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Ed
 Post subject: Assassin 250
PostPosted: Fri Nov 23, 2012 5:54 am 
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Posts: 1044
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Another milestone puzzle and is a bit harder than normal with a very high SudokuSolver Score. Even JSudoku has to work to get it so am very chuffed I was able to get it out. I found a nice quick way to start getting somewhere and so was hooked.
If you're not getting anywhere with this puzzle, a vague hint:
r8c3 doesn't see all of r9
explicit hint/step:
r8c3 repeats in r9 in 13(2)r9c89 -> r89c3 cannot sum to 13 -> from innies n7, r7c1 cannot = 8
After that, it's still no gimmie but at least you can chip away. My optimised Walkthrough gets it properly cracked in 20 steps (without prelims, sorry Andrew).

Assassin 250

Image

code: paste into solver:
3x3::k:5376:5376:4609:4609:3330:3330:3330:2307:2307:5376:4868:4868:4609:2309:5126:5126:7431:7431:2824:2824:4868:4609:2309:5126:7431:7431:3337:5386:2824:4868:4609:4619:5126:7431:3852:3337:5386:5386:5386:4619:4619:8461:8461:3852:3337:5902:5902:5902:5647:5648:5648:8461:8461:3857:5902:1810:1810:5647:5647:5648:8461:8461:3857:2067:2067:9492:5647:9492:9492:8461:3857:3857:2325:2325:9492:9492:9492:9492:9492:3350:3350:
solution: 
+-------+-------+-------+
| 6 7 2 | 8 9 1 | 3 5 4 |
| 8 9 3 | 4 2 5 | 1 6 7 |
| 5 4 1 | 3 7 6 | 9 2 8 |
+-------+-------+-------+
| 9 2 6 | 1 4 8 | 5 7 3 |
| 4 1 7 | 9 5 3 | 6 8 2 |
| 3 5 8 | 2 6 7 | 4 9 1 |
+-------+-------+-------+
| 7 3 4 | 5 8 9 | 2 1 6 |
| 2 6 9 | 7 1 4 | 8 3 5 |
| 1 8 5 | 6 3 2 | 7 4 9 |
+-------+-------+-------+
Cheerio
Ed
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Frank
 Post subject: Re: Assassin 250
PostPosted: Sun Nov 25, 2012 3:50 pm 
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Joined: Mon Apr 28, 2008 10:58 pm
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Phew! What a monster. :)

Your start was quite cute. After that your chip away suggestion was more like a scrape scratch and grind - but I got there in the end.

Well done Ed - but don't do it again. :)

Thanx - Frank
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Andrew
 Post subject: Re: Assassin 250
PostPosted: Mon Nov 26, 2012 1:22 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for a landmark Assassin! As you said a nice quick start. I'll guess that Frank, you and I all found the same step to get into the puzzle, although it's possible we may have seen the step in different ways.

My final breakthrough wasn't until step 24 (in the re-worked version) but my solving path isn't optimised; I have, of course, started with Prelims. ;)

Thanks Ed for pointing out that I’d omitted a permutation in step 22a; this resulted in re-work of many of the remaining steps.

Here is my walkthrough for Assassin 250:
Prelims

a) R1C89 = {18/27/36/45}, no 9
b) R23C5 = {18/27/36/45}, no 9
c) R45C8 = {69/78}
d) R7C23 = {16/25/34}, no 7,8,9
e) R8C12 = {17/26/35}, no 4,8,9
f) R9C12 = {18/27/36/45}, no 9
g) R9C89 = {49/58/67}, no 1,2,3
h) 21(3) cage at R1C1 = {489/579/678}, no 1,2,3
i) 11(3) cage at R3C1 = {128/137/146/236/245}, no 9
j) 22(3) cage at R6C5 = {589/679}
k) 18(5) cage at R1C3 = {12348/12357/12456}, no 9
l) 37(8) cage at R8C3 = {12345679}, no 8

[Only one “step resulting from Prelims”.]
1. 22(3) cage at R6C5 = {589/679}, CPE no 9 in R45C6

