Official Unofficial Assassin 100

[mhparker]

Hi folks,

Well, we made it! 100 Assassins notched up. Bring on the fireworks! To celebrate in style, this Assassin is a bit tougher than usual. Your creativity is called for.

(Unofficial) Assassin 100 (UA100) (Est. rating: 1.5)



3x3::k:7168:7168:7168:5891:5891:5891282271685643:5643:5643:5891:4367:6160:6160:53943604:56431303:43676160:53943604:56431303:43676160:5394:5394115421154231155165414311542:721854285165414311542:721854285165:5165:4143:4930:7218:7218:7218:542836563656:4930:4930:49303911

Solution:

7 4 9 8 1 5 2 3 6
8 1 2 6 3 9 4 5 7
3 5 6 7 2 4 8 1 9
6 2 8 4 7 1 5 9 3
5 7 1 3 9 8 6 2 4
9 3 4 2 5 6 7 8 1
1 8 7 9 4 2 3 6 5
4 6 5 1 8 3 9 7 2
2 9 3 5 6 7 1 4 8

SudokuSolver v3.0 scores this at 1.41, so it can't be that difficult...

P.S. Could this be my last puzzle on sudocue.net?

[Afmob]

What a tough Killer! It reminded me of Maverick 1 because of the use of (standard) Sudoku techniques (apart from step 6a which also uses cage properties) to crack it though UA 100 was a bit tougher.

UA 100 Walkthrough:

1. R123
a) Outies R1 = 17(2) = {89} locked for R2
b) 28(4) = 89{47/56} -> 8,9 locked for N1
c) 14(2) = [59/68]
d) 28(4) = {4789} because R3C3 = (56) blocks {5689} -> 4,7 locked for R1+N1
e) 11(3) = 2{18/36} -> 2 locked for R1+N3
f) 23(4) = 59{18/36} -> 5,9 locked for N2
g) 10(2): R4C8 <> 8
h) 8(3) = 1{25/34} -> 1 locked for C2

2. R789
a) Outies R9 = 3(2) = {12} locked for R8
b) 12(4) = 12{36/45} -> R5C8 = (12) because R8C9 = (12) blocks 2 of (12) in R567C9
c) Killer pair (12) locked in 12(4) + R8C9 for C9

3. C789
a) Innies = 15(2) = {69/78}
b) Outies C89 = 3(2) = {12} locked for C7
c) 10(2) @ C7 <> 8,9
d) 5 locked in 17(3) @ C7 = 5{39/48}
e) 15(4) = 12{39/48/57} <> 6 because R8C9+R9C7 = {12} -> 1,2 locked for N9; R9C8 <> 1,2
f) 12(4) = 12{36/45} -> 1,2 locked for N6
g) 10(2) @ N3: R3C8 <> 8,9

4. C123
a) Innies = 3(2) = {12} locked for C3
b) Outies C12 = 12(2): R9C3 = (3458)
c) 1 locked in R79C1 for C1
d) Killer pair (12) locked in R2C3+8(3) for N1 because R23C2 can't be {35}

5. R5
a) Naked pair (12) locked in R5C38 for R5
b) 12(4) = 12{36/45} -> R6C9 = (12)

6. N6+R789 !
a) ! Consider candidates of R5C8 = (12) -> R234C4 <> 1,2
- i) R5C8 = 1/2 -> R5C3 = 2/1 -> R2C3 @ 22(5) = 1/2 -> R234C4 @ 22(5) <> 1/2
- ii) R5C8 = 1/2 -> R6C9 = 2/1 -> R8C9 = 1/2 -> R8C4 = 2/1 -> R234C4 <> 2/1
-> So all in all R2C3+R8C4 = {12}
b) Colouring 1 in N6 -> R1C4 <> 1
- i) R5C8 = 1 -> R1C7 = 1 (HS @ N3) -> R1C4 <> 1
- ii) R6C9 = 1 -> R8C4 = 1 (HS @ R8) -> R1C4 <> 1
c) 1 locked in R89C4 for N8
d) Hidden Single: R7C1 = 1 @ R7
e) ! Colouring 2 in C9 -> R9C7 <> 2:
- i) R6C9 = 2 -> R5C3 = 2 (HS @ R5) -> R9C1 = 2 (HS @ C1) -> R9C7 <> 2
- ii) R8C9 = 2 -> R9C7 <> 2
f) R9C7 = 1, R8C9 = 2, R6C9 = 1, R5C8 = 2, R5C3 = 1, R2C3 = 2

7. N12
a) Hidden Single: R4C6 = 1 @ N5 -> R3C6 = 4, R3C5 = 2 @ N2
b) Outies N2 = R4C4 = 4
c) 8(3) = {125} -> R4C2 = 2, R23C2 = {15} locked for C2+N1
d) R3C3 = 6 -> R4C3 = 8, R3C1 = 3

