SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Wed Apr 24, 2024 6:13 pm

View unanswered posts | View active topics


Board index » Puzzles and Solutions » Killer Puzzles

All times are UTC




Post new topic Reply to topic  Page 1 of 1
  [ 8 posts ] 
  Print view Previous topic | Next topic 
Author Message
Ed
 Post subject: Assassin 290
PostPosted: Thu Apr 17, 2014 11:01 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
Wonderful Assassin to celebrate Easter! Started out as the "Easy" version below but took a couple of solves to find the 'easy' way to solve it. Then changed the cage pattern to close the front door but still let me use an over-the-top trick to solve A290. If you want to try both puzzles, perhaps do the "Easy" one first so less risk of a spoiler.

Assassin 290 SudokuSolver score 1.60
puzzle pic:
Image
code: paste into solver:
3x3::k:6912:8705:8705:8705:8705:8705:1282:1282:7427:6912:2308:2308:3589:8705:1798:4103:4103:7427:6912:6912:2312:3589:3589:1798:8713:7427:7427:6912:8202:2312:8713:8713:8713:8713:8713:7427:8202:8202:8202:8202:8202:2571:8713:3084:3084:7949:8202:5134:5134:5134:2571:3087:3087:3084:7949:7949:5134:4368:4368:4881:3087:4882:4882:3091:7949:7949:4368:4368:4881:4882:4882:4116:3091:7949:5397:5397:5397:4881:4881:4116:4116:


A290 "Easy" SudokuSolver score 1.35
puzzle pic:
Image
code: paste into solver:
3x3::k:6912:8705:8705:8705:8705:8705:1282:1282:7427:6912:2308:2308:3589:8705:1798:4103:4103:7427:6912:6912:2312:3589:3589:1798:8713:7427:7427:6912:8202:2312:8713:8713:8713:8713:8713:7427:8202:8202:8202:8202:8202:2571:8713:3084:3084:7949:8202:2318:2831:2831:2571:3088:3088:3084:7949:7949:2318:4369:4369:4882:3088:4883:4883:3092:7949:7949:4369:4369:4882:4883:4883:4117:3092:7949:5398:5398:5398:4882:4882:4117:4117:


Solution
same solution for both puzzles: 
+-------+-------+-------+
| 7 4 6 | 9 8 5 | 2 3 1 |
| 3 1 8 | 6 2 4 | 9 7 5 |
| 2 9 5 | 1 7 3 | 4 6 8 |
+-------+-------+-------+
| 6 2 4 | 3 1 7 | 8 5 9 |
| 5 3 1 | 4 9 8 | 6 2 7 |
| 9 8 7 | 5 6 2 | 1 4 3 |
+-------+-------+-------+
| 1 5 2 | 8 3 6 | 7 9 4 |
| 8 7 3 | 2 4 9 | 5 1 6 |
| 4 6 9 | 7 5 1 | 3 8 2 |
+-------+-------+-------+
Cheers
Ed
Top
 Profile  
Reply with quote  
Afmob
 Post subject:
PostPosted: Fri Apr 18, 2014 12:58 pm 
Offline
Grand Master
Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thank you for the new Assassin, Ed! I found it easier than SudokuSolver suggests but the standard version will be harder since I can't use one of my breakthrough moves (step 4a).

A290 Easy Walkthrough:
1. R1234
a) 16(2) = {79} locked for R2+N3
b) 29(5) must have one of (79) -> R4C9 = (79)
c) Innies+Outies N3: 5 = R4C9 - R3C7 -> R3C7 = (24)
d) Innies+Outies R1234: 4 = R5C7 - R4C2 -> R5C7 = (56789), R4C2 = (12345)

2. R789 !
a) Innies N9 = 10(2) <> 5
b) ! Innies+Outies N8: -9 = R9C7 - R9C45 -> R9C45 <> 9 (IOU @ R9)
c) 21(3): R9C3 <> 4,5 since R9C45 <> 9
d) Outies N8 = 12(2) = [84/93]
e) Innies N9 = 10(2) = [64/73]
f) Innies+Outies N7: 7 = R6C13 - R9C3: R6C13 = (6789) and R6C1 <> 6 since R9C3 >= 8 and R6C3 <> 9

3. R456
a) 34(7) = 13568{29/47} since 12479{38/56} blocked by R4C9 = (79); R4C45678 <> 2,4 since R3C7 = (24); 1,3 locked for R4
b) Outies N12 = 10(2) = {28/46}
c) Innies+Outies R1234: 4 = R5C7 - R4C3: R5C7 <> 5,7
d) 34(7) = 13568{29/47} -> 5 locked for R4
e) Innies+Outies R1234: 4 = R5C7 - R4C4: R5C7 <> 9
f) Killer pair (24) locked in Outies N12+R4C2 for N4
g) 1,3,5 locked in 32(7) @ N4 = 12358{49/67} for 32(7)

4. C789+N45 !
a) ! Innies C789+N5 = 16(2+1) <> 2 since R9C7 <= 4
b) 32(7) = 12358{49/67} -> R4C2 = 2
c) Outies N12 = 10(2) = {46} locked for R4+N4

5. R56789
a) Outie R1234 = R5C7 = 6
b) Innies N9 = 10(2) = [73] -> R7C7 = 7, R9C7 = 3
c) Outie N8 = R9C3 = 9
d) Outies N7 = 16(2) = {79} -> R6C3 = 7, R6C1 = 9
e) Cage sum: R7C3 = 2
f) 11(2) <> 2,4
g) 2 locked in 10(2) @ N5 = {28} locked for C6+N5
h) 11(2) = {56} locked for R6+N5
i) 32(7) = {1234589} -> 4,5,9 locked for R5; 9 locked for N5

