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Ed
 Post subject: Assassin 294
PostPosted: Fri Jun 13, 2014 5:50 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
8 years of Assassins! Got stuck looking in the "wrong" area since I found some interesting interactions. Once I got more broadly focused it started to crumble. Then found a couple of interesting steps to make this worthy as an Assassin. Very satisfying solution. SudokuSolver score, 1.50
Assassin 294

Image

code: paste into solver:
3x3::k:3072:3072:5633:5633:5633:3074:6659:6659:6659:2564:2564:3077:5633:3074:3074:6659:8454:6659:5639:2564:3077:6152:6152:6152:6152:8454:3337:5639:5639:5639:5639:8454:8454:8454:8454:3337:5130:5130:5130:2571:6668:6668:6668:3337:3337:4365:4365:5130:2571:6668:5902:5902:5902:5902:4365:4365:4111:3344:6673:2578:2578:4371:5902:3860:3860:4111:3344:6673:6673:6673:4371:5902:2325:2325:4111:3344:6673:4374:4374:4374:4374:
solution: 
+-------+-------+-------+
| 4 8 5 | 6 3 1 | 2 7 9 |
| 1 2 9 | 8 4 7 | 5 6 3 |
| 6 7 3 | 5 2 9 | 8 4 1 |
+-------+-------+-------+
| 8 1 4 | 3 7 2 | 9 5 6 |
| 3 9 6 | 1 5 8 | 7 2 4 |
| 7 5 2 | 9 6 4 | 1 3 8 |
+-------+-------+-------+
| 2 3 1 | 7 8 6 | 4 9 5 |
| 9 6 7 | 4 1 5 | 3 8 2 |
| 5 4 8 | 2 9 3 | 6 1 7 |
+-------+-------+-------+
Cheers
Ed
ps Go the Socceroos!!
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Afmob
 Post subject:
PostPosted: Sat Jun 14, 2014 5:26 pm 
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for this week's Assassin, Ed! This is another Killer where my most important steps wheren't necessarily the technical hardest. I didn't use any fancy moves but maybe step 3c is interesting?

Edit: Ed was right in telling me that step 4a can be simplified.
Step 4a:
16(3) <> {349} also follows from Killer pair (34) in Innies N7. This removes the need to use a Killer quad though it doesn't change the rating since step 5e is at least of rating 1.25.

A294 Walkthrough:
1. R1234
a) Hidden Killer pair (26) in 10(3) + Innies N1 = 11(2) for N1 since each can only have one of them -> Innies N1 = 11(2) = {29/56} and 10(3) <> 4
b) Outies N47 = 9(2) = [27/54/63]
c) Innies N1 = 11(2) = {56}/[92]
d) Outies R1234 = 6(2) = {15/24}
e) Innies R1234 = 7(2) = {16/34} since (25) is a Killer pair of Outies R1234

2. R6789
a) 17(2) = {89} locked for C8+N9
b) Innies N7 = 5(2) = {14/23}
c) Outies N7 = 12(2) <> 1,2,6
d) Innies N89 = 7(2) <> 7
d) Innies R6789 = 17(3) <> 1 because {179} blocked by Killer triple (789) in Outies N7 + 23(6)
e) 1 locked in 23(6) @ R6 for 23(6)
f) Innies N89 = 7(2) <> 6

3. C789 !
a) 13(4): R5C8 <> 1 because {246/345}1 blocked by Killer pairs (24,35) of Innies N89
b) Outies R1234 = 6(2) = {24}/[51]
c) ! 23(6) = 1234{58/67}: R6C6 = (124) since R5C9 = (124) sees all of 23(6) but R6C6
d) Killer pair (24) locked in 13(4) + Innies N89 for C9 since 13(4) can't have 3 of (136)