2. 45 rule on N14 1 outie R7C1 = 1 innie R1C3 + 5, R1C3 = {1234}, R7C1 = {6789}

3. 9 in N7 only in R7C1 + R89C3
3a. 45 rule on N7 3 innies R7C1 + R89C3 = 21 = {489/579}, no 1,2,3,6,clean-up: no 1 in R1C3 (step 2)
3b. R9C12 = {18/27/36} (cannot be {45} which clashes with R7C1 + R89C3), no 4,5

4. 18(5) cage at R1C3 = {12348/12357/12456}, 1 locked for C4

5. 45 rule on N1 2 outies R4C23 = 1 innie R1C3 + 6, IOU no 6 in R4C2

6. 45 rule on R6789 2 outies R5C67 = 9 = {18/27/36/45}, no 9

7. 45 rule on R1 2 innies R1C34 = 1 outie R2C1 + 2
7a. Min R2C1 = 4 -> min R1C34 = 6, no 1 in R1C4

[Don’t know whether this step can be described as locking-out cages; it’s more complex than what is usually considered by that description.]
8. Hidden killer pair 4,9 in R9C34567 and R9C89 for R9, R9C89 must have both or neither of 4,9 -> R9C34567 must have both or neither of 4,9 -> R7C1 + R89C3 (step 3a) = {579} (only remaining combination, cannot be {489} because R89C3 = {49} prevents both of 4,9 in R9C34567), locked for N7, 5 also locked for C3 and 37(8) cage at R8C3, no 5 in R8C56 + R9C4567, clean-up: no 3 in R1C3 (step 2), no 2 in R7C23, no 1,3 in R8C12, no 2 in R9C12
8a. Naked pair {26} in R8C12, locked for R8 and N7, clean-up: no 1 in R7C23, no 3 in R9C12
8b. Naked pair {34} in R7C23, locked for R7
8c. Naked pair {18} in R9C12, locked for R9, clean-up: no 5 in R9C89

9. R9C3 = 5 (hidden single in R9)
9a. 37(8) cage at R8C3 = {12345679}, 6 locked for R9, clean-up: no 7 in R9C89
9b. Naked pair {49} in R9C89, locked for R9 and N9
9c. Naked triple {2367} in R9C4567, locked for 37(8) cage -> R8C3 = 9, R7C1 = 7, R1C3 = 2 (step 2), R8C56 = {14}, locked for R8 and N8, clean-up: no 7 in R1C89
9d. R1C3 = 2 -> R4C23 (step 5) = 8 = [17/26/53/71], no 4,8, no 3 in R4C2

10. 15(4) cage at R6C9 = {1257/1347/1356} (cannot be {1239/1248/2346} because R8C89 only contain 3,5,7,8), no 8,9
10a. R8C89 = {357} -> R67C9 = {12/14/16}, 1 locked for C9, clean-up: no 8 in R1C8
10b. 13(3) cage at R3C9 = {238/247/256/346}, no 9

11. 8 in N9 only in R7C78 + R8C7, locked for 33(7) cage at R5C6, no 8 in R5C67 + R6C78, clean-up: no 1 in R5C67 (step 6)
11a. 33(7) cage = {1234689/1245678}, CPE no 4 in R5C9

12. R1C34 = R2C1 + 2 (step 7), R1C3 = 2 -> R1C4 = R2C1, no 3,7 in R1C4, no 9 in R2C1
12a. 21(3) cage at R1C1 = {489/579/678}
12b. 5 of {579} must be in R2C1 -> no 5 in R1C12
12c. 7 of {678} must be in R1C2 -> no 6 in R1C2
12d. 21(3) cage at R1C1, R1C4 = R2C1 -> R1C124 = 21 = {489/579/678}

13. 5,8,9 in N8 only in R7C456 + R8C4, 22(4) cage at R6C4 cannot contain all of 5,8,9 -> R7C6 = {589}, no 5,8,9 in R6C4

14. 45 rule on N8 2(1+1) remaining outies R6C4 + R9C7 = 1 innie R7C6
14a. R7C6 = {589} -> R6C4 + R9C7 = {23/26/27/36}, no 4 in R6C4

15. 45 rule on C1234 2 remaining innies R59C4 = 1 outie R7C5 + 7, IOU no 7 in R5C4
[I ought to have taken this step further, but only did so in step 22.]