6. C456+N3
a) 34(7) = {1345678} since R4C456 = (137) -> R3C7 = 4; 7 locked for R4; R4C78 = (58) locked for N6
b) 5(2) = {23} -> R1C7 = 2, R1C8 = 3
c) 21(3) = 9{48/57}
d) 19(4) = {1369} since {3457} blocked by Killer pair (45) of 21(3) -> 1,6,9 locked for C6+N8
e) 7(2) = {34} -> R3C6 = 3, R2C6 = 4
f) R4C6 = 7, R1C6 = 5, R4C9 = 9
g) 14(3) = {167} locked for N2; 7 locked for R3
h) 34(6) = {245689} since R1C45+R2C5 = (289) -> R2C5 = 2; R1C23 = (46) locked for R1+N1; 8 locked for R1

7. R789+N1
a) 9(2) @ R2 = {18} locked for R2+N1
b) R1C1 = 7
c) 12(2) = {48} locked for C1+N7
d) 21(3) = {579} since {489} blocked by R9C1 = (48) -> 5,7 locked for R9+N8
e) 16(3) = {268} locked for N9

8. Rest is singles.

Rating:
Hard 1.0. I used IOU.


Last edited by Afmob on Sat Apr 19, 2014 10:56 am, edited 1 time in total.

Top
 Profile  
Reply with quote  
Afmob
 Post subject:
PostPosted: Fri Apr 18, 2014 4:26 pm 
Offline
Grand Master
Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
And there goes the other Assassin. :D I didn't use any fancy moves so I'm interested in Ed's OTT way to solve this Killer.

A290 Walkthrough:
1. R1234
a) 16(2) = {79} locked for R2+N3
b) 29(5) must have one of (79) -> R4C9 = (79)
c) Innies+Outies N3: 5 = R4C9 - R3C7 -> R3C7 = (24)
d) Innies+Outies R1234: 4 = R5C7 - R4C2 -> R5C7 = (56789), R4C2 = (12345)

2. R789 !
a) Innies N9 = 10(2) <> 5
b) ! Innies+Outies N8: -9 = R9C7 - R9C45 -> R9C45 <> 9 (IOU @ R9)
c) 21(3): R9C3 <> 4,5 since R9C45 <> 9
d) Outies N8 = 12(2) = [84/93]
e) Innies N9 = 10(2) = [64/73]
f) 12(3): R6C78 = (12345) since R7C7 >= 6
g) Innies+Outies N7: -2 = R6C1 - R79C3: R7C3 = (123) and R6C1 = (789) since R9C3 >= 8

3. R456
a) 34(7) = 13568{29/47} since 12479{38/56} blocked by R4C9 = (79); R4C45678 <> 2,4 since R3C7 = (24); 1,3 locked for R4
b) Outies N12 = 10(2) = {28/46}
c) Innies+Outies R1234: 4 = R5C7 - R4C3: R5C7 <> 5,7
d) 34(7) = 13568{29/47} -> 5 locked for R4
e) Innies+Outies R1234: 4 = R5C7 - R4C4: R5C7 <> 9
f) Killer pair (24) locked in Outies N12+R4C2 for N4
g) 12(3) @ N9 = {147/156/237/246} since R7C7 = (67)
h) 12(3) @ R5 <> {345} since it's a Killer triple of 12(3) @ N9
i) Killer pair (12) locked in both 12(3) for N6
j) 34(7) must have 1 -> 1 locked for N5

4. C456+N6 !
a) Innies+Outies C6: -9 = R9C7 - R14C6: R14C6 <> 1,2 since R9C7 >= 3
b) Innies+Outies C6789: -1 = R4C45 - R1C6 -> R1C6 <> 3,4,6 since R4C45 <> 2,4; R4C45 <> 8,9
c) 19(4): R789C6 <> 3,4 since R9C7 = (34) and {3457} blocked by Killer pair (47) of 21(3)
d) Hidden Killer pair (78) in R9C45 since 21(3) can only have one of (456)
e) 19(4) <> 7 since R9C7 = (34) and 7{138/246} blocked by Killer pairs (47,78) of 21(3) -> 19(4) must have one of (56)
f) ! 10(2) <> {46} since it's blocked by Killer triple (456) in 7(2) and 19(4)
g) 4 locked in 7(2) @ C6 = {34} locked for C6+N2
h) 10(2) = {28} locked for C6+N5

5. R456
a) 32(7) must have 2 -> R4C2 = 2
b) Outie R1234 = R5C7 = 6
c) Outies N12 = 10(2) = {46} locked for N4
d) 32(7) = {1234589} -> 8 locked for N4, 4 locked for R5+N5

6. R789
a) Innies N9 = 10(2) = [73] -> R7C7 = 7, R9C7 = 3
b) Outie N8 = R9C3 = 9
c) 19(4) = {1369} -> 1,6,9 locked for C6+N8
d) Innies+Outies N7: 7 = R6C1 - R7C3 -> R6C1 = 9, R7C3 = 2

7. R123
a) 14(3) = 1{58/67} since {257} blocked by R1C6 = (57) -> 1 locked for N2
b) 2,9 locked in 34(6) @ N2 = 2589{37/46} for 34(6)
c) Outies N2 = 10(2) = {37/46}
d) 34(6) = 2589{37/46}: R1C456+R2C5 = {2589} since R1C23 = {37/46} -> R1C6 = 5; 8 locked for N2
e) R4C6 = 7
f) 34(7) = {1345678} -> R3C7 = 4
g) 5(2) = {23} -> R1C7 = 2, R1C8 = 3
h) Outies N1 = 10(2) = {46} locked for R1+N1
i) 9(2) @ R2 = {18} locked for R2+N1
j) R1C1 = 7

8. R789
a) 12(2) = {48} locked for C1+N7
b) 21(3) = {579} since {489} blocked by R9C1 = (48) -> 5,7 locked for R9+N8
c) 16(3) <> 4

9. Rest is singles.

Rating:
1.25. I used IOU and two Killer triples.


