locked for C1

2. 45 rule on R1 4 innies R1C4569 = 13 = {1237/1246/1345}, no 8,9

3. 45 rule on R1 2 innies R1C49 = 1 outie R2C5 + 4, IOU no 4 in R1C9

4. 45 rule on N1 2 innies R23C3 = 12 = {39/48/57}, no 1,2,6

5. 45 rule on N2 2 outies R2C37 = 12 = {39/48/57}, no 1,2,6

6. 45 rule on N9 2 innies R89C7 = 4 = {13}, locked for C7 and N9, clean-up: no 9 in R2C3 (step 5), no 3 in R3C3 (step 4), no 6,8 in R6C6, no 6,8 in R89C8
6a. Naked pair {45} in R89C8, locked for C8 and N9, clean-up: no 8,9 in R1C7
6b. Naked triple {268} in 16(3) cage in N9, locked for R7, clean-up: no 3,5,9 in R6C2, no 1,5 in R6C4
6c. 3 in N3 only in 8(3) cage + R23C8, CPE no 3 in R4C9

7. 9(3) cage at R7C6 = {135/234} (cannot be {126} because 2,6 only in R8C6), no 6, CPE no 3 in R8C45
7a. 2 of {234} must be in R8C6 -> no 4 in R8C6

8. 45 rule on R9 3 outies R8C589 = 21 = {489/579} (cannot be {678} because R8C8 only contains 4,5), no 1,2,6
8a. R8C8 = {45} -> no 4,5 in R8C5

9. 31(5) cage at R8C5 = {16789/34789/35689} (other combinations don’t contain 1 or 3), no 2, 8 locked for N8
9a. R9C7 = {13} -> no 1,3 in R9C456
9b. 2 in N8 only in R8C46, locked for R8

10. 2 in R9 only in 10(3) cage = {127/235}, no 4,6

11. 6 in R9 only in R9C456, locked for N8
11a. 31(5) cage at R8C5 (step 9) = {16789/35689}, no 4
11b. 6 in R8 only in R8C123, locked for 45(9) cage at R4C1, no 6 in R456C1

12. R9C8 = 4 (hidden single in R9), R8C8 = 5
12a. R8C589 (step 8) = {579} (only remaining combination) -> R8C59 = {79}, locked for R8
12b. 4 in R8 only in R8C1234, locked for 45(9) cage at R4C1, no 4 in R4567C1 + R7C5
12c. 8 in R8 only in R8C123, locked for 45(9) cage at R4C1, no 8 in R456C1

13. 9(3) cage at R7C6 (step 7) = {135/234}
13a. 4,5 only in R7C6 ->R7C6 = {45}
13b. R8C67 = {13/23}, 3 locked for R8

[I was slow spotting the next step but since it simplified the lower part of the grid I’ve re-worked this area to include it.]
14. 45 rule on N89 3 innies R7C45 + R8C4 = 9 = {135/234}, no 7, 3 locked for N8
14a. 1,2 of {135/234} must be in R8C4 -> R8C4 = {12}
14b. Naked pair {12} in R8C46, locked for R8 and N8 -> R8C7 = 3, R9C7 = 1, clean-up: no 6 in R6C4, no 7 in 10(3) cage in N7 (step 10)
14c. Naked triple {345} in R7C456, locked for R7 and N8, clean-up: no 6,7,8 in R6C2
14d. 7 in 45(9) cage at R4C1 only in R4567C1, locked for C1, clean-up: no 2 in R3C2

15. 1 in N1 only in R2C12 = {14} or R3C12 = {18} -> R3C12 = {18/36}/[27] (cannot be {45}, locking-out cages), no 4,5
15a. R2C12 = {14} or R3C12 = {18} -> R23C3 = [39/57/75] (cannot be {48}, locking-out cages), no 4,8, clean-up: no 4,8 in R2C7 (step 5)
[I hope I’ve now described these steps correctly.]
15b. Min R3C3 = 5 -> max R4C23 = 9, no 9 in R4C23

