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(unofficial) Assassin 98
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sudokuEd
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PostPosted: Fri Apr 11, 2008 7:43 am    Post subject: (unofficial) Assassin 98 Reply with quote

This one started out fairly symmetrical but couldn't get a unique solution. Solving is like a lazy tropical river with 16 bridges & many back-waters to explore. Couldn't get a solving strategy idea to work for this design but still an interesting puzzle to relax with.

SS(v3)score is 1.25. Feels spot on.

Just realized I hadn't checked the Assassin page puzzle before submitting this. Ruud's getting too reliable Crying or Very sad . On that note - anyone want to volunteer for uA99?

(unofficial) Assassin 98 (uA98)



PS code:
3x3::k:4353:4353:4098:4098:4098:1283:1283:6148:6148:4353:5381:6406:6406:6406:3079:3079:3079:6148:4353:5381:3848:3848:6406:3079:2313:2313:3082:4363:5381:5381:3848:3852:3852:3341:2574:3082:4363:3087:3087:3088:3088:3088:3341:2574:3082:4363:3601:786:1555:1555:5396:5397:5397:2070:4363:3601:786:3863:4120:5396:5396:5397:2070:5401:3863:3863:3863:4120:3354:3354:5397:4635:5401:5401:2332:2332:1309:1309:4635:4635:4635:

Solution:
615742389
843956127
279183456
328569714
457831692
961427835
182675943
734298561
596314278


Cheers
Ed


Last edited by sudokuEd on Sun Apr 13, 2008 4:07 am; edited 1 time in total
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mhparker
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PostPosted: Fri Apr 11, 2008 9:09 am    Post subject: Reply with quote

sudokuEd wrote:
Just realized I hadn't checked the Assassin page puzzle before submitting this. Ruud's getting too reliable Crying or Very sad

Maybe we should start thinking about looking for a new home? Assuming Ruud is fit and well (which appears to be the case), he's obviously completely lost interest in doing anything further around here. In particular, I'm concerned about potential new members not being able to join the forum to replace the inevitable loss of current forum regulars in the long run.
If someone would create a new Killer forum in the same style as this one, we regulars could all move across in one go and continue the great work there. If we stick together, others (including newbies) would be sure to follow. How about it, guys?
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Afmob
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PostPosted: Fri Apr 11, 2008 9:24 am    Post subject: Reply with quote

I'm afraid we might have to do this though not in a hurry. Is it really impossible to register to this forum without Ruud's confirmation?

If Ruud is ok I wonder why he didn't tell us that he (might have) lost interest in maintaining his site because a simple message wouldn't be so difficult, would it?

Back to this assassin, I found a nice and very helpful Hidden Killer quint which cracks this puzzle which you don't see to often (though it might be a bit of a overkill compared to the suggested rating). I'll post my wt later (this afternoon or evening).
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sudokuEd
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PostPosted: Fri Apr 11, 2008 10:25 am    Post subject: Reply with quote

Afmob wrote:
If Ruud is ok I wonder why he didn't tell us that he (might have) lost interest in maintaining his site because a simple message wouldn't be so difficult, would it?
I agree. So something must be very wrong. This makes me patient. Though a message from Ruud to that effect wouldn't be so difficult either. Hmm.

Moving to djape is the obvious killer alternative, though we have quite a different culture. Personally, I'd love to keep the Assassin origins/culture/collective memory and would like to have Ruud's Assassins 1-90 publicly available where-ever we call "home".

With sudocue.net still live (assuming new members can join), I'd prefer we stay. But, if it suddenly goes black, a "Plan B" would be useful. I'm not ready to quit Assassin strength killers yet. Too much fun still! (though have been a bit grumpy the last few weeks Confused )

Any forum members 249+ lurking??. If new members cannot join, an urgent email to Ruud asking him to give someone the power to do this (a moderator?) would be appropriate.

Thanks for getting us thinking Mike.

Cheers
Ed
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Afmob
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PostPosted: Fri Apr 11, 2008 5:18 pm    Post subject: Reply with quote

Nice puzzle Ed!

This is probably the first time I used a Hidden Killer quint though one could express step 2d with a Killer quad but the way I spotted it was through the 5 candidates.