Last edited by Afmob on Sat Apr 19, 2014 11:26 am, edited 2 times in total.

Top
 Profile  
Reply with quote  
wellbeback
 Post subject: Re: Assassin 290
PostPosted: Fri Apr 18, 2014 6:00 pm 
Offline
Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 282
Location: California, out of London
Thanks Ed and Happy Easter!

Here is how I did the main one. Now to compare it to Afmob's wt!

Hidden Text:
1. 16/2@r2c7 = {79}
Innies - Outies n3 -> r4c9 = r3c7 + 5
-> r4c9 is >= 6
-> Whatever value is in r4c9 can only go in n3 in the 16/2@r2c7
-> r4c9 from (79) and r3c7 from (24)

2. Whatever is in r3c7 (2 or 4) can only go in r4 in r4c123
Also the 34/7@r3c7 is missing two values which = +11, including the value at r4c9 (7 or 9)
-> The other missing value (4 or 2) must go in r4 in r4c123.
-> Both 2 and 4 in r4 are in r4c123

3. Outies n12 -> r4c13 = +10
-> r4c2 from (24) and r4c13 from {46} or {28}

4. Outies n8 -> r9c37 = +12 (no 126)
The cells in 31/6@r6c1 and 12/2@r8c1 are all buddies with each other
-> Those cages formed together are 43/8 -> No 2 in either cage
-> HS 2 in n7 -> r7c3 = 2

5. -> 2 in r4 in r4c12
Outies n2 -> r1c23 = +10
-> Since r4c13 = +10 -> whatever goes in r4c1 can only go in n1 in r1c3 or r2c23
Since 2 cannot go in any of those three cells -> 2 not in r4c1
-> r4c2 = 2
-> r4c13 = {46}

6. Innies - Outies r1234 -> r5c7 = r4c2 + 4
-> r5c7 = 6
-> 6 not in 32/7@r4c2
-> 7 not in 32/7@r4c2 (I.e., 32/7@r4c2 = {1234589})
-> 7 in n4 in r6c13
Also 4 in r5c45
-> 6 in n5 in r6c45

7. Innies n9 -> r79c7 = +10
-> 5 not in r9c7
-> 7 not in r9c3
Whatever goes in r6c1 can only go in n7 in r9c3
-> 7 not in r6c1
-> r6c3 = 7
-> 20/4@r6c3 = [7{56}2]

8. 2 in n5 only in r56c6 -> 10/2@r5c6 = {28}
-> 7 in n5 only in r4c456
-> r4c9 = 9
-> r3c7 = 4
-> 5/2@r1c7 = {23}
-> 29/5@r1c9 = {1568}[9]

9. Also 9 in n5 in r5c56
-> r4c456 = {137}
-> r4c78 = {58}
Also HS 9 in n4 -> r6c1 = 9
-> r9c3 = 9
-> r9c7 = 3
-> r7c7 = 7
-> r2c78 = [97]
-> r5c9 = 7
etc.
Top
 Profile  
Reply with quote  
Andrew
 Post subject: Re: Assassin 290
PostPosted: Tue Apr 22, 2014 4:26 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassins! As you suggested, I tried the "Easier" one first; I found it more than "Easy" as some steps were hard to find.

Here is my walkthrough for A290 "Easier":
Prelims

a) R1C78 = {14/23}
b) R2C23 = {18/27/36/45}, no 9
c) R23C6 = {16/25/34}, no 7,8,9
d) R2C78 = {79}
e) R34C3 = {18/27/36/45}, no 9
f) R56C6 = {19/28/37/46}, no 5
g) R67C3 = {18/27/36/45}, no 9
h) R6C45 = {29/38/47/56}, no 1
i) R89C1 = {39/48/57}, no 1,2,6
j) 21(3) cage at R9C3 = {489/579/678}, no 1,2,3

1. Naked pair {79} in R2C78, locked for R2 and N3, clean-up: no 2 in R2C23

2. 45 rule on N3 1 outie R4C9 = 1 innie R3C7 + 5, R3C7 = {1234}, R4C9 = {6789}
2a. 6,8 in N3 only in R12C9 + R3C89, locked for 29(5) cage at R1C9, no 6,8 in R4C9, clean-up: no 1,3 in R3C7
[Alternatively 29(5) cage at R1C9 must contain at least one of 7,9 -> R4C9 = {79} -> R3C7 = {24}.]
2b. Killer pair 2,4 in R1C78 and R3C7, locked for N3

3. 34(7) cage at R3C7 = {1235689/1345678} (cannot be {1234789/1245679} which clash with R4C9
3a. R3C7 = {24} -> no 2,4 in R4C45678 + R5C7
3b. 2,4 in R4 only in R4C123, locked for N4, clean-up: no 5,7 in R7C3

4. 45 rule on N7 2 outies R6C13 = 1 innie R9C3 + 7, IOU no 7 in R6C1
4a. Min R9C3 = 4 -> min R6C13 = 11, no 1 in R6C13, clean-up: no 8 in R7C3