4. C1234 !
a) ! 16(3) <> 3 and <> {268} because 6{28/37} blocked by Killer pairs (67,68) of 15(2), (358) is a Killer triple of 12(2) @ C3 and {349} blocked by Killer quad (1234) in R7C12 + 9(2)
b) Innies C3 = 17(4) <> {2348} since R1C3 = (569)
c) ! Killer pair (15) locked in Innies C3 + 16(3) for C3
d) 12(2) @ C3 <> 7
e) Innies C3 <> 9 because {1259} blocked by Killer pair (15) of 16(3) and {1349} blocked by Killer pair (34) of 12(2)
f) Innies N1 = 11(2) = {56} locked for N1
g) Outies N47 = 9(2) = [54/63]

5. R1234+N6 !
a) Outies N2 = 13(1+1) = [58/67]
b) 22(5) must contain Outies N47 = 9(2) -> 22(5) = 3{1459/1468/1567/2458/2467} -> 3 locked for R4
c) Innies R1234 = 7(2) = {16}/[34]
d) 13(4) = 14{26/35} -> 4 locked for N6
e) ! Hidden Killer triple (124) in R6C789 for 23(6) since Innies N89 can only have one of (24)
f) Killer pair (12) locked in Outies R1234 + 23(6) for N6
g) R6C78 <> 2 since it sees all 2 of C9
h) 2 locked in Outies R1234 = 6(2) @ N6 = {24} locked for R5+N6
i) ! 24(4) <> {3489} since it's blocked by R3C3 = (3489)
j) Killer pair (56) locked in R3C1 + 24(4) for R3

6. R1234+N6 !
a) 13(4) = {1246} -> R3C9 = 1, R4C9 = 6
b) 23(6) = {123458} -> 8 locked for R6+N6
c) 9 locked in 26(5) @ C9 = 29{348/357/456} for 23(6) -> 2 locked for N3
d) ! Innies R123 = 16(2+1) = 5+{47} / 6+{37}/[64] -> R2C8 <> 5
e) 5 locked in 26(5) @ N3 = 259{37/46}
f) Hidden Single: R3C7 = 8 @ N3
g) Outie N2 = R1C3 = 5
h) Outies N47 = 9(2) = [63] -> R3C1 = 6, R4C4 = 3

7. R6789
a) 5 locked in 9(2) @ N7 = {45} locked for R9+N7
b) Innies N7 = 5(2) = {23} locked for R7+N7+17(4)
c) 17(4) @ N7 = {2357} -> 5,7 locked for R6+N4
d) 5 locked Innies N89 = 7(2) @ 23(6) = {25} -> R7C9 = 5, R8C9 = 2
e) 17(4) @ N9 = {1367} locked for R9 since R9C9 = (37)
f) 7 locked in 16(3) @ C3 = {178} locked for C3+N7; R9C3 = 8
g) 23(6) = {123458} -> R6C6 = 4, R6C9 = 8
h) 13(3) = 2{47/56} since R9C4 = (29) -> R9C4 = 2
i) 10(2) @ R6 = {19} -> R6C4 = 9, R5C4 = 1
j) R9C5 = 9
k) 10(2) @ R7 = {46} -> R7C6 = 6, R7C7 = 4

8. N12
a) 8 locked in 22(4) @ C4 = 58{27/36} for N2; R1C5 = (23)
b) Hidden Single: R1C6 = 1 @ R1
c) 12(3): R2C6 <> 2
d) 10(3) = {127} locked for N1

9. Rest is singles.

Rating:
Hard 1.25. I used a Killer quad and some Killer triples.


Last edited by Afmob on Wed Jun 18, 2014 5:34 am, edited 2 times in total.

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Andrew
 Post subject: Re: Assassin 294
PostPosted: Wed Jun 18, 2014 3:22 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin! After an easy start, I struggled to find how to make progress. It took me a long time to find step 27, then when I did step 28 I realised how important step 22b was.

It was interesting how:
Afmob and I found such different reasons to give the initial combinations for Innies N1. I liked Afmob's "cage clone" in step 3c; I hope/think that I'd have spotted that if I'd reduced R5C9 to {124}, but I didn't spot step 3a.

Here is my walkthrough for Assassin 294:
Thanks Ed for your simpler way to do step 27a.