I also think that the SudokuSolver rating is spot on, but I rate my wt (Hard) 1.25 because of the "overkill" move Wink. By the way, is there a name for this move, when you have a (Hidden) Killer subset and one cage must contain exactly one of the numbers in the subset? I remember several assassins where I encountered this.

Note that the structure of the puzzle also allows one of JC's favorite moves: R19C19 = 28(2+2) (using overlap of R1+C1+R9+C9)

UA 98 Walkthrough:

1. R6789
a) 3(2) = {12} locked for C3
b) 16(2) = {79} locked for C5+N8
c) Outies R9 = 8(2) = [53/62/71]
d) 21(3) @ N7 = 7{59/68} because R8C1 <> 4,8,9 -> 7 locked for N7
e) 13(2): R8C7 <> 4,6
f) 9(2): R9C4 <> 2,8
g) Killer pair (12) locked in R6C3 + 6(2) for R6
h) Innies = 10(2) = [46/64/73/82/91] <> 5
i) Outies = 7(2) <> 7,8,9
j) 8(2): R7C9 <> 6,7

2. C1+R1 !
a) Outies C1 = 10(2) = [19/28/37/46] <> 5
b) ! Hidden Killer pair (56) in R1C1 + 16(3) for R1 since 16(3) can't have both
-> R1C1 = (56) and 16(3) <> {178/349}
c) 17(4) @ N1 <> 4{139/238} because R1C1 = (56)
-> 17(4) must contain two of (56789)
d) ! 17(4) @ N4 can only have one of (56789) because other 17(4) + R89C1 @ C1 already contain four of them
e) 17(4) @ N4 = 34{19/28} -> R45C1 = {34} (step 1i) locked for C1+N4

3. N457
a) 12(2) = {57} locked for R4+N4
b) Hidden pair (12) in R4C2+R6C3 for N4 -> R4C2 = (12)
c) 12(3) <> 9 because {129} blocked by Killer pair (12) of 6(2)
d) Hidden pair (79) in R46C6 for C6 locked for N5; R46C6 = {79}
e) Naked pair (12) locked in R7C13 for R7+N7
f) 15(4) must have 1 or 2 and it's only possible @ R8C4 -> R8C4 = (12)
g) 15(4) can only have one of (12) -> 15(4) = 36{15/24} -> R8C6 <> 6
h) 14(2): R7C2 <> 9
i) 9 locked in 21(3) = {579} locked for N7 -> 9 locked for R9, 5 locked for C1

4. C123
a) R1C1 = 6
b) Outies C1 = 10(2) = [19/37]
c) 2 locked in 21(4) @ C2 = 2{379/469/478/568} <> 1
d) R4C2 = 2
e) 14(2) = {68} locked for C2
f) 21(4) <> 5 because (68) only possible @ R4C3
g) R6C3 = 1, R7C3 = 2, R7C1 = 1 -> R6C1 = 9

5. N58
a) R6C6 = 7, R4C6 = 9 -> R4C5 = 6
b) Innies N5 = 12(2) = [57] -> R4C4 = 5
c) 15(4) = {2346} -> R8C4 = 2; R8C6 <> 4
d) 13(2) = {58} locked for R8
e) 5(2) = {14} locked for R9+N8

6. N6
a) 8(2) = {35} locked for C9
b) R8C9 = 1
c) 12(3) = {246} -> R4C9 = 4, {26} locked for C9
d) 13(2) = {67} -> R4C7 = 7, R5C7 = 6
e) R5C9 = 2, R3C9 = 6

7. N13
a) 24(3) = {789} locked
b) 9(2) = {45} locked for R3+N3
c) R4C3 = 8
d) 21(4) = {2478} -> R3C2 = 7, R2C2 = 4
e) 15(3) = {159} -> R3C3 = 9, R3C4 = 1
f) 25(4) = 9{268/358/367} -> R2C4 = 9

8. Rest is singles.

Rating: (Hard) 1.25. I used a Hidden Killer quint to crack it.