5. 45 rule on N2 2 outies R1C23 = 10 = {19/28/37/46}, no 5

6. 45 rule on N12 2 outies R4C13 = 10
6a. Hidden killer pair 2,4 in R4C13 and R4C2 for R4, R4C13 = 10 cannot contain both of 2,4 -> R4C13 = {28/46}, R4C2 = {24}, clean-up: no 2,4,6,8 in R3C3
6b. 1 in N4 only in R5C123 + R6C2, locked for 32(7) cage at R4C2, no 1 in R5C45

7. 45 rule on N8 2 outies R9C37 = 12 = {48/57}/[93], no 1,2,6, no 9 in R9C7
7a. 45 rule on N9 2 innies R79C7 = 10 = [28/37/64/73], no 5, no 1,4,8,9 in R7C7, clean-up: no 7 in R9C3

8. R9C37 = 12 (step 7)
8a. R9C34 and R9C35 cannot total 12 (which would clash with R9C39, CCC) -> no 9 in R9C45
[With hindsight 45 rule on N8 2 innies R9C45 = 1 outie R9C7 + 9, IOU no 9 in R9C45. Where there’s a CCC there’s usually an IOU available, and frequently the other way round.]

9. 21(3) cage at R9C3 = {489/579/678}
9a. 8 of {678} must be in R9C3, 9 of {489/579} must be in R9C3 -> R9C3 = {89}, R9C7 = {34} (step 7). R7C7 = {67} (step 7a)
9b. Min R7C7 = 6 -> max R6C78 = 6, no 6,7,8,9 in R6C78

10. R6C13 = R9C3 + 7 (step 4)
10a. R9C3 = {89} -> R6C13 = 15,16 = [87/96/97], clean-up: R7C3 = {23}

11. 45 rule on R1234 1 outie R5C7 = 1 innie R4C2 + 4, R4C2 = {24} -> R5C7 = {68}

12. 45 rule on C6789 1 innie R1C6 = 2 outies R4C45 + 1
12a. Min R4C45 = 4 -> min R1C6 = 5
12b. Max R4C45 = 8, no 8,9 in R4C45
12c. R4C45 cannot total 5 -> no 6 in R1C6

13. 45 rule on N36 4(3+1) outies R4C456 + R7C7 = 18
13a. R7C7 = {67} -> R4C456 = 11,12 = {137/138/156}, no 9, 1 locked for R4 and N5, clean-up: no 9 in R56C6
13b. R1C6 = 2 outies R4C45 + 1 (step 12)
13c. R1C6 = {5789} -> R4C45 = 4,6,7,8 = {13/15/16/17} (cannot be {35} because R4C456 only contains one of 3,5), 1 locked for R4
13d. 9 in R4 only in R4C789, locked for N6

14. 45 rule on N1247 2 outies R5C45 = 1 innie R9C3 + 4
14a. Min R9C3 = 8 -> min R5C45 = 12, no 2 in R5C45

15. Deleted. I found a blocking cages step, but it’s not needed after the next step.

[I was a bit slow to spot that after step 14a …]
16. 32(7) cage at R4C2 must contain 2 -> R4C2 = 2, R5C7 = 6 (step 11), R7C7 = 7, R9C7 = 3 (step 7a), R9C3 = 9 (step 7), R2C78 = [97], clean-up: no 1 in R1C2, no 8 in R1C3 (both step 5), no 2 in R1C8, no 8 in R4C13 (step 6a), no 1,7 in R3C3, no 4 in R6C6, no 3 in R8C1
[Cracked, the rest is fairly straightforward.]
16a. Naked pair {46} in R4C13, locked for N4 -> R6C3 = 7, R7C3 = 2, clean-up: no 3,8 in R1C2 (step 5), no 3 in R5C6, no 4 in R6C45
16b. R4C456 (step 13a) = {137/138}, no 5, 3 locked for R4 and N5, clean-up: no 7 in R5C6, no 8 in R6C45
16c. 34(7) cage at R3C7 (step 3) = {1235689/1345678}, 5 locked for N6

17. R7C7 = 7 -> R6C78 = 5 = {14}/[23]
17a. 12(3) cage at R5C8 = {147/237} (cannot be {138} which clashes with R6C78) -> R5C9 = 7, R4C9 = 9, R3C7 = 4 (step 2), clean-up: no 1 in R1C78, no 3 in R2C6
17b. R1C78 = [23] -> R6C78 = [14], R5C8 = 2, R6C9 = 3, clean-up: no 7 in R1C2 (step 5), no 8 in R6C6

18. 45 rule on R6789 2 remaining innies R6C26 = 10 = [82] -> R5C6 = 8, R6C1 = 9, clean-up: no 1 in R2C3, no 5 in R23C6
18a. Naked pair {56} in R6C45, locked for N5

19. 16(3) cage at R8C9 = {268} (only remaining combination), locked for N9 -> R8C7 = 5, R4C78 = [85], clean-up: no 7 in R9C1
19a. Naked pair {19} in R78C8, locked for C8 and N9 -> R7C9 = 4
19b. R9C9 = 2 (hidden single in R9)

20. 2,7 in N1 only in 27(5) cage at R1C1 = {23679/24579/24678} (cannot be {12789} because R4C1 only contains 4,6), no 1

21. R9C3 = 9 -> R9C45 = 12 = {48/57}
21a. R9C7 = 3 -> 19(4) cage at R7C6 = {1369} (only remaining combination, cannot be {3457} which clashes with R9C45), 1,6,9 locked for C6 and N8 -> R23C6 = [43] -> R14C6 = [57], R3C3 = 5 -> R4C3 = 4, R4C1 = 6, clean-up: no 6 in R1C2 (step 5)
21b. Killer triple 3,5,8 in R7C45 and R9C45, locked for N8, 3 also locked for R7

22. 14(3) cage at R2C4 = {167} (only remaining combination), locked for N2, 7 also locked for R3 -> R3C2 = 9, R1C2 = 4, R1C3 = 6 (step 5), R2C2 = 1 (hidden single in N1) -> R2C3 = 8, R1C1 = 7, clean-up: no 5 in R9C1

23. R9C45 (step 21) = {57} (cannot be {48} which clashes with R9C1), locked for R9 and N8 -> R9C2 = 6

and the rest is naked singles.