8. C1234
a) Outies C12 = 12(2) = [75/93]
b) Hidden Single: R9C1 = 2 @ C1
c) 14(3) = 2[75/93]
d) 11(2) = [38/47/74]
e) 21(4) = 35{49/67} -> 5 locked for C1+N4
f) 6 locked in 20(4) @ N7 = {1469} for R8; R6C1 <> 6

9. R789
a) Hidden Single: R7C5 = 4 @ 45(9)
b) 4 locked in 15(4) @ R9 = {1248} -> {48} locked for R9+N9
c) 21(3) = 7{59/68} because R78C8 <> 4,8 -> 7 locked for C8
d) R3C8 = 1 -> R4C8 = 9
e) 21(3) = {678} -> R8C8 = 7, R7C8 = 6, R6C8 = 8
f) R8C7 = 9
g) 28(5) = {23689} -> R6C6 = 6, R7C6 = 2; {38} locked for R8+N8

10. Rest is singles.

Rating: 1.5. I used colouring thrice.

[gary w]

A nice puzzle involving,as it did,lots of 1/2 combos.
Many thanks Mike.

Many regards

Gary

P.S.Hopefully the number of people enjoying the assassin is not reflected in the number of replies.

[mhparker]

Thanks, Gary.

BTW, don't forget to sign up at http://www.rcbroughton.co.uk/sudoku/forum, as we are planning to publish all further Assassins there.

If anyone else reading this wants to join us there, please register. The more the merrier, and you can help shape the site!

[zoltag]

I tried his software and I don't like it for clueless.

I may have to switch but I don't think it will be soon.

Does it work well for assassins? ( I haven't tried them.)

[Afmob]

Though this software talk is a bit off-topic, I'll give you my opinion on SudokuSolver.

If you want to let the software solve the Assassin for you then SudokuSolver is the best software I know (I use SumoCue, JSudoku and SudokuSolver on my computer) and it's usually getting better with lots of updates still to come.
But if you want to solve Assassins by yourself then I'll recommend SumoCue since it's simple but functional and of all three programms I use, it's the easiest the make eliminations with. Though it lacks a nifty feature which SS possesses - saving your grid state which is really helpful for tough Killers you can't solve in one session. If SumoCue would have got this feature, then it would be the one software for solving Assassins.

But like I said for getting information on how to solve the Assassin SudokuSolver is the best software I know.

[Andrew]

If you want to solve Assassins by yourself then I can recommend using an Excel worksheet as an electronic paper and pencil, with Ruud's combination calculator as an excellent aid. Most Assassins are too hard for genuine paper and pencil solving.

I've never understood why people solving Assassins use software solvers. I hope they are being used in such a way that the software solver is only being used as an electronic editor and not taking away the human thinking necessary to work out clashes of combinations between cages which IMHO is part of the solving process.

One thing I will really miss if this site disappears is Ruud's combination calculator. It has just the right balance, allowing one to specify required and forbidden numbers and presenting all valid combinations in a neat row, but leaving analysis of clashes to the solver.

Software solvers clearly have value for those creating puzzles, for giving a software rating and for finding out how to solve a puzzle if one has given up.

[Andrew]

Getting back on topic, I finished uA100 last night and went through Afmob's walkthrough today.

Thanks Mike for a really challenging puzzle. At one time I thought I wasn't going to manage to solve it. I mostly used conventional killer steps with interesting combination analysis in C89 which I felt was the key area in this puzzle. I found the contradiction move in step 35 after looking at the combinations in the 20(4) cage at R6C1 and thinking that it would be helpful if there were only two candidates in R8C7.

I'll rate uA100 at 1.5. It was hard work until the 5th placement but then crumbled.

Here is my walkthrough. Thanks Afmob for pointing out typos and an incorrect elimination; I've reworked the steps after that which fortunately was easy .

Prelims

a) R34C3 = {59/68}
b) R34C6 = {14/23}
c) R34C8 = {19/28/37/46}, no 5
d) R67C2 = {29/38/47/56}, no 1
e) R67C4 = {29/38/47/56}, no 1
f) R67C7 = {19/28/37/46}, no 5
g) R1C789 = {128/137/146/236/245}, no 9
h) R234C2 = {125/134}, 1 locked for C2
i) R678C8 = {489/579/678}, no 1,2,3
j) 28(4) cage in N1 = {4789/5689}, 8,9 locked for N1, clean-up: no 5,6 in R4C3
k) 12(4) cage at R5C8 = {1236/1245}, CPE no 1,2 in R4C9

1. 45 rule on R1 2 outies R2C16 = 17 = {89}, locked for R2
1a. 9 in N3 locked in R3C789, locked for R3

2. 28(4) cage in N1 = {4789} (cannot be {5689} which clashes with R3C3), locked for N1
2a. 4,7 locked in R1C123, locked for R1

