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 Post subject: Assassin 278
PostPosted: Thu Dec 05, 2013 9:30 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Had to keep mucking around with the cage pattern to get this one just right. Really like the wave cages - must be ready for summer. It gets a score of 1.65. I used one advanced step.

Assassin 278

Image

code: paste into solver:
3x3::k:6400:2817:5378:5378:3843:4356:4356:3333:3333:6400:2817:5378:5378:3843:4356:4356:3846:2311:6400:6400:5378:4872:3843:3593:3846:3846:2311:1546:1546:4872:4872:8203:3593:3593:2060:2060:3853:3853:7694:7694:8203:8203:3593:3855:3855:5648:7697:7697:7694:7694:8203:8203:3602:3602:5648:5648:7697:7697:7694:7694:4371:4371:3602:8212:5648:8212:7697:7697:7694:4371:6421:3602:8212:8212:8212:8212:7697:6421:6421:6421:6421:
solution:
+-------+-------+-------+
| 3 7 1 | 5 2 8 | 6 4 9 |
| 5 4 6 | 7 9 1 | 2 3 8 |
| 9 8 2 | 3 4 6 | 5 7 1 |
+-------+-------+-------+
| 1 5 7 | 9 8 4 | 3 2 6 |
| 6 9 4 | 2 5 3 | 1 8 7 |
| 8 2 3 | 1 6 7 | 9 5 4 |
+-------+-------+-------+
| 7 1 5 | 8 3 9 | 4 6 2 |
| 2 6 8 | 4 1 5 | 7 9 3 |
| 4 3 9 | 6 7 2 | 8 1 5 |
+-------+-------+-------+
Cheerio
Ed


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 Post subject: Re: Assassin 278
PostPosted: Mon Dec 09, 2013 5:33 pm 
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Grand Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thanks Ed - I didn't find this one as difficult as the score suggests. One breakthrough opened it up pretty quickly.

Errors corrected thanks to Andrew's eagle eyes!
Hidden Text:
1. Outies - Innies r1234 -> r4c5 = r5c7 + 7
-> (r4c5,r5c7) from [81] or [92]

2. Innies r5 -> r5c34567 = {12345}

3. In 32/5@r4c5: Max r4c5+r6c67 = +24 -> Min r5c56 = +8
-> r5c56 from {35} or {45}

Whichever pair it is - those two numbers must also go somewhere in the 30/7@r5c3
-> one in r7c5 and the other in r78c6

-> Those 2 numbers must go in r123c4 in n2

4. Outies n1 -> r12c4 = +12
Outies n3 -> r12c6 = +9
-> Innies n2 -> r3c46 = +9

-> Those two numbers ((35) or (45)) cannot go both in r12c4
-> One of them must go in r3c4.

-> (45) cannot both go in r123c4 since either of them in r3c4 would put the other in r3c6

-> r5c56 = {35}
-> r4c5,r6c67 = {789} with 7 in r6c67

5. 30/7@r5c3 is {12345(69|78)}
But r5c34 = {14} or {24}
and r6c45 is buddies with the (789) in the 32/5@r4c5
and (r7c5,r78c6) already contains a (35)
-> No place for both a 7 and a 8.
-> 30/7@r5c3 = {1234569} with 9 in r78c6 and 6 in r6c45.

6. r3c4 from (35)
But putting r3c4 = 5 puts r4c34 = [68] and r12c4 = {39}
which leaves no solution for innies n1 r123c3 = +9.

-> r3c4 = 3
-> r12c4 = {57}
Also -> r3c6 = 6
-> r12c6 = {18}
-> 15/3@r1c5 = {249}
Also r4c34 = [79]
-> r4c5 = 8
-> r5c7 = 1
-> r5c34 = {24}
-> 6/2@r4c1 = {15}
-> 8/2@r4c8 = {26}
-> 15/2@r5c8 = {78}
-> 15/2@r5c1 = {69}
Also r6c67 = [79]
Also r4c67 = [43]
-> r5c34 = [42]
-> r123c3 = {126}

Also r6c89 = {45}
-> Outies n9 -> r9c6 = 2
Also HS 5 in 30/7@r6c2 -> r7c3 = 5
-> HP (23) in 30/7@r6c2 -> r6c23 = [23]
etc.