Rating Comment:
Although I could have rated it lower, based on my technically hardest steps which were a CCC, a hidden killer pair and a killer triple, I'll go a bit higher because I found some steps hard to find. I'll rate my walkthrough at 1.25.

I'll try the main version when I've got time; other things take priority this week.
Top
 Profile  
Reply with quote  
Ed
 Post subject: Re: Assassin 290
PostPosted: Thu Apr 24, 2014 3:36 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
I did "Easy" pretty much the same way as Afmob. Been a long time since that has happened! (Though only on the second solve). Andrew's step 14a gets the same key eliminations to crack the puzzle.

A290 "Easy"
21 steps:
Prelims
Cage 16(2) n3 - cells ={79}
Cage 5(2) n3 - cells only uses 1234
Cage 7(2) n2 - cells do not use 789
Cage 12(2) n7 - cells do not use 126
Cage 9(2) n47 - cells do not use 9
Cage 9(2) n14 - cells do not use 9
Cage 9(2) n1 - cells do not use 9
Cage 10(2) n5 - cells do not use 5
Cage 11(2) n5 - cells do not use 1
Cage 21(3) n78 - cells do not use 123

1. 16(2)n3 = {79}: both locked for r2 and n3
1a. no 2 in 9(2)r2c2

2. "45" on n3: 1 innie r3c7 + 5 = 1 outie r4c9 (IODn3=-5)
2a. r3c7 = (1234), r4c9 = (6789)

3. 6,8 in n3 only in 29(5) -> no 6,8 in r4c9
3a. -> no 1,3 in r3c7 (IODn3=-5)

4. 34(7)r3c7: {1234789/1245679} both blocked by r4c9 = (79)
4a. = {1235689/1345678}
4b. can only have one of 2 or 4 which must be in r3c7 -> no 2 or 4 anywhere else in that cage

5. "45" on n12: 2 outies r4c13 = 10
5a. 2 and 4 in r4 are only in r4c123 -> the h10(2)r4c13 must have one of 2 or 4 (Hidden killer pair)
5b. ->r4c13 = {28/46}(no 1,3,5,7,9)
5c. and r4c2 must have the other one of 2 or 4 for r4 -> r4c2 = (24)
5d. 2 & 4 both locked for n4
5e. no 5,7 in r7c3
5f. r3c3 = (1357)

6. "45" on r1234: 1 innie r4c2 + 4 = 1 outie r5c7 (IODr1234=-4)
6a. r4c2 = (24) -> r5c7 = (68)

7. "45" on n8: 2 innies r9c45 - 9 = 1 outie r9c7
7a. they are all in the same row -> neither innie can equal the outie -> the Innie/outie difference of 9 cannot go in r9c45 -> no 9 in r9c45 (IOU)

8. 21(3)r9c3 = {489/579/678}; ie, must have 9 in r9c3 or be {678}
8a. -> r9c3 = (6789)

9. "45" on n9: 2 innies r79c7 = 10 (no 5)

10. "45" on n8: 2 outies r9c37 = 12
10a. = [93/84] only permutations
10b. r7c7 = (67)(h10(2)r79c7)

This is the step that eluded me on the first solve. This is why I like making 'messy' cage patterns, you can get some unusual "45"s.
11. "45" on n3569: 3 innies r5c45+r9c7 = 16
11a. r9c7 = (34) -> r5c45 = 12 or 13
11b. -> no 1,2 in r5c45

Missing routine clean-up from here.
12. 32(7)r4c2 = {1234589/1234679/1235678}
12a. must have 2 which is only in r4c2 -> r4c2 = 2
12b. -> r5c7 = 6 (IODr1234=-4)
12c. r7c7 = 7 -> r9c7 = 3 (h10(2)r79c7) -> r9c3 = 9 (h12(2)r9c37)
12d. r2c78 = [97]

13. "45" on n6: 3 remaining innies r4c789 = 22 = {589} only -> r4c9 = 9, r4c78 = {58} only: both locked for r4 and n6
13a. r3c7 = 4 (IODn3=-5)
13b. r1c78 = [23] only permutation -> r6c78 = [14] (cage sum) -> r5c8 = 2

14. "45" on n7: 2 outies r6c13 = 16 = [97] only permutation; r56c9 = [73]
14a. r7c3 = 2

15. 11(2)n5 = {56} only combination: both locked for r6 and n5 -> r6c2 = 8, r56c6 = [82] (cage sum)

16. 21(3)r9c3 = [9]{48/57}(no 6) = 4/5..]
16a. -> {457}[3] blocked from 19(4)r7c6
16b. 19(4) = {169}[3] only: 1,6,9 locked for c6 & n8
16c. 7(2)n2 = [43] only permutation; r4c6 = 7; r1c6 = 5