Prelims

a) R1C12 = {39/48/57}, no 1,2,6
b) R23C3 = {39/48/57}, no 1,2,6
c) R56C4 = {19/28/37/46}, no 5
d) R7C67 = {19/28/37/46}, no 5
e) R78C8 = {89}
f) R8C12 = {69/78}
g) R9C12 = {18/27/36/45}, no 9
h) 10(3) cage at R2C1 = {127/136/145/235}, no 8,9
i) 13(4) cage at R3C9 = {1237/1246/1345}, no 8,9
j) 26(4) cage at R5C5 = {2789/3689/4589/4679/5678}, no 1
k) 23(6) cage at R6C6 = {123458/123467}, no 9

1. Naked pair {89} in R78C8, locked for C8 and N9, clean-up: no 1,2 in R7C6
1a. Killer pair 8,9 in R8C12 and R8C8, locked for R8
1b. 9 in C9 only in R12C9, locked for N3

2. 45 rule on N7 2 outies R6C12 = 12 = {39/48/57}, no 1,2,6
2a. 45 rule on N7 2 innies R7C12 = 5 = {14/23}

3. 45 rule on N89 2 innies R78C9 = 7 = {16/25/34}, no 7

4. 45 rule on R1234 2 outies R5C89 = 6 = {15/24}
4a. 45 rule on R1234 2 innies R34C9 = 7 = {16/34} (cannot be {25} which clashes with R5C89)
4b. 13(4) cage at R3C9 = {1246/1345}, CPE no 1,4 in R6C9

5. 45 rule on N1 2 innies R1C3 + R3C1 = 11 = {29/56} (cannot be {38/47} which clash with the two 12(2) cages in N1, blocking cages)
5a. 8 in N1 only in one of the 12(2) cages = {48}, 4 locked for N1
5b. 1 in N1 only in 10(3) cage at R2C1 = {127/136}, no 5

6. 45 rule on N47 2(1+1) outies R3C1 + R4C4 = 9 = [27/54/63], clean-up: no 2 in R1C3 (step 5)

7. 45 rule on C1234 1 innie R3C4 = 1 outies R1C5 + 2, no 8,9 in R1C5, no 1,2 in R3C4

8. 45 rule on N12 1 outie R3C7 = 1 innie R3C1 + 2 -> R3C7 = {478}

9. 24(4) cage at R3C4 = {2589/2679/3489/3579/3678/4569/4578} (cannot be {1689} because {169}8 is blocked by R3C17 = [68], IOD block), no 1 in R3C56

10. Hidden killer triple 7,8,9 in R6C12, R6C345 and 23(6) cage at R6C6 for R6, R6C12 contains one of 7,8,9, 23(6) cage contains one of 7,8 in R6 -> R6C345 must contain one of 7,8,9
10a. 45 rule on R6789 3 innies R6C345 = 17 = {269/359/368/458/467} (cannot be {179/278} which contain two of 7,8,9), no 1, clean-up: no 9 in R5C4
10b. 9 in R6 only in R6C12 = {39} or in R6C345 = {269/359} -> R6C345 = {269/359/458/467} (cannot be {368}, locking-out cages)

11. 1 in R6 only in R6C678, locked for 23(6) cage at R6C6, no 1 in R78C9, clean-up: no 6 in R78C9 (step 3)

12. 45 rule on R9 3 innies R9C345 = 19, no 1

13. 16(3) cage at R7C3 = {169/178/259/457} (cannot be {268/367} which clash with R8C12, cannot be {349} which clashes with R7C12, cannot be {358} which clashes with R23C3), no 3
13a. Killer pair 7,9 in 16(3) cage and R8C12, locked for N7, clean-up: no 2 in R9C12