16. 19(3) cage in N1 = {289/469/568} (cannot be {379} which clashes with R23C3, cannot be {478} which clashes with R1C78), no 3,7
16a. 7 in N1 only in R2C3 + R3C23, CPE no 7 in R3C45
16b. 3 in R1 only in R1C4569 (step 2) = {1237/1345}, no 6

17. 45 rule on N36 2 innies R26C7 = 1 outie R5C6 + 4
17a. Min R26C7 = 7 -> min R5C6 = 3

18. 14(3) cage in N6 = {158/248/257/347/356} (cannot be {149/167} because 1,7,9 only in R6C8, cannot be {239} which clashes with 8(3) cage in N3), no 9
18a. 8 of {248} must be in R56C9 (R56C9 cannot be {24} which clashes with 8(3) cage in N3) -> no 8 in R6C8
18b. 6 of {356} must be in R56C9 (R56C9 cannot be {35} which clashes with 8(3) cage in N3) -> no 6 in R6C8

19. 45 rule on C89 2 innies R15C8 = 1 outie R7C7 + 5
19a. Max R7C7 = 8 -> max R15C8 = 13, min R1C8 = 6 -> max R5C8 = 7

20. Killer pair 4,5 in 8(3) cage in N3 and 14(3) cage in N6, locked for C9
[I ought to have spotted this killer pair while I was analysing step 18.]
20a. 22(4) cage at R2C8 = {1678/2389} -> R4C8 = {123} (R23C8 + R4C9 cannot contain both of 2,3 which would clash with 8(3) cage in N3 because R23C8 + R4C9 are common peers of the 8(3) cage)

21. 9 in N6 only in R45C7, locked for C7 and 29(5) cage at R3C7, no 9 in R5C6, clean-up: no 3 in R2C3 (step 5), no 9 in R3C3 (step 4)

22. Naked pair {57} in R2C37, locked for R2

23. Naked pair {57} in R23C3, locked for C3 and N1, clean-up: no 2 in R3C1

24. 19(3) cage in N1 (step 16) = {289/469}, 9 locked for R1, clean-up: no 4 in R1C7

25. Killer pair 5,7 in R1C78 and R2C7, locked for N3, clean-up: no 2 in 8(3) cage in N3

26. Naked triple {134} in 8(3) cage in N3, locked for C9 and N3

27. 22(4) cage at R2C8 (step 20a) = {2389} (only remaining combination) -> R4C8 = 3, R23C8 = {289}, R4C9 = {28}

28. 5 in C9 only in R56C9, locked for N6, clean-up: no 4 in R6C6
28a. 14(3) cage in N6 (step 18) = {158/257}, no 6
28b. Naked triple {258} in R456C9, locked for C9 and N6 -> R7C9 = 6, clean-up: no 1,7 in R6C6

29. Naked triple {289} in R237C8, locked for C8, clean-up: no 5 in R1C7
29a. Naked pair {67} in R1C78, locked for R1 and N3 -> R2C8 = 5, R23C3 = [75]

30. 19(3) cage in N1 (step 24) = {289} (only remaining combination), locked for R1 and N1, clean-up: no 3 in R2C12, no 1 in R3C12
30a. Naked pair {14} in R2C12, locked for R2 -> R2C9 = 3, R13C9 = [14]
30b. Naked pair {36} in R3C12, locked for R3

31. 9(3) cage in N2 = {234} (only remaining combination) -> R2C5 = 2, R1C56 = {34}, locked for R1 -> R1C4 = 5, clean-up: no 2 in R6C4