17. 14(3)n2 = {167} only combination: all locked for n2, 7 locked for r3
17a. Naked pair {89} in r1c45, both locked for r1, 8 for n2 -> r2c5 = 2
17b. 9(2)r3c3 = [54] only permutation, r4c1 = 6

18. "45" on n2: 2 outies r1c23 = 10 = [46] only permutation
18a. 9(2)n1 = [18] only permutation; r123c1 = [732], r3c2 = 9

19. 12(2)n7 = {48} only combination: both locked for c1

20. 21(3)r9c3: [9]{48} blocked by r9c1 = (48)
20a. -> r9c345 = [9]{57} only: 5 & 7 locked for r9 and n8

21. 16(3)n9 = {268} only combination: all locked for n9

on from there.
Cheers
Ed
Top
 Profile  
Reply with quote  
Andrew
 Post subject: Re: Assassin 290
PostPosted: Sun Apr 27, 2014 9:38 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for the main version of A290, quite a lot harder than the "Easier" version.

My solving path was more like wellbeback's, with my key steps 15 and 20 being equivalent to his steps 4 and 5, although we saw each of these steps in different ways.

Here is my walkthrough for Assassin 290:
Prelims

a) R1C78 = {14/23}
b) R2C23 = {18/27/36/45}, no 9
c) R23C6 = {16/25/34}, no 7,8,9
d) R2C78 = {79}
e) R34C3 = {18/27/36/45}, no 9
f) R56C6 = {19/28/37/46}, no 5
g) R89C1 = {39/48/57}, no 1,2,6
h) 21(3) cage at R9C3 = {489/579/678}, no 1,2,3

1. Naked pair {79} in R2C78, locked for R2 and N3, clean-up: no 2 in R2C23

2. 45 rule on N3 1 outie R4C9 = 1 innie R3C7 + 5, R3C7 = {1234}, R4C9 = {6789}
2a. 6,8 in N3 only in R12C9 + R3C89, locked for 29(5) cage at R1C9, no 6,8 in R4C9, clean-up: no 1,3 in R3C7
[Alternatively 29(5) cage at R1C9 must contain at least one of 7,9 -> R4C9 = {79} -> R3C7 = {24}.]
2b. Killer pair 2,4 in R1C78 and R3C7, locked for N3

3. 34(7) cage at R3C7 = {1235689/1345678} (cannot be {1234789/1245679} which clash with R4C9
3a. R3C7 = {24} -> no 2,4 in R4C45678 + R5C7
3b. 2,4 in R4 only in R4C123, locked for N4

4. 45 rule on N2 2 outies R1C23 = 10 = {19/28/37/46}, no 5

5. 45 rule on N12 2 outies R4C13 = 10
5a. Hidden killer pair 2,4 in R4C13 and R4C2 for R4, R4C13 = 10 cannot contain both of 2,4 -> R4C13 = {28/46}, R4C2 = {24}, clean-up: no 2,4,6,8 in R3C3

6. 45 rule on R1234 1 outie R5C7 = 1 innie R4C2 + 4, R4C2 = {24} -> R5C7 = {68}

7. 45 rule on N8 2 outies R9C37 = 12 = {48/57}/[93], no 1,2,6, no 9 in R9C7
7a. 45 rule on N9 2 innies R79C7 = 10 = [28/37/64/73], no 5, no 1,4,8,9 in R7C7, clean-up: no 7 in R9C3

8. R9C37 = 12 (step 7)
8a. R9C34 and R9C35 cannot total 12 (which would clash with R9C39, CCC) -> no 9 in R9C45
[With hindsight 45 rule on N8 2 innies R9C45 = 1 outie R9C7 + 9, IOU no 9 in R9C45. Where there’s a CCC there’s usually an IOU available, and frequently the other way round.]

9. 21(3) cage at R9C3 = {489/579/678}
9a. 8 of {678} must be in R9C3, 9 of {489/579} must be in R9C3 -> R9C3 = {89}, R9C7 = {34} (step 7). R7C7 = {67} (step 7a)
9b. Min R7C7 = 6 -> max R6C78 = 6, no 6,7,8,9 in R6C78

10. 45 rule on C789 3 outies R4C456 = 1 innie R9C7 + 8
10a. R9C7 = {34} -> R4C456 = 11,12 = {137/138/156}, no 9, 1 locked for R4 and N5, clean-up: no 9 in R56C6
10b. 9 in R4 only in R4C789, locked for N6

11. 45 rule on C6789 1 innie R1C6 = 2 outies R4C45 + 1
11a. Min R4C45 = 4 -> min R1C6 = 5
11b. Max R4C45 = 8, no 8 in R4C45
11c. R4C45 cannot total 5 -> no 6 in R1C6
11d. R1C6 = {5789} -> R4C45 = 4,6,7,8 = {13/15/16/17} (cannot be {35} because R4C456, step 10a, only contains one of 3,5), 1 locked for R4

12. 21(3) cage at R9C3 = {489/579/678}
12a. 19(4) cage at R7C6 = {1369/1459/1468/2359/2368/2458} (cannot be {1279/1567} because R9C7 only contains 3,4, cannot be {1378/2467/3457} which clash with 21(3) cage), no 7
12b. R9C7 = {34} -> no 3,4 in R789C6

13. 34(6) cage at R1C2 must contain 9, locked for R1

14. 45 rule on N7 2 innies R79C3 = 1 outie R6C1 + 2
14a. Min R79C3 = 9 -> min R6C1 = 7
14b. Max R79C3 = 11 -> max R7C3 = 3

15. 6 in N7 only in 31(6) cage at R6C1 = {134689/135679/145678} (cannot be {125689/234679/235678} which clash with R89C1), no 2

16. R7C3 = 2 (hidden single in N7), clean-up: no 8 in R1C2 (step 4), no 7 in R3C3, no 8 in R4C1 (step 5a)
16a. 45 rule on N7 1 remaining innie R9C3 = 1 outie R6C1, R9C3 = {89} -> R6C1 = {89}
16b. R7C3 = 2 -> 20(4) cage at R6C3 = {2369/2378/2459/2468/2567} (cannot be {1289} which clashes with R6C1), no 1
[Alternatively 32(7) cage at R4C2 must contain 1, locked for N4.]