CPFC now 4-1-10!


Last edited by wellbeback on Fri Dec 13, 2013 8:10 am, edited 1 time in total.

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 Post subject: Re: Assassin 278
PostPosted: Fri Dec 13, 2013 5:01 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin!

Ed wrote "Really like the wave cages - must be ready for summer":
Not here, it isn't. ;) This photo was taken of our deck about a week ago. The thermometer on next door's shed is showing about -15C, which was warm for those days of very cold weather.

Image
I used several of your favourite type of steps, then after getting stuck I found a wellbeback-type step to crack the puzzle.

Here is my walkthrough for Assassin 278:
Prelims

a) R12C2 = {29/38/47/56}, no 1
b) R1C89 = {49/58/67}, no 1,2,3
c) R23C9 = {18/27/36/45}, no 9
d) R4C12 = {15/24}
e) R4C89 = {17/26/35}, no 4,8,9
f) R5C12 = {69/78}
g) R5C89 = {69/78}
h) 19(3) cage at R3C4 = {289/379/469/478/568}, no 1
i) 14(4) cage at R3C6 = {1238/1247/1256/1346/2345}, no 9
j) 14(4) cage at R6C8 = {1238/1247/1256/1346/2345}, no 9
k) 32(5) cage at R4C5 = {26789/35789/45689}, no 1

1. Naked quad {6789} in R5C1289, locked for R5

2. 32(5) cage at R4C5 = {35789/45689} (cannot be {26789} because R5C56 only contain 2,3,4,5), no 2
2a. R5C56 = {35/45} -> no 3,4,5 in R4C5 + R6C67
2b. R5C56 = {35/45}, 5 locked for R5 and N5
2c. 32(5) cage = {35789/45689}, CPE no 8,9 in R6C45

3. 45 rule on R1234 1 innie R4C5 = 1 outie R5C7 + 7, R4C5 = {89}, R5C7 = {12}
3a. 3,4 in R5 only in R5C3456, CPE no 3,4 in R6C45

4. 45 rule on N1 3 innies R123C3 = 9 = {126/135/234}, no 7,8,9
4a. Max R123C3 + R5C3 = 13(4), must contain 1, locked for C3
4b. 45 rule on N1 2 outies R12C4 = 12 = {39/48/57}, no 1,2,6

5. 45 rule on N3 2 outies R12C6 = 9 = {18/27/36/45}, no 9
5a. 45 rule on N3 2 innies R12C7 = 8 = {17/26/35}, no 4,8,9

6. 45 rule on C12 3 outies R8C3 + R9C34 = 1 innie R6C2 + 21
6a. Max R8C3 + R9C34 = 24 -> max R6C2 = 3
6b. Min R8C3 + R9C34 = 22, no 1,2,3,4
6c. Min R8C3 + R9C34 = 22 -> max R8C1 + R9C12 = 10, no 8,9 in R8C1 + R9C12
[Alternatively 45 rule on C12 4(1+3) innies R6C2 + R8C1 + R9C12 = 11 -> max R8C1 + R9C12 = 10, no 8,9 in R8C1 + R9C12]

7. R4C12 = {15/24}, R4C89 = {17/26/35} -> combined cage R4C1289 = {15}{26}/{24}{17}/{24}{35}, 2 locked for R4
7a. 19(3) cage at R3C4 = {379/469/478/568} (cannot be {289} which clashes with R4C5), no 2

8. 45 rule on N7 2(1+1) outies R6C1 + R9C4 = 1 innie R7C3 + 9
8a. Min R7C3 = 2 -> min R6C1 + R9C4 = 11, no 1 in R6C1

9. 45 rule on N9 3(2+1) outies R6C89 + R9C6 = 11
9a. Min R6C89 = 3 -> max R9C6 = 8

10. 45 rule on R123 2 innies R3C46 = 9, no 9 in R3C4
10a. Min R3C3 = 3 -> max R3C6 = 6

11. 30(7) cage at R5C3 = {1234569/1234578}, 5 locked for N8
11a. 30(7) cage at R6C2 = {1234569/1234578}, 5 locked for C3
11b. Caged X-Wing for 5 in 32(5) cage at R4C5 and 30(7) cage at R5C3, no other 5 in C56, clean-up: no 4 in R12C6 (step 5), no 4 in R3C4 (step 10)
[With hindsight 5 in C4 only in R123C4, locked for N2 … is simpler.]