32. Naked pair {34} in R67C4, locked for C4

33. R2C7 = 5 -> R23C6 = 13 = [67]

34. 45 rule on N36 2 outies (no remaining innies) R56C6 = 10 = [82], R6C7 = 7, R1C78 = [67], R3C7 = 2, R56C8 = [61], R6C2 = 4, R7C2 = 7, R67C4 = [34], R78C6 = [51], R7C5 = 3, R7C78 = [82], R8C4 = 2, R9C6 = 9, R8C5 = 7, R89C9 = [97], R4C6 = 4, R45C7 = [94], R2C12 = [41]
34a. R8C3 = 4 (hidden single in R8)

35. 14(3) cage in N6 (step 28a) = {158} (only remaining combination) -> R56C9 = [58]

36. R5C23 = {23} (hidden pair in R5) = 5 -> R5C4 + R67C3 = 22 = [769]

and the rest is naked singles.
Thanks Ed for the feedback about how I described step 15 and for correcting a couple of typos.


Last edited by Andrew on Tue Apr 12, 2011 4:26 am, edited 1 time in total.

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Ed
 Post subject: Re: Assassin 208
PostPosted: Thu Mar 24, 2011 9:25 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Andrew wrote:
Thanks Ed for continuing to post Assassins! :D
You're welcome! I'm really enjoying making them since I'm finding interesting puzzles without too much effort. Perhaps the non-symmetrical shapes with at least one big cage helps this. And I enjoy getting your feedback! I'm a couple ahead so should be able to continue fortnightly.

I missed Andrew's nifty blocks (18 and 21a) even though I looked hard in that area. Instead, my key move (16a) gets chunkier progress in the middle stages of this puzzle. Very satisfied.

I'll start with an alternate way to do Andrew's step 15a which is around the same difficulty level I guess.

Alternate breakthrough for A208
7 steps:
Alternative way to get the elimination in Andrew's 15a.

Before Andrew's step 15a here; use "Paste Into" A208 in
SudokuSolver
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 234568    23456789  23456789  | 1234567   123456    123456    | 4567      6789      1235      |
| 1234      1234      34578     | 123456789 123456    123456789 | 45789     236789    12345     |
| 12368     13678     45789     | 123456789 123456789 123456789 | 2456789   236789    12345     |
:-------------------------------+-------------------------------+-------------------------------:
| 123579    123456789 123456789 | 123456789 123456789 123456789 | 2456789   1236789   24568     |
| 123579    123456789 123456789 | 123456789 123456789 123456789 | 2456789   1236789   234568    |
| 123579    24        123456789 | 234       123456789 123457    | 245678    1236789   234568    |
:-------------------------------+-------------------------------+-------------------------------:
| 179       79        179       | 345       35        45        | 268       268       268       |
| 468       468       468       | 12        79        12        | 3         5         79        |
| 235       235       235       | 6789      6789      6789      | 1         4         79        |
'-------------------------------.-------------------------------.-------------------------------'

15a. r123c1 must have two of 4,6,8 for c1 since the only other place is r8c1 -> {48} blocked from h12(2)r23c3 (no 4,8)
15b. no 4,8 in r2c7 (h12(2)r2c37)
15c. 9 in n1 only in r1 or r3c3 (no eliminations yet)

16. "45" on n12: 1 outie r2c7 = 1 innie r3c3
16a. -> from step 15c. no 9 in r1c8 (Clone CPE)
16b. no 4 in r1c7

17. 9 in r1 only in n1: locked for n1
17a. no 3 in r2c3, no 9 in r2c7

18. Killer pair 5,7 in n3 in 15(2) + r2c7: both locked for n3

19. 8(3)n3 = {134} only: 3,4 locked for n3 & c9

20. 14(3)n6 = {158/257/356} ({167} blocked by 1,7 only in r6c8;{239} blocked by 3,9 only in r6c8)
20a. must have 5; 5 locked for n6 & c9
20b. must have 1/3/7 -> r6c8 = (137)
20c. no 4 in r6c6

21. 22(4)r2c8: {1678} blocked by 1,7 only in r4c8
21a. = {2389} only

Back to Andrew's step 27
Cheers
Ed
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