17. Hidden killer triple 1,3,5 in R2C23, R3C3 and rest of N1 for N1, R2C23 contains one of 1,3,5, R3C3 = {135} -> rest of N1 only contains one of 1,3,5
17a. 2 in C1 only in 27(5) cage at R1C1 = {23679/24579/24678} (cannot be {12789} which clashes with R6C1 + R89C1, killer ALS block, cannot be {23589} which contains two of 1,3,5), no 1, 7 locked for N1, clean-up: no 3 in R1C23 (step 4)
17b. 27(5) cage can only have one of 7,8,9 in R123C1 (R123C1 cannot contain {78/79} which would clash with R6C1 + R89C1, killer ALS block) -> R3C2 = {789}
17c. Killer triple 7,8,9 in 27(5) cage, R6C1 and R89C1, locked for C1

18. 45 rule on N2 4 innies R1C456 + R2C5 = 24 = {2589/3579/3678/4578} (cannot be {1689/2679/3489} which clash with R1C23, cannot be {4569} which clashes with R23C6), no 1

19. 34(6) cage at R1C2 = {136789/145789/235789/245689/345679}
19a. 6 of {136789/245689/345679} must be in R1C2345 (R1C2345 cannot contain {13/24/34} which would clash with R1C78), no 6 in R2C5

[It took me a long time to find the breakthrough step.]
20. R4C13 = [28]/{46}, R4C2 = {24} (step 5a) -> R4C123 = [248/426/624]
20a. R1C23 = 10 (step 4) = {19/46} (cannot be [28] which clashes with R4C123, killer combo clash), no 2,8

21. R4C2 = 2 (hidden single in C2), clean-up: no 8 in R4C3 (step 5a), no 1 in R3C3
21a. Naked pair {46} in R4C13, locked for R4 and N4

22. 2 in N5 only in R56C6 = {28}, locked for C6 and N5, clean-up: no 5 in R23C6

23. R4C456 (step 10a) = {137} (only remaining combination), locked for R4 and N5 -> R4C9 = 9, R3C7 = 4 (step 2), R9C7 = 3, R7C7 = 7 (step 7a), R9C3 = 9 (step 7), R6C1 = 9 (step 16a), R2C78 = [97], clean-up: no 1 in R1C2 (step 4), no 1 in R1C7, no 1,2 in R1C8, no 3 in R2C6, no 3 in R8C1
23a. Naked pair {58}, locked for N6 -> R5C7 = 6
23b. R1C78 = [23] -> R6C7 = 1, R6C8 = 4 (cage sum), R5C8 = 2, R56C6 = [82]

24. Naked pair {56} in R6C45, locked for R6 and N5, R6C3 = 7 (cage sum), R56C9 = [73], R6C2 = 8, clean-up: no 1 in R2C3

25. 2 in N9 only in 16(3) cage at R8C9 = {268}, locked for N9 -> R8C7 = 5, R4C78 = [85], clean-up: no 7 in R9C1
25a. Naked pair {19} in R78C8, locked for C8 and N9 -> R7C9 = 4

26. 19(4) cage at R7C6 (step 12a) = {1369} (only remaining combination), locked for C6 and N8 -> R23C6 = [43], R14C6 = [57], R3C3 = 5 -> R4C3 = 4, R4C1 = 6, clean-up: no 6 in R1C2 (step 4)

27. R9C3 = 9 -> R9C45 = 12 = {48/57}
27a. Killer triple 3,5,8 in R7C45 and R9C45, locked for N8, 3 also locked for R7
27b. R7C45 = {38} (hidden pair in R7), locked for N8, clean-up: no 4 in R9C45
27c. Naked pair {57} in R9C45, locked for R9 and N8, clean-up: no 7 in R8C1
27d. Naked pair {24} in R8C45, locked for R8 -> R89C1 = [84], R1C1 = 7, R3C2 = 9, R1C2 = 4, R1C3 = 6 (step 4)

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A290 at (Hard?) 1.25. I used a killer combo clash.
Top
 Profile  
Reply with quote  
Ed
 Post subject: Re: Assassin 290
PostPosted: Tue Apr 29, 2014 9:33 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
Andrew wrote:
My solving path was more like wellbeback's, with my key steps 15 and 20 being equivalent to his steps 4 and 5, although we saw each of these steps in different ways.
Loved these two steps from these guys! I used the first one (though saw it another completely different way to both, step 11) and then one more trick (step 12). Andrew's first 12 steps are very similiar to Afmob's way with Afmob's step 4f being the point of departure. Very impressive how both of them work with such large bunches of combo's. These days I try and avoid looking at combos unless I can get them down to 4 or less remaining sets fairly easily.