If the time comes that we have to use a new forum, I think it should not only be for the assassin fanatics but other users of Sudocue.net too (like the very active clueless fraction). But if rumours are true then this forum at least exists until December 2008, so we have more then enough time to discuss the future of this forum and its users.
I also think it's better if we discuss this topic in a different thread and section (in General website comments?), so that everybody can participate.

But I still have lots of hope that Ruud comes back or at least posts a message some time.


Last edited by Afmob on Thu Apr 17, 2008 6:27 am; edited 3 times in total
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mhparker
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PostPosted: Fri Apr 11, 2008 7:02 pm    Post subject: Reply with quote

Hi guys,

No chance of beating Afmob these days (unless he's got an imminent math exams, that is Smile), but here's my WT anyway. Unlike Afmob, I'll rate it as a middle-of-the-road 1.25, because I didn't use any "overkill" moves.

Thanks for the enjoyable puzzle, Ed. Very Happy

Afmob wrote:
If the time comes that we have to use a new forum... I also think it's better if we discuss this topic in a different thread and section (in General website comments?), so that everybody can participate.

I agree. Just wanted to "test the water" here first. BTW, congratulations on creating your first killer last week, which was a very pleasant surprise on returning from my week's hols in Egypt. Applause

So, without further ado, here's my UA98 WT:

Edit: A couple of typos fixed. Thanks Afmob!

Triple click (if not using Safari, as I've recently noticed) to see what I wrote:
UA98 Walkthrough

Prelims

a) 5(2) at R1C6 and R9C5 = {14/23} (no 5..9)
b) 24(3) at R1C8 = {789}, locked for N3
c) 12(4) at R2C6 = {1236/1245} (no 7..9); no 1,2 in R2C45 (CPE)
d) 9(2) at R3C7 = {36/45} (no 1,2)
e) 15(2) at R4C5 = {69/78} (no 1..5)
f) 13(2) at R4C7 and R8C6 = {49/58/67} (no 1..3)
g) 10(2) at R4C8 = {19/28/37/46} (no 5)
h) 12(2) at R5C2 = {39/48/57} (no 1,2,6)
i) 14(2) at R6C2 = {59/68} (no 1..4,7)
j) 3(2) at R6C3 = {12}, locked for C3
k) 6(2) at R6C4 = {15/24} (no 3,6..9)
l) 21(3) at R6C6 and R8C1 = {489/579/678} (no 1..3)
m) 8(2) at R6C9 = {17/26/35} (no 4,8,9)
n) 16(2) at R7C5 = {79}, locked for C5 and N8; no 6,8 in R4C6 (cleanup); no 4,6 in R8C7 (cleanup)
o) 9(2) at R9C3 = [36/45/54/63/72/81] (no 9 in R9C3, no 8 in R9C4)

1. R6C3 and 6(2) at R6C4 form killer pair on {12} within R6
1a. -> no 1,2 elsewhere in R6
1b. cleanup: no 6,7 in R7C9

2. 12(3) at R3C9 and 10(2) at R4C8 form hidden killer pair on {12} within N6
2a. -> 10(2) at R4C8 = {19/28} (no 3,4,6,7)
2b. 12(3) at R3C9 = {129/138/147/156/237/246} (no {345})

3. Innies N5: R4C4+R6C6 = 12(2) = {39/48/57} (no 1,2,6)
3a. no 9 in R4C4

4. Outies R9: R8C19 = 8(2) = [53/62/71] (no 4,8,9)
4a. no 5,6,7 in R8C9

5. 21(3) at R8C1 = {579/678} (no 4) ({489} blocked because none of these digits in R8C1)
5a. 7 locked for N7
5b. cleanup: no 2 in R9C4

6. Outies C1: R19C2 = 10(2) = [19/28/37/46] (no 5)
6a. no 6..9 in R1C2

7. R1C1 and 16(3) at R1C3 form hidden killer pair on {56} within R1
7a. -> R1C1 = {56}; 16(3) at R1C3 = {169/259/268/358/367/457} (no {178/349})

8. 17(4) at R1C1 = {(5/6)..} = {1259/1268/1358/1367/1457/2357/2456} (no {1349/2348}) (no eliminations yet)
8a. -> must contain exactly 2 of {1..4}, 1 of which is in R1C2
8b. -> exactly 1 of {1..4} in R23C1