16. 11(3) cage at R3C1 = {128/137/146/236/245}
16a. 2 of {245} must be in R4C2 -> no 5 in R4C2, clean-up: no 3 in R4C3 (step 9d)

17. 23(4) cage at R6C1 contains 7 = {2678/3479/3578} (cannot be {1679} which clashes with R4C23, cannot be {2579} because no 2,5,9 in R6C3), no 1
17a. 1 in R6 only in R6C789, locked for N6
17b. 22(3) cage at R6C5 = {589/679}
17c. 5 of {589} must be in R6C56 (R6C56 cannot be {89} which clashes with 23(4) cage), no 5 in R7C6

18. 45 rule on N2 4(2+2) remaining outies R12C7 + R4C46 = 13
18a. Min R4C46 = 4 (cannot be {12} which clashes with R4C23) -> max R12C7 = 9, no 9

19. 45 rule on C9 3 outies R189C8 = 1 innie R2C9 + 5
19a. Min R189C8 = 8 -> min R2C9 = 3
19b. 9 in C9 only in R29C9
19c. R189C8 cannot total 14 with 9 in R9C8 -> no 9 in R2C9
[Maybe this step is better expressed as R18C8 cannot total 5 -> R9C8 not equal to R2C9, 9 in R9C89 -> no 9 in R2C9. I don’t know whether this is one of Ed’s IOE steps.]

20. R9C9 = 9 (hidden single in C9), R9C8 = 4, clean-up: no 5 in R1C9
20a. 45 rule on C9 2 outies R18C8 = 1 innie R2C9 + 1
20b. R18C8 cannot total 5,7 -> no 4,6 in R2C9
20c. 9 in N3 only in R2C8 + R3C78, locked for 29(5) cage at R2C8, no 9 in R4C7

21. 19(4) cage at R2C2 = {1369/1378/1468/1567} (cannot be {1459} because 5,9 only in R2C2, cannot be {3457} which clashes with R7C3)
[Please feel free to ignore steps 21a and 21b; the same result is obtained in step 28.]
21a. Variable hidden killer triple 3,4,5 in 21(3) cage at R1C1, 19(4) cage and R3C12 for N1, 21(3) cage cannot contain both of 4,5, 19(4) cage contains one of 3,4,5 -> R3C12 must contain at least one of 3,4,5
21b. 11(3) cage at R3C1 = {137/146/236/245} (cannot be {128} which doesn’t contain any of 3,4,5), no 8

22. R59C4 = R7C5 + 7 (step 15)
22a. R7C5 = {25689} -> R59C4 = 9,12,13,15,16 = [27/57/93/67/87/96/97] (cannot be {36} which clash with 18(5) cage at R1C3), no 3,4 in R5C4, no 2 in R9C4
[Thanks Ed for pointing out that I’d overlooked [93]; maybe I got distracted when I eliminated {36}.]

23. 4 in C4 only in 18(5) cage at R1C3 = {12348/12456}, no 7
23a. 5 in N8 only in R7C45 + R8C4 -> 22(4) cage at R6C4 = {2569/2578} (cannot be {3568} which clashes with 18(5) cage, ALS block), no 3
23b. 3 in N8 only in R9C456, locked for R9
[The rest of step 23 and the next few steps don’t work until 3 has been eliminated from R9C4. I’ve now gone directly to my original step 28, which is now step 24; then re-worked using several of my original steps.]