A290
23 steps:
Prelims courtesy of SudokuSolver
Cage 16(2) n3 - cells ={79}
Cage 5(2) n3 - cells only uses 1234
Cage 7(2) n2 - cells do not use 789
Cage 12(2) n7 - cells do not use 126
Cage 9(2) n14 - cells do not use 9
Cage 9(2) n1 - cells do not use 9
Cage 10(2) n5 - cells do not use 5
Cage 21(3) n78 - cells do not use 123

1. 16(2)n3 = {79}: both locked for r2 and n3
1a. no 2 in 9(2)r2c2

2. "45" on n3: 1 innie r3c7 + 5 = 1 outie r4c9 (IODn3=-5)
2a. r3c7 = (1234), r4c9 = (6789)

3. 6,8 in n3 only in 29(5) -> no 6,8 in r4c9
3a. -> no 1,3 in r3c7 (IODn3=-5)

4. 34(7)r3c7: {1234789/1245679} both blocked by r4c9 = (79)
4a. = {1235689/1345678}
4b. can only have one of 2 or 4 which must be in r3c7 -> no 2 or 4 anywhere else in that cage

5. "45" on n12: 2 outies r4c13 = 10
5a. 2 and 4 in r4 are only in r4c123 -> the h10(2)r4c13 must have one of 2 or 4 (Hidden killer pair)
5b. ->r4c13 = {28/46}(no 1,3,5,7,9)
5c. and r4c2 must have the other one of 2 or 4 for r4 -> r4c2 = (24)
5d. 2 & 4 both locked for n4
5e. r3c3 = (1357)

6. "45" on r1234: 1 innie r4c2 + 4 = 1 outie r5c7 (IODr1234=-4)
6a. r4c2 = (24) -> r5c7 = (68)

7. "45" on n8: 2 innies r9c45 - 9 = 1 outie r9c7
7a. they are all in the same row -> neither innie can equal the outie -> the Innie/outie difference of 9 cannot go in r9c45 -> no 9 in r9c45 (IOU)

8. 21(3)r9c3 = {489/579/678}; ie, must have 9 in r9c3 or be {678}
8a. -> r9c3 = (6789)

9. "45" on n9: 2 innies r79c7 = 10 (no 5)

10. "45" on n8: 2 outies r9c37 = 12
10a. = [93/84] only permutations
10b. r7c7 = (67)(h10(2)r79c7)

Loved wellbeback's step 4 to do this next bit.
11. r6c1 sees all of n9 except r79c3 so must repeat in one of those
11a. "45" on n7: 1 outie r6c1 + 2 = 2 innies r79c3
11b. since r6c1 = one of those two innies -> the other innie must make up the innie/outie difference of 2 (IOE)
11c. -> r7c3 = 2
11d. -> r6c1=r9c3 = (89)
11e. no 8 in r4c1 (h10(2)r4c13)

The cracker
12. 8 in r4 in the 34(7)r3c7 or in r4c3 -> r5c7+r6c1 cannot be [88]
12a. "45" on r789: 1 outie r6c1 - 2 = 1 remaining innie r7c7
12b. but [86] blocked since it forces 8 also into r5c7 (Killer Y-wing?)
12c. -> r6c1 = 9, r7c7 = 7, r9c7 = 3 (h10(2)r79c7) -> r9c3 = 9 (h12(2)r9c37)
12d. r2c78 = [97]

13. "45" on n6: 4 remaining innies r4c789+r5c7 = 28 = {5689} only -> r4c9 = 9, r4c78+r5c7 = {568}: all locked for n6 & 34(7)r3c7 -> no 5,6,8 in r4c456
13a. r3c7 = 4 (IODn3=-5)
13b. r1c78 = [23] only permutation -> r6c78 = [14] only permutation -> r5c8 = 2

14. 32(7)r4c2 = {1234589/1234679/1235678}
14a. must have 2 which is only in r4c2 -> r4c2 = 2
14b. -> r5c7 = 6 (IODr1234=-4)

15. Hidden single 2 in r6 -> r6c6 = 2, r5c6 = 8

16. h10(2)r4c13 = {46} only: 6 locked for n4

17. 32(7)r4c2 = {1234589} only (no 7) -> r6c2 = 8
17a. Must have 4 & 9 which are only in r5c45 -> r5c45 = {49}
17b. Hidden pair {56} in n5 in r6c45 -> r6c3 = 7 (cage sum)

18. 21(3)r9c3 = [9]{48/57}(no 6) = [4/5..]
18a. -> {457}[3] blocked from 19(4)r7c6
18b. 19(4) = {169}[3] only: 1,6,9 locked for c6 & n8
18c. 7(2)n2 = [43] only permutation; r4c6 = 7; r1c6 = 5

19. 14(3)n2 = {167} only combination: all locked for n2, 7 locked for r3
19a. Naked pair {89} in r1c45, both locked for r1, 8 for n2 -> r2c5 = 2
19b. 9(2)r3c3 = [54] only permutation, r4c1 = 6

20. "45" on n2: 2 outies r1c23 = 10 = [46] only permutation
20a. 9(2)n1 = [18] only permutation; r123c1 = [732], r3c2 = 9

21. 12(2)n7 = {48} only combination: both locked for c1

22. 21(3)r9c3: [9]{48} blocked by r9c1 = (48)
22a. -> r9c345 = [9]{57} only: 5 & 7 locked for r9 and n8

23. 16(3)n9 = {268} only combination: all locked for n9

on from there.
Cheers
Ed
Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  Page 1 of 1
  [ 8 posts ] 

Board index » Puzzles and Solutions » Killer Puzzles

All times are UTC


Who is online

Users browsing this forum: No registered users and 15 guests

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB® Forum Software © phpBB Group