9. Outies R6789: R45C1 = 7(2)
9a. -> R67C1 = 10(2) (17(4) cage split)
9b. 17(4) at R4C1 must contain remaining 3 of {1..4} in C1 (step 8b)
9c. split 10(2) at R67C1 must contain exactly 1 of {1..4}
9d. -> split 7(2) at R45C1 must contain 2 of {1..4}
9e. -> split 7(2) at R45C1 = {34}, locked for C1 and N4
9f. split 10(2) at R67C1 = [82/91] (no 5..7 in R6C1; no 6,8,9 in R7C1)
9g. cleanup: no 8,9 in R5C23

10. Naked pair (NP) at R5C23 = {57}, locked for R5 and N4
10a. cleanup: no 6,8 in R4C7; no 9 in R7C2

11. NP at R7C13 = {12}, locked for R7 and N7
11a. cleanup: no 6,7 in R6C9

12. NP at R67C9 = {35}, locked for C9
12a. cleanup: no 5 in R8C1 (step 4)

13. 21(3) at R8C1 = {579/678} (step 5)
13a. -> 21(3) at R8C1 and R7C2 together lock 5 for N7
13b. cleanup: no 4 in R9C4

14. 15(4) at R7C4 = {1356/2346} (7 unavailable, {1239/1248} unplaceable)
14a. must contain 1 of {12}, only possible in R8C4
14b. -> R8C4 = {12}
14c. {1356} combo blocked by R8C19 (step 4)
14d. -> 15(4) at R7C4 = {2346} (no 1,5,8,9)
14e. -> R8C4 = 2
14f. cleanup: no 4 in R6C5; no 3 in R9C56

15. R8C19 (step 4) = [71]
15a. cleanup: no 6 in R8C6; no 9 in R9C1

16. R78C5 = [79]
16a. cleanup: no 4 in R8C6

17. Hidden single (HS) in N7 at R9C2 = 9
17a. -> R9C1 = 5 (cage sum)
17b. -> R1C1 = 6; R1C2 = 1 (step 6)
17c. cleanup: no 4 in R1C67; no 4 in R9C3

All singles and simple cage sums to end now!

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Mike
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mhparker
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PostPosted: Sat Apr 12, 2008 10:50 am    Post subject: Reply with quote

Hi folks,

V1 not enough of a challenge? If so, here's a variation that should get those brain cells ticking over a bit faster. May the magic of the Pharaohs assist you in your task: farao

(Unofficial) Assassin 98 V2 (UA98V2) (Est. rating: 1.75)



3x3::k:4352:4352:5378:5378:5378:3077:3077:2055:2055:4352:5386:4875:4875:4875:5390:5390:5390:2055:4352:5386:4372:4372:4875:5390:2328:1817:7194:4635:5386:5386:4372:3359:3359:2328:1817:7194:4635:1829:1829:3623:3623:3623:2346:2346:7194:4635:2350:4143:3376:3376:4146:4659:4659:7194:4635:2350:4143:4409:5434:4146:4146:4659:4670:3647:4409:4409:4409:5434:5434:5434:4659:4670:3647:3647:2634:2634:3148:3148:3148:4670:4670:

Solution:

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

SudokuSolver v3.0 scores this at 2.28, but of course, we know better... Wink

P.S. The original (more legible) image is available here.
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Cheers,
Mike


Last edited by mhparker on Mon Apr 14, 2008 9:11 pm; edited 1 time in total
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Afmob
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PostPosted: Sat Apr 12, 2008 4:24 pm    Post subject: Reply with quote

This was a Killer that despite its difficulty was really fun to solve. Thanks Mike!

I thought that I had to use chains to crack it because of SS's rating and JSudoku needs XY-Chains to solve it, but in the end only Innies+Outies analysis was needed to solve it.

I hope to see some other wts for V1 (and V2 too Smile) since Mike's and my breakthrough move for V1 are quite similar but it can be solved in a different way which isn't more difficult.