12. R123C3 (step 4) = {126/234}, 2 locked for C3 and N1, clean-up: no 9 in R12C2
12a. R12C2 = {38/47/56}, R123C3 = {126/234} -> combined cage R12C2 + R123C3 = {38}{126}/{47}{126}/{56}{234}, 6 locked for N1
12b. Min R7C3 = 3 -> min R6C1 + R9C4 = 12 (step 8), no 2 in R6C1

13. 2 in N5 only in R5C4 + R6C45, locked for 30(7) cage at R5C3, no 2 in R7C56 + R8C6

14. 32(6) cage at R8C1 cannot contain all four of 6,7,8,9 (because 1,2,6,7,8,9 total 33)
14a. R8C3 + R9C34 = {6789} -> no 6,7 in R8C1 + R9C12

15. 4 in N3 only in R1C89 = {49} or 15(3) cage at R2C8 or R23C9 = {45} -> 15(3) cage cannot be {159} (blocking cages)
15a. 9 in N3 only in R1C89 = {49} or 15(3) cage = {249} (locking cages), 4 locked for N3, clean-up: no 5 in R23C9
15b. 15(3) cage = {168/249/258/267/357} (cannot be {348} because of step 15a, 15(3) cage must contain both or neither of 4,9)

16. 9 in N2 only in R12C4 (step 4b) = {39} or in 15(3) cage at R1C5 = {249} -> 15(3) cage = {168/249/267} (cannot be {348} (blocking cages), no 3
16a. 9 in N2 only in R12C4 = {39} or in 15(3) cage = {249} -> R12C4 = {39/57} (cannot be {48}, locking-out cages), no 4,8 in R12C4
16b. 15(3) cage = {168/249/267}, R12C6 (step 5) = {18/27/36} -> combined cage 15(3) + R12C6 = {168}{27}/{249/267}with rest of R12C6, 2 locked for N2, clean-up: no 7 in R3C4 (step 10)

17. 19(3) cage at R3C4 (step 7a) = {379/469/478/568}
17a. 3 of {379} must be in R3C4 -> no 3 in R4C34

18. 45 rule on C6789 2 innies R78C6 = 2 outies R45C5 + 1
18a. Min R45C5 = 11 -> min R78C6 = 12, no 1 in R78C6

19. 1,2 in 30(7) cage at R5C3 must be in R5C34 + R6C45 (R5C34 + R6C45 cannot contain both of 3,4 which would clash with R5C56, R5C34 + R6C45 cannot contain both of 6,7 because 30(7) cage only contains one of 6,7) -> no 1 in R7C5
19a. One of 1,2 in 30(7) cage must be in R5C34 (R5C34 cannot be {34} which clashes with R5C56) and one in 1,2 must be in R6C45 (because R6C45 cannot contain both of 6,7) -> R6C45 must contain one of 6,7 -> no 6,7 in R7C56 + R8C6 (because 30(7) cage only contains one of 6,7)
19b. Killer pair 6,7 in R6C45 and 32(5) cage at R4C5, locked for R6
19c. Min R78C6 = 12 (step 18a) -> R78C6 must contain one of 8,9 (cannot be both because 30(7) cage only contains one of 8,9) -> no 8,9 in R7C5

20. Variable hidden killer triple 1,2,3 in R4C89, R5C7 and R6C89 for N6, R4C89 contains one of 1,2,3, R5C7 = {12} -> R6C89 cannot contain more than one of 1,2,3 (may contain none of them)
20a. R6C89 + R9C6 = 11 (step 9)
20b. Min R6C89 = 5 (because cannot contain more than one of 1,2,3) -> max R9C6 = 6