24. 45 rule on N5 4 innies R4C46 + R5C6 + R6C4 = 1 outie R7C6 + 5
24a. R7C6 = {89} -> R4C46 + R5C6 + R6C4 = 13,14 must either contain 1 in R4C46, locked for R4 => R4C23 (step 9d) = [26] or R4C46 + R5C6 + R6C4 = {2345} => R6C4 = 2
-> 23(4) cage at R6C1 (step 17) = {3479/3578}, no 2,6, 3 locked for R6 and N4
[I tried to find a simpler way but once I’d spotted this step it was so powerful that I couldn’t resist it. The rest is fairly straightforward.]

25. 22(3) cage at R6C5 = {589/679}
25a. 9 of {589/679} must be in R7C6 (R6C56 cannot be {59} which clashes with 23(4) cage at R6C1) -> R7C6 = 9
25b. 22(4) cage at R6C4 (step 23a) = {2578} (only remaining combination), no 6, 7 locked for C4
25c. 6 in N8 only in R9C456, locked for R9

26. R5C4 = 9 (hidden single in C4), clean-up: no 6 in R4C8

27. R1C5 = 9 (hidden single in C5), R1C67 = 4 = {13}, locked for R1, clean-up: no 6,8 in R1C89, no 4,5 in R2C1 (step 12)

28. Naked pair {68} in R12C1, locked for C1 and N1 -> R1C2 = 7, R9C12 = [18]
[Clean-ups omitted, unless required]

29. R2C2 = 9 (hidden single in N1) -> R234C3 = 10 = {136} (only remaining combination) -> R4C3 = 6, R23C3 = {13}, locked for C3 -> R7C23 = [34], R56C3 = [78]
29a. Naked pair {45} in R3C12, locked for R3, R4C2 = 2 (cage sum)

30. R6C1 = 3 (hidden single in N4), R6C2 = 5 (cage sum), R5C12 = [41], R4C1 = 9
30a. Naked pair {67} in R6C56, locked for R6 and N5 -> R6C4 = 2, R6C789 = [491]
30b. Naked pair {58} in R7C45, locked for R7 and N8 -> R8C4 = 7, R8C89 = [35], R7C9 = 6 (cage sum), R8C7 = 8

31. R45C8 = {78} (only remaining combination) -> R4C8 = 7, R5C8 = 8, R45C9 = [32], R3C9 = 8 (cage sum), R4C7 = 5, R5C7 = 6, R5C6 = 3 (cage sum), R5C5 = 5, R4C5 = 4 (cage sum)

32. R7C45 = [58] -> 18(5) cage at R1C3 (step 23) = {12348} (only remaining combination), 3 locked for C4 -> R9C4 = 6, R1C4 = 8, R234C4 = [431]

33. R23C5 = {27} (only remaining combination), locked for C5 and N2

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A250 at Hard 1.5.

I'll guess that Sudoku Solver's high score is because it can't find the early break-in step.
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Ed
 Post subject: Re: Assassin 250
PostPosted: Thu Nov 29, 2012 9:05 am 
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Joined: Wed Apr 16, 2008 1:16 am
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Location: Sydney, Australia
Glad you enjoyed this monster guys....and won't do it again to you for a while. Really enjoyed Andrew's start. He saw the key way to get into the puzzle very differently to me. Take your pick. Then we basically followed the same path until the middle but then veered apart. Looks like my step 15 is the difference until we came back together again very quickly. Good to have a couple of ways to crack this one. [Thanks Andrew for some typos and noticings]

Assassin 250
20 steps:
1. n7: 7(2) no 7,8,9; 8(2) no 4,8,9; 9(2) no 9
1a. "45" on n7: 3 innies r7c1+r89c3 = 21 and must have 9 for n7
1b. = {489/579}(no 1,2,3,6)

2. 37(8)r8c3: no 8
2a. r8c3 sees all of r9 except r9c89 -> must be one of 13(2) -> r89c3 cannot sum to 13 -> no 8 in r7c1 (h21(3)n7) (combo Crossover Clash - CCC)

3. h21(3)n7 = {579} only: 5 & 7 locked for n7
3a. 8(2) = {26} only: locked for r8 and n7
3b. 7(2) = {34} only: locked for r7 and n7
3c. 9(2) = {18} only: locked for r9