3. 45 rule on R9 2 outies R8C49 = 3 = {12}, locked for R8

4. 45 rule on C12 2 outies R19C3 = 12 = {48}/[75/93], no 1,2,6,7,9 in R9C3

5. 45 rule on C123 2 innies R25C3 = 3 = {12}, locked for C3
5a. 1 in N7 locked in R79C1, locked for C1

6. R234C2 = {125/134}
6a. 4 of {134} must be in R4C2 -> no 3 in R4C2
6b. 5 of {125} must be in R23C2 (R23C2 cannot be {12} which clashes with R2C3) -> no 5 in R4C2

7. Hidden killer triple 3,5,6 in R23C2, R3C1 and R3C3 -> R3C1 = {356}
7a. 6 in N1 locked in R3C13, locked for R3, clean-up: no 4 in R4C8

8. R678C3 = {349/367/457} (cannot be {358} which clashes with R34C3), no 8

9. 45 rule on C89 2 outies R19C7 = 3 = {12}, locked for C7, clean-up: no 8,9 in R67C7

10. Naked pair {12} in R8C9 + R9C7, locked for N9
10a. 15(4) cage at R8C9 = {1239/1248/1257}, no 6

11. 12(4) cage at R5C8 = {1236/1245}, 1,2 locked for N6, clean-up: no 8,9 in R3C8
11a. R5C89 must contain one of 1,2 (R5C89 cannot be {12} which clashes with R5C3) -> R6C9 = {12}
11b. Naked pair {12} in R68C9, locked for C9 -> R5C8 = {12} (step 11a)
11c. Naked pair {12} in R5C38, locked for R5

12. 45 rule on C789 2 innies R58C7 = 15 = {69/78}

13. 5 in C7 locked in R234C7 = {359/458}, no 6,7
[Alternatively killer pair 6,7 in R58C7 and R67C7, locked for C7]

14. 45 rule on C8 4 innies R1259C8 = 14 = {1238/1256/1346/2345} (cannot be {1247} which clashes with R678C8), no 7,9, clean-up: no 3,5 in R9C9 (step 10a)

15. R1C789 = {128/236}, no 5, 2 locked for R1 and N3, clean-up: no 8 in R4C8
15a. 8 of {128} must be in R1C9 -> no 8 in R1C8

16. 5 in R1 locked in R1C456, locked for N2

17. 45 rule on N3 3 outies R4C789 = 17 = {359/368/467} (cannot be {458} because R4C8 only contains 3,6,7,9)
17a. 4 of {467} must be in R4C7 -> no 4 in R4C9

18. 24(4) cage at R2C8 = {3579/4569/4578} (cannot be {1689} because 1,6 must be in R2C89 clashing with R1C789, cannot be {3489/3678} which clash with R1C789 which cannot be {128} when 8 in R34C9), no 1
18a. 6 of {4569} must be in R2C8 (R234C9 = {469/569} clash with 12(4) cage in R5C8) -> no 6 in R24C9

19. R4C789 (step 17) = {359/368/467}
19a. 6 of {467} must be in R4C8 -> no 7 in R4C8, clean-up: no 3 in R3C8

20. R1259C8 (step 14) = {1238/1256/2345} (cannot be {1346} which clashes with R34C8)
20a. 1,2 of {1256} must be in R15C8 -> no 6 in R1C8
20b. 8 of {1238} must be in R9C8, 3 of {2345} must be in R1C8 -> no 3 in R9C8, clean-up: no 9 in R9C9 (step 10a)
20c. 3 in N9 locked in R7C79, locked for R7, clean-up: no 8 in R6C2, no 8 in R6C4

21. R1C789 = {128/236}
21a. 6,8 only in R1C9 -> R1C9 = {68}

22. 9 in C9 locked in R34C9 -> 24(4) cage at R2C8 (step 18) = {3579/4569}, no 8
22a. 6 in N3 must be in R2C8 or R1C9
22b. 3 of {3579} must be in R234C9 (R234C9 cannot be {579} because R1C9 = 6 and R1234C9 clash with 12(4) cage at R5C8) -> no 3 in R2C8
22c. 6 of {4569} must be in R2C8 (step 18a) -> no 4 in R2C8

23. R1259C8 (step 20) = {1256/2345} (cannot be {1238} because R2C8 only contains 5,6), no 8, clean-up: no 4 in R9C9 (step 10a)
23a. 5 locked for C8

24. R34C8 = [19/73] (cannot be [46} which clashes with R1259C8), no 4,6

25. R4C789 (step 17) = {359} (only remaining combination), locked for R4 and N6 -> R4C3 = 8, R3C3 = 6, clean-up: no 4 in R19C3 (step 4), no 2 in R3C6, no 7 in R7C7, no 4,6 in R7C9 (step 11), no 6 in R8C7 (step 12)
25a. 8 in R5 locked in R5C4567, locked for 45(9) cage -> no 8 in R367C5