21. Hidden killer pair 6,7 in R4C3 and R5C12 for N4, R5C12 must contain one of 6,7 -> R4C3 = {67}
21a. 19(3) cage at R3C4 (step 7a) = {379/478/568} (cannot be {469} because 4,9 only in R4C4)
21b. R4C3 = {67} -> no 6,7 in R34C4, clean-up: no 3 in R3C6 (step 10)
21c. 9 in R4 only in R4C45, locked for N5

22. Hidden killer pair 8,9 in R5C12 and R6C13 for N4, R5C12 must contain one of 8,9 -> R6C13 must contain one of 8,9
22a. Killer pair 8,9 in R6C13 and R6C67, locked for R6

23. 9 in N6 only in R5C89 = {69} or in R6C7 = 9 -> no 6 in R6C7 (locking-out cages)
23a. 6 in R6 only in R6C456, locked for N5

24. 3,4 in R5 only in R5C3456
24a. Whichever of 3,4 is in R5C56 must also be in R7C56 + R8C6 and in R123C4
24b. R123C4 doesn’t contain 4 -> no 4 in R5C56
24c. Naked pair {35} in R5C56, locked for R5 and N5
24d. 4 in R5 only in R5C34, locked for 30(7) cage at R5C3, no 4 in R7C56 and R8C6
24e. 3,5 in 30(7) cage at R5C3 only in R7C56 + R8C6, locked for N8
24d. Killer pair 3,5 in R5C6 and R78C6, locked for C6, clean-up: no 6 in R12C6 (step 5)
24e. R12C7 (step 5a) = {26/35} (cannot be {17} which clashes with R12C6)
24f. Killer pair 1,4 in R4C12 and R5C3, locked for N4

25. R5C56 = {35} -> 32(5) cage at R5C5 (step 2c) = {35789}, 7 locked for R6

26. 6 in R6 only in 30(7) cage at R5C3 = {1234569} (only remaining combination), 9 locked for N8

27. Min R8C3 + R9C34 = 22 (step 6c), must contain 9 in R89C3, locked for C3 and N7

28. 30(7) cage at R6C2 = {1234578} (only remaining combination), no 6
28a. 6 in N8 only in R9C4, locked for R9

[I’d seen this 45 a long time ago, but it’s much more powerful now …]
29. 45 rule on C6789 5(4+1) innies R5678C6 + R6C7 = 33
29a. R578C6 = {359} = 17 -> R6C67 = 16 = [79], clean-up: no 2 in R12C6 (step 5), no 6 in R5C89

30. Naked pair {18} in R12C6, locked for C6 and N2 -> R34C6 = [64], R9C6 = 2, R9C4 = 6 (hidden single in N8), R3C4 = 3 (step 10), clean-up: no 9 in R12C4 (step 4b), no 3,6 in R2C9, no 2 in R4C12
30a. Naked pair {15} in R4C12, locked for R4 and N4 -> R5C3 = 4
30b. R3C4 = 3 -> R4C34 = 16 = [79], R4C5 = 8, R5C7 = 1 (step 3), R4C7 = 3 (cage sum), clean-up: no 5 in R12C7 (step 5a)
30c. R6C89 = {45} (hidden pair in N6), locked for R6 and 14(4) cage at R6C8, no 4,5 in R78C9

31. 30(7) cage at R6C2 (step 28) = {1234578} -> R6C2 = 2, R67C3 = [35]

32. R6C1 = 8, 6,7 in N7 only in R7C12 + R8C2 -> R7C12 + R8C2 = 14 = {167}, locked for N7
32a. Naked pair {34} in R9C12, locked for R9 and N7 -> R8C1 = 2

33. Naked pair {57} in R12C4, locked for C4 and N2
33a. Naked pair {26} in R12C7, locked for C7 and N3, clean-up: no 7 in R1C89, no 7 in R23C9
33b. Naked pair {18} in R12C9, locked for C9 and N3 -> R5C89 = [87], clean-up: no 5 in R1C89
33c. Naked pair {49} in R1C89, locked for R1 and N3 -> R1C5 = 2, clean-up: no 7 in R2C2
33d. Naked pair {57} in R3C78, locked for R3 and N3 -> R2C8 = 3, clean-up: no 8 in R1C2