14. 45 rule on C3 4 innies R1456C3 = 17 = {1268/1367/2357/2456} (cannot be {1259/1349/1358/1457} which clash with 16(3) cage at R7C3, cannot be {2348} because R1C3 only contains 5,6,9), no 9
14a. R1C3 + R3C1 (step 5) = {56} (only remaining combination), locked for N1, clean-up: no 4 in R3C7 (step 8), no 7 in R4C4 (step 6)
14b. Naked pair {56} in R1C3 + R3C1, CPE no 5,6 in R4C3
14c. 10(3) cage at R2C1 = {127} (only remaining combination), locked for N1

15. R3C1 + R4C4 = 9 (step 6) -> R4C123 = 13 = {139/148/157/238/247} (cannot be {256} which clashes with R3C1, cannot be {346} which clashes with R4C4), no 6 in R4C12

16. 6 in N4 only in 20(4) cage at R5C1 = {1469/1568/2369/2468/2567} (cannot be {3467} which clashes with R6C12)
16a. R1456C3 (step 14) = {1268/2357/2456} (cannot be {1367} = 6{137} because 20(4) cage doesn’t contain two of 1,3,7), 2 locked for C3 and N4

17. 2 in N7 only in R7C12 = {23} (step 2a), locked for R7, N7 and 17(4) cage at R6C1, no 3 in R6C12, clean-up: no 9 in R6C12 (step 2), no 7,8 in R7C6, no 7 in R7C7, no 4,5 in R8C9 (step 3), no 6 in R9C12
17a. 7 in N9 only in R8C7 + R9C789, CPE no 7 in R9C5

18. 9 in R6 only in R6C45, locked for N5
18a. R6C345 (step 10a) = {269/359}, no 4,7,8, clean-up: no 2,3,6 in R5C4

19. 23(6) cage at R6C6 = {123458/123467}
19a. 5 of {123458} must be in R7C9 (R6C6789 cannot contain both of 5,8 which would clash with R6C12), no 5 in R6C6789
[Alternatively hidden killer pair 4,8 in R6C12 and R6C6789 for R6, both of 4,8 must be in R6C12 or in R6C6789 -> 4,8 of {123458} must be in R6C6789 with 5 in R7C9.]

20. R9C345 = 19 (step 12) = {289/379/469} (cannot be {478/568} which clash with R9C12), no 5, 9 locked for R9

21. R4C123 (step 15) = {139/148/157/238} (cannot be {247} which clashes with R6C12)
21a. 20(4) cage at R5C1 (step 16) = {2369/2468/2567} (cannot be {1469} which clashes with R5C89, cannot be {1568} which clashes with R4C123), no 1, 2 locked for N4
21b. 1 in N4 only in R4C123, locked for R4, clean-up: no 6 in R3C9 (step 4a)

22. R1456C3 (step 16a) = {1268/2357/2456}
22a. 1 of {1268} must be in R4C3 -> no 8 in R4C3
22b. 5 of {2357/2456} must be in R1C3 (R456C3 cannot be 4{25} which clashes with R6C12), no 5 in R56C3

23. R6C345 (step 18) = {269/359}
23a. 3 of {359} must be in R6C3 -> no 3 in R6C45, clean-up: no 7 in R5C4

24. 45 rule on C4 4 innies R1234C4 = 22 = {2389/3469/3478/3568/4567} (cannot be {1489/1678/2479/2569} which clash with R56C4, cannot be {1579/2578} because R4C4 only contains 3,4), no 1

25. R3C1 + R4C4 (step 6) = [54/63]
25a. 1 in N4 only in R4C123 (step 21) = {139/148/157} -> R3C1 + R4C1234 = 5{139}4/6{148}3/6{157}3, 3 locked for R4, clean-up: no 4 in R3C9 (step 4a)

26. 13(4) cage at R3C9 (step 4b) = {1246/1345}, 4 locked for N6
26a. 23(6) cage at R6C6 = {123458/123467} -> 4 in R6C6 + R7C9, CPE no 4 in R7C6, clean-up: no 6 in R7C7
26b. 6 in N9 only in R8C7 + R9C789, CPE no 6 in R9C5

27. Hidden killer quad 3,6,7,9 in 20(4) cage at R5C1 and 26(4) cage at R5C5 for R5
27a. 20(4) cage at R5C1 (step 21a) = {2369/2567} (cannot be {2468} because 26(4) cage at R5C5 cannot contain all of 3,7,9), no 4,8
27b. 26(4) cage at R5C5 = {2789/3689/4679/5678} (cannot be {4589} because 20(4) cage cannot contain all of 3,6,7)
[Ed pointed out the technically simpler 26(4) cage at R5C5 must contain at least one of 4,8 in R5 -> 20(4) cage = {2369/2567} (cannot be {2468} which clashes with 26(4) cage).]