UA 98 V2 Walkthrough:

1. C123
a) Outies C1 = 4(2) = {13} locked for C2
b) 9(2) = {27/45}
c) Innies+Outies C12: -4 = R45C3 - R8C2
-> R8C2 = (789) and R45C3 <= 5 -> R45C3 <> 5,6,7,8,9
d) 7(2) = [43/52/61]
e) 14(3) must have 1 xor 3 because R9C2 = (13) -> R89C1 <> 1,3
f) 16(2) = {79} locked for C3
g) 10(2): R9C4 <> 1,3
h) 21(3): R1C45 <> 5 because R1C3 <> 7,9
i) 21(4) <> {1389} because 1,3 only possible @ R4C3
j) Hidden Killer pair (89) in 21(4) + R8C2 for C2
-> R8C2 <> 7 and 21(4) <> {3567}
k) 17(4) @ N7 must have 8 xor 9 because R8C2 = (89) -> R78C4+R8C3 <> 7,8,9

2. C789
a) Outies C9 = 9(2): R9C8 <> 1,2,3,9
b) 28(4) = 89{47/56} -> 8,9 locked for C9
c) 8(3) = 1{25/34} -> 1 locked for N3
d) 9(2) @ N3: R4C7 <> 8
e) 7(2): R4C8 <> 6
f) Innies+Outies C89: -2 = R56C7 - R2C8
-> R2C8 <> 2,3,4 and R56C7 <= 7 -> R56C7 <> 7,8,9
g) 9(2) @ R5: R5C8 <> 1,2

3. R5+N5
a) Innies R5 = 15(2) = {69/78}
b) Innies N5 = 5(2) = {14/23}
c) 17(3) must have 1,2,3 xor 4 and R4C4 = (1234) -> R3C34 <> 1,2,3,4
d) 17(3) <> 1 because R3C3 <> 7,9
e) Innies N5 = 5(2): R6C6 <> 4
f) 16(3) must have 1,2 xor 3 because R6C6 = (123) -> R7C67 <> 1,2,3
g) 14(3) <> 6 because {167} blocked by Killer pair (67) of Innies R5 and
{356} blocked by Killer triple (356) of 7(2)
h) 14(3) <> 7 since one of 13(2) @ N5 must be {67}
i) Killer pair (89) locked in 14(3) + Innies for R5
j) 9(2) <> 1

4. R9
a) Outies = 9(2+1) <> 8,9; R7C9+R8C1 <> 7
b) Outies = 9(2+1): R8C9 <> 7 because R8C1 >= 2
c) Outies = 9(2+1): R7C9 <> 5 because R8C1 <> 1,3
d) 14(3): R9C1 <> 2,4 because R8C1+R9C2 <= 9
e) Innies+Outies: -9 = R8C1 - R9C89
- R9C9 <> 1,2 because R8C1 >= 2 and R9C8 <= 8

5. R1234 !
a) Innies R1 = 12(4) <> 7,8,9
b) Innies = 15(2+1): R4C1 = (1234) because R34C9 @ 28(4) >= 11
c) ! Innies+Outies R123: 1 = R4C234 - R3C789
- R3C789 >= 13 because R1C7+R2C78 @ N3 <= 24
- R4C234 >= 14 -> R4C2 = (789) because R4C34 <= 7
d) ! Innies+Outies R123: 1 = R4C234 - R3C789
- R3C789 = 13/14/15(3) because R4C234 <= 16
- R1C7+R2C78 @ N3 = 22/23/24(3) <> 2,3,4 and 9 locked for N3
e) R1C6 <> 8,9
f) 28(4) = 89{47/56} -> 9 locked for N6

6. N123689
a) Outies N1236 = 27(3+2): R78C8 = 11/12/13(2) <> 1 because R4C234 = 14/15/16(3) (step 5d)
b) 18(4): R6C8 <> 7,8 because R78C8 >= 11
c) 8 locked in R456C9 for C9
d) Outies N89 = 22(3+3): R9C3 <> 8 because R8C2 = (89) and R8C23+R9C3 <= 16
e) 10(2): R9C4 <> 2
f) Outies N89 = 22(3+3): R6C678 = 6/7/8/9/10(3) because R6C6 = (123) and R6C78 = 5/6/7(2) (step 6a)
-> R8C23+R9C3 = 12/13/14/15/16(3)