34. R1C6 = 8 (hidden single in R1), R2C6 = 1, R23C9 = [81], R123C3 = [162], clean-up: no 3,5 in R1C2, no 5 in R2C2
34a. R12C2 = [74]

35. R6C89 = {45} = 9 -> R78C9 = 5 = [23]

36. R7C56 = [39], R8C6 = 5

37. 17(3) cage at R7C7 = {467} (only remaining combination) -> R7C8 = 6, R78C7 = {47}, locked for C7 and N9 -> R3C7 = 5

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A278 at Hard 1.5. I used several locking/locking-out/blocking cages steps; then the final breakthrough in step 24a was hard for me to find. I don't know whether SudokuSolver would be able to find that step and use it. It's more a "human solvable" step.


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 Post subject: Re: Assassin 278
PostPosted: Sun Dec 15, 2013 12:50 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Hey wellbeback and Andrew. Loved both your WTs. Neat trick you both used. Even though Andrew's WT takes much longer to get to it, it reflects how much trouble I had with this puzzle. I used a different trick which is also deceptively simple once you see it. It is also available very near the start of the puzzle. Here's my start.

A278
8 steps:
Prelims courtesy of SudokuSolver
Preliminaries
Cage 6(2) n4 - cells only uses 1245
Cage 15(2) n6 - cells only uses 6789
Cage 15(2) n4 - cells only uses 6789
Cage 8(2) n6 - cells do not use 489
Cage 13(2) n3 - cells do not use 123
Cage 9(2) n3 - cells do not use 9
Cage 11(2) n1 - cells do not use 1
Cage 19(3) n245 - cells do not use 1
Cage 14(4) n69 - cells do not use 9
Cage 14(4) n256 - cells do not use 9
Cage 32(5) n56 - cells do not use 1

1. Naked quad {6789} in r5c1289: all locked for r5

2. 32(5)r4c5 must have two of 2,3,4,5 for r5c56 = {35789/45689}(no 2)
2a. -> r5c56 = {35/45} -> no 3,4,5 elsewhere in 32(5) cage and 5 locked for r5 and n5
2b. 32(5) must have both 8 & 9 and r6c45 see all of that cage -> no 8 or 9 in r6c45 (Common Peer Elimination CPE)

3. 30(7)r5c3 = {1234569/1234578}: ie, must have 3, 4 & 5
3a. -> to avoid clashing with r5c56, 5 and one of 3 or 4 must hide in n8 in r7c56+r8c9
3b. and those three cells in n8 must have one of 8 or 9
3c. -> r7c56+r8c9 from {34589} only: no 1,2,6,7
3d. 5 locked for n8

4. "45" on r1234: 1 innie r4c5 - 7 = 1 outie r5c7 = [82/91]

The key. Interesting that Andrew found this early but used this "45" much later than me. Hopefully mine is valid this early.
5. "45" on c6789: 5 innies r5678c6+r6c7 = 33
5a. also 30(7)r5c3 = {1234569/1234578} note: if it has 9, must also have 6 (ie[9->6]
5b. max. r578c6 = {459} = 18 (30(7)r5c3 can't have both of {89})-> min. r6c67 = 15 but {69} in r6c67 blocked by [9->6] in 30(7)r5c3
5c. -> no 6 in r6c67
5d. 32(5)r4c5 = {35789}(no 4)
5e. r5c56 = {35}: 3 locked for r5 and n5
5f. 32(5) must have 7: r6c45 sees all of that cage -> no 7 in r6c45 (CPE)
5g. 30(7)r5c3 = {1234569}(no 8)
5h. Hidden triple {359} in 30(7)r5c3 -> r7c56+r8c6 = {359} only: 3 and 9 both locked for n8
5i. 4 in r5 only in r5c34 -> no 4 in r6c45 (same cage)

6. Naked triple {359} in r578c6: all locked for c6

7. "45" on c6789: 5 innies r578c6 + r6c67 = 33
7a. r578c6 = 17 -> r6c67 = 16 = [79] only permutation
7b. r4c5 = 8 -> r5c7 = 1 (IODr1234=+7)

8. Hidden single 9 in n5 -> r4c4 = 9

On from there. Much easier now.
Cheerio
Ed


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