26. R9C123 = {239/257/356} (cannot be {149/167/248} because R9C3 only contains 3,5, cannot be {158/347} which clash with 15(4) cage at R8C9), no 1,4,8

27. R7C1 = 1 (hidden single in C1)

28. 45 rule on N7 3 outies R6C123 = 16 = {259/349/367/457}

29. 21(4) cage at R3C1 = {3459/3567} (cannot be {2379} which clashes with R6C123, cannot be {2469} because R3C1 only contains 3,5), no 2, CPE no 3,5 in R6C1
29a. 4 of {3459} must be in R4C1 -> no 4 in R5C12

30. 45 rule on N9 2 outies R6C78 = 2 innies R7C9 + R8C7 + 1
30a. R7C9 + R8C7 = 10,11,12,13,14 -> R6C78 = 11,12,13,14,15
30b. Only combinations for R6C78 including 4 are {47/48}
30c. R7C9 + R8C7 = 10 = [37] -> R6C78 = 11 = [47]
30d. R7C9 + R8C7 = 11 -> R6C78 = 12 = [48]
30e. -> no 4 in R6C8

31. 4 in C8 locked in R789C8, locked for N9, clean-up: no 6 in R6C7

32. R678C8 = {489/678}
32a. 6 of {678} must be in R78C8 (R78C8 cannot be {78} which clashes with R9C9) -> no 6 in R6C8
32b. 6 in N6 locked in R5C79, locked for R5

33. 21(4) cage at R3C1 (step 29) = {3459/3567}
33a. 6 of {3567} must be in R4C1 -> no 7 in R4C1
33b. 7 in R4 locked in R4C45, locked for N5, clean-up: no 4 in R7C4
[Afmob pointed out that 7 in C6 is now locked in R789C6 for N8.]

34. 9 in N2 locked in 23(4) cage at R1C4 = {1589/3569}
34a. Hidden killer pair 6,8 in 23(4) cage and 22(5) at R2C3 for N2 -> 22(5) cage at R2C3 must contain one of 6,8 within N2 and can also contain 6 in R4C4
34b. 22(5) cage at R2C3 = {12478/13468/23467}
34c. 8 of {12478} must be in R3C4, 2 of {23467} must be in R2C3 -> no 1,2 in R3C4

35. R8C7 cannot be 7, here’s how
35a. R8C7 = 7 => R9C9 = 8, R9C8 = 4 (step 10a) => R678C8 = {678} clashes with R8C7 + R9C9
35b. -> no 7 in R8C7, clean-up: no 8 in R5C7 (step 12)
35c. 8 in R5 locked in R5C456, locked for N5

36. R6C8 = 8 (hidden single in R6)

37. 20(4) cage at R6C1 = {1379/1469/1478/1568} (cannot be {1289} which clashes with R8C7), no 2

38. R9C1 = 2 (hidden single in C1), R9C7 = 1, R8C9 = 2, R8C4 = 1, R1C7 = 2, R6C9 = 1, R5C8 = 2, R5C3 = 1, R2C3 = 2, clean-up: no 9 in R6C2
38a. R4C6 = 1 (hidden single in R4), R3C6 = 4

[Re-worked from here.]

39. R3C5 = 2 (hidden single in R3)

40. 22(5) cage at R2C3 (step 34b) = {12478/23467} -> R4C4 = 4, R4C12 = [62], R4C5 = 7, R5C7 = 6 [Nearly missed that one with my manual elimination!], R5C9 = 4, R67C7 = [73], R7C9 = 5, R9C8 = 4, R9C9 = 8, R8C7 = 9, R4C7 = 5, R23C7 = [48], R1C9 = 6, R1C8 = 3 (step 21), R2C89 = [57], R3C89 = [19], R4C89 = [93], clean-up: no 6 in R6C4, no 4,9 in R7C2, no 7 in R7C4
40a. R4C2 = 2 -> R23C2 = [15] (step 6), R3C1 = 3, R3C4 = 7, clean-up: no 6 in R7C2

[Back to my original steps now, renumbered after inserting some extra steps. I’ve also split the next two into separate steps because they aren’t connected.]

41. R7C5 = 4 (hidden single in 45(9) cage)

42. R6C46 = [26] (hidden pair in R6), R7C4 = 9, R7C23 = [87], R7C6 = 2, R78C8 = [67], R6C2 = 3, R1C3 = 9, R2C16 = [89]

43. R9C6 = 7 (hidden single in C6), R8C4 + R9C6 = 8 -> R9C45 = 11 = {56}, locked for R9 and N8 -> R9C23 = [93], R5C2 = 7, R1C12 = [74], R8C2 = 6, R5C1 = 5 (step 29)

and the rest is naked singles