4. "45" on r9: 3 outies r8c356 = 14
4a. = {149/347}(no 5)
4b. must have 4 which is only in n8: 4 locked for n8 and for 37(8)
4c. no 4 in r9c7

5. 4 in r9 only in 13(2)n9 = {49} only: both locked for n9 and 9 for r9

6. 1 and 4 must be in 37(8)r8c3 -> hidden pair 1,4 -> r8c56 = {14}
6a. 1 locked for n8 and r8
6b. r8c56 = 5 -> r8c3 = 9 (h14(3)r8c356)

7. "45" on n14: 1 innie r1c3+5 = 1 outie r7c1 = [27] only
7a. r9c3 = 5

8. 18(5)r1c3 = {12348/12357/12456}(no 9): must have 1: 1 locked for c4

9. r7c1 = 7 -> r6c123 = 16 = {169/259/268/349/358} = [8/9..] (no eliminations yet)
9a. 22(3)r6c5 = {589/679}(no 1,2,3,4)
9b. but {89}[5] blocked by r6c123 = [8/9..]
9c. no 5 in r7c6

10. 5 in n8 in 22(4)r7c4 only
10a. no 5 in r6c4
10b. 22(4) must have 5 = {2569/2578/3568/4567}
10c. can't have both 8 & 9 (no eliminations yet)

11. Hidden killer pair 8,9 in n8 -> r7c6 = (89)
11a. 22(4)r6c4 must have 8 or 9 = {2569/2578/3568}(no 4)
11b. r7c45+r8c4 must have one of 8 or 9 -> no 8 or 9 in r6c4

12. 2 in r1c3 and 18(5) must have 1 -> other three cells = 15 = {348/357/456} = [3]/{56}
12a. 22(4)r6c4 = {2569/2578/3568}: but {3568} clashes with r1234c4 since it must have 3 in c4 and at least one of 5 or 6 in c4
12b. 22(4) = {2569/2578}(no 3)

13. 15(4)r6c9 must have two of {3578} for r8c89
13a. -> {1239} blocked
13b. = {1239/1257/1347/1356}(no 8) [This also locks 1 for c9 but is not essential to get to the breakthrough]
13c. cannot have three of 3,5,7,8 -> no 3,5,7 in r6c9

14. 8 in n9 only in 33(7)r5c6: locked for 33(7)
14a. no 8 in r5c67+r6c78
14b. 33(7) must have 8 = {1234689/1245678}: ie must have each of 1,2,4 & 6

15. "45" on r6789: 2 outies r5c67 = 9 = {27/36/45}(no 1,9) = [2/4/6..]
15a. r5c67 = 9 -> r67c78+r8c7 = 24 and must have both 1 & 8 and two of 2, 4 or 6 for 33(7) (step 14b)
15b. h24(5) = {12489/12678/14568}(no 3)

16. 3 in r6 only in h16(3)r6c123
16a. = {349/358}(no 1,2,6) = [5/9..]

17. 22(3)r6c5 = {589/679}
17a. but {59}[8] blocked by r6c123 = [5/9..]
17b. no 8 in r7c6
17c. r7c6 = 9
17d. 22(4)r6c4 = {2578} only
17e. 7 locked for c4

18. 9(2)n2: no 9
18a. Hidden single 9 in n2 in r1c5
18b. r1c5 = 9
18c. r1c67 = 4 = {13} only: both locked for r1
18d. 9(2)n3 = {45} only: both locked for r1 and n3

19. "45" on r1: 1 outie r2c1 = 1 remaining innie r1c4
19a. r2c1 = (68)
[Andrew noticed that r1c2 = 7 (hidden single for r1) -> r12c1 = {68} at this point so 20 is redundant]

20. 21(3)n1 = {678} only
20a. r1c2 = 7
20b. r12c1 = {68}: both locked for c1 and n1

on from there.
Cheerio
Ed
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