28. R1456C3 (step 22) = {2357/2456} -> R1C3 = 5, R456C3 = {237/246}, no 1, clean-up: no 7 in R3C4 (step 7)
28a. Killer pair 3,4 in R23C3 and R456C3, locked for C3
28b. R9C12 = {45} (hidden pair in N7), locked for R9
28c. R9C345 (step 20) = {289/379}, no 6
[Cracked. The rest is straightforward.]

29. R3C1 = 6, R3C7 = 8 (step 8), R4C4 = 3 (step 6), clean-up: no 1,4,6 in R1C5 (step 7), no 4 in R2C3, no 9 in R8C2

30. R6C9 = 8 (hidden single in C9), clean-up: no 4 in R6C12 (step 2)
30a. Naked pair {57} in R6C12, locked for R6 and N4 -> R4C3 = 4, R4C9 = 6, R3C9 = 1 (step 4a), clean-up: no 8 in R2C3, no 5 in R5C89 (step 4)
30b. Naked pair {24} in R5C89, locked for R5 and N6
30c. Naked triple {369} in R5C123, locked for R5 and N4 -> R6C3 = 2
30d. R5C4 = 1 (hidden single in R5) -> R6C4 = 9, clean-up: no 7 in R1C5 (step 7)

31. Naked pair {13} in R6C89, locked for 23(6) cage at R6C6 -> R8C9 = 2, R7C9 = 5 (step 3), R5C89 = [24]

32. 17(4) cage at R9C6 = {1367} (only remaining combination, cannot be {1268} because 2,8 only in R9C6), locked for R9

33. Naked pair {39} in R23C3, locked for C3 and N1 -> R5C3 = 6, R9C3 = 8, R9C45 = [29], R7C6 = 6 -> R7C7 = 4
33a. R9C4 = 2 -> R78C4 = 11 = [74]

34. 45 rule on N3 2 remaining innies = 10 = [64] (cannot be {37} which clashes with R12C9, ALS block), R3C4 = 5, R1C5 = 3 (step 7)

35. R1C6 = 1 (hidden single in R1)

36. R3C47 = [58] = 13 -> R3C56 = 11 = [29]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A294 at Easy 1.5. I used blocking cages and a hidden killer quad. Ed pointed out a simpler way which avoids the hidden killer quad; I'll stick with my rating.
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Ed
 Post subject: Re: Assassin 294
PostPosted: Tue Jun 24, 2014 9:44 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Really enjoyed both walkthroughs. Great solution Afmob!. I found his step 3a first time I tried it but never found his 3c since I was too distracted looking at the split cages! Then I had a hard time finding the other key area which Andrew also used. Loved Andrew's 16a. I rarely find those. So overall, I found this puzzle much harder though hope my WT is no harder to follow than the other two. My optimised solution followed Andrew's start so have pinched it.

A294 Alt breakthrough
11 more steps:
candidates end of Andrew's step 15 or download attached file and open with SudokuSolver at the correct spot: 
.-------------------------------.-------------------------------.-------------------------------.
| 3489      3489      56        | 123456789 1234567   123456789 | 12345678  1234567   123456789 |
| 127       127       3489      | 123456789 123456789 123456789 | 12345678  1234567   123456789 |
| 56        127       3489      | 3456789   23456789  23456789  | 78        1234567   1346      |
:-------------------------------+-------------------------------+-------------------------------:
| 12345789  12345789  123478    | 34        123456789 123456789 | 123456789 1234567   1346      |
| 123456789 123456789 12345678  | 1234678   23456789  23456789  | 23456789  1245      1245      |
| 345789    345789    2345678   | 2346789   23456789  12345678  | 12345678  1234567   235678    |
:-------------------------------+-------------------------------+-------------------------------:
| 1234      1234      12456789  | 123456789 123456789 346789    | 123467    89        2345      |
| 6789      6789      124567    | 1234567   1234567   1234567   | 1234567   89        2345      |
| 134568    134568    2456789   | 23456789  23456789  123456789 | 1234567   1234567   1234567   |
'-------------------------------.-------------------------------.-------------------------------'

End Andrew's step 15 above.

Couple of big combo steps to get started.
16. 22(5)r3c1 must have [63/54] for h9(2)r3c1+r4c4 = {13459/13468/13567/23458/23467}
16a. Must have 3 which is only in r4 -> 3 locked for r4
16b. no 4 in r3c9 (h7(2)r34c9)

17. 13(4)r3c9 = {1246/1345}: must have 4 which is only in n6 -> 4 locked for n6

18. h16(4)r6c6789 = {1258/1267/1348}: ie if it has 3, must have 4 in r6c6
18a. 26(4)r5c5: only combo with 3 is{3689}: ie if it has 3 in r5c7, must have {689} in n5
18b. 3 in n6 only in r6c789 or in r5c7 -> r56c56 = [4]/{689} = [4/6,4/8..]
18c. -> {46} blocked from 10(2)n5 = [19]/{28/37}(no 4,6) (Blocking cages)
18d. and {458} as (45)8(45) only, blocked from h17(3)r6c345 ={269/359/467}(no 8)
18e. no 2 in r5c4

19. h16(4)r6c6789 = {1258/1267/1348}: ie if it has 3, must have 4 in r6c6 -> 3 in r4c4
19a. or 3 in n6 in r5c7
19b. -> 3 locked in r4c4 or r5c7: no 3 in common peers r5c456+r6c5
19c. and no 3 in r6c6 (Locking-out cages: this one not needed but love em! edit: Andrew noticed that simple cage placement also does this elimination, 4 in {1348} must be in r6c6 -> no 3 in r6c6. Thanks!)
19d, no 7 in r6c4

Much more straightforward now. Missing some routine clean-ups
20. h17(3)r6c345 must have 2,3,9 for r6c4 = {269/359}(no 4,7)
20a. must have 9 which is only in n5: locked for n5 and r6
20b. no 3 in r6c12 (h12(2))

21. 6 in n4 only in 20(4)
21a. but {1469} blocked by h6(2)r5c89 = 1/4
21b. and {1568/3467} blocked by h12(2)r6c12 = 5/8 or 4/7
21c. = {2369/2468/2567}(no 1)
21d. must have 2: 2 locked for n4

22. 2 in r4 only in 33(6)r2c8 = {126789/234789/2355689/245679}
22a. must have 9 ->r4c7 = 9
22b. 2 in 33(6) must be in r4 -> no 2 in r23c8

23. 9 in r5 only in 20(4)n4 = {2369} only: 3 locked for n4

24. Hidden single 3 in r4 ->r4c4 = 3
24a. ->r3c1 = 6 (outies n47=9)
24b. ->r3c7 = 8 (IODn12=-2)
24c. no 7 in r5c4
24d. no 1 in r4c9 (h7(2)r34c9)

25. 26(4)r5c5 = {2789/3689/4589/4679/5678}
25a. but {2789/3689/4589} all blocked by 10(2)n5 = 8/9
25b. 26(4)r5c5 = {4679/5678}(no 2,3)

26. 3 in n6 only in h16(3)r6c6789 = {1348} only -> r6c6 = 4, r6c9 = 8, r6c78 = {13} only: locked for r6, n6 and no 3 in r78c9
26a. -> h7(2)r67c9 = {25} only: both locked for c9 and n9


on from there
Cheers
Ed


Attachments:
A294 Andrew WTend step 15.ssv [111.32 KiB]
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