7. C123
a) 8 locked in R123C3 for N1
b) ! Innies+Outies N47: -5 = R23C2 - (R8C23+R9C3)
- R23C2 = 7/8/9/10/11(2) because of step 6f
-> R23C2 = 8/9/10/11(2) = {26/27/29/45/46/56} since (25,47) are Killer pairs of 9(2)
c) Hidden Killer pair (79) in 17(4) + R23C2 @ 21(4) for N1 since neither of them can have both
-> 17(4) <> {2456}
d) ! Using step 7b: R23C2 = 2{7/9} -> 2 locked for C2+N1 + 21(4)
e) 9(2) = {45} locked for C2
f) R5C2 = 6 -> R5C3 = 1

8. N356
a) Hidden Single: R6C6 = 1 @ N5
b) Innies N5 = 5(2) = [41] -> R4C4 = 4
c) 14(3) = {239} locked for R5+N5
d) 9(2) @ R5 = {45} locked for N6
e) 28(4) must have 4 xor 5 and it's only possible @ R3C9 -> R3C9 = (45)
f) Killer pair (45) locked in 8(3) + R3C9 for N3
g) 7(2) = {16} -> R3C8 = 6, R4C8 = 1
h) 1 locked in R12C9 for C9
i) 21(4): R23C6 <> 5,6,7,8,9 because R2C78 >= 15 and R23C6 <> 1
j) Naked triple (789) locked in R1C7+R2C78 for N3
k) 9(2) @ N3: R4C7 <> 2,3

9. C789
a) Hidden pair (23) in R6C78 for N6 locked for R6 + 18(4); R6C7 <> 6
b) 18(4) @ N6 = 23{49/58}
c) Killer pair (45) locked in R5C8 + 18(4) for C8
d) Outies C9 = 9(2) = {27} -> R1C8 = 2, R9C8 = 7
e) 8(3) = {125} -> {15} locked for C9
f) 18(4) @ R7C9 = {2367} -> {236} locked for C9+N9

10. R789
a) Innies+Outies R9: -2 = R8C1 - R9C9 -> R8C1 = 4, R9C9 = 6
b) 10(2) = {28} -> R9C3 = 2, R9C4 = 8
c) 14(3) = {149} -> R9C1 = 9, R9C2 = 1
d) R7C3 = 7
e) 16(3) = {169} -> R7C7 = 9, R7C6 = 6

11. N2
a) 17(3) = {458} -> R3C4 = 5, R3C3 = 8
b) 12(2) = {48} -> R1C6 = 4, R1C7 = 8

12. Rest is singles.

Rating: 1.5. I used Innies+Outies analysis of multiple nonets to solve it.


Last edited by Afmob on Sat Apr 19, 2008 9:04 am; edited 3 times in total
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HATMAN
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PostPosted: Mon Apr 14, 2008 10:30 pm    Post subject: Reply with quote

In terms of going to a new site, I believe it is best if you can find a way to stay here.

If change is necessary DJApe's would, I think, be better than starting anew. Although, as has been pointed out, the "ethos" is different. I think the variation in nomenclature can be sorted out (Given that you always post walkthoughs (and we don't) I would be happy to fit in with your stuff, Udosuk is flexible enough and JC is already aligned).

These are the two main English language killer sites. which presently coordinate reasonably well with a lot of cross-usage. I would like us to continue with our core strenghts ( DJ variety: Ruud difficulty) and promote Ms Miyuki Misawa’s world.

I find it easy to envisage the Assasins thread on the "Apes" website.

On this subject I think that CathyW can give best advice as a regular member of both forums.
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PostPosted: Tue Apr 15, 2008 10:35 am    Post subject: Reply with quote

Judging from my post count you can see how commited I am here. I'm not posting too much on sudoku.com either, which was my #1 staying place. But I'm sure some of the up-and-comers in djape's site would love to crack the plain killers here. These days I'm focusing on the variants, e.g. Bossdoku (my own creation Cool). But I'll support if you guys decide to all move to djape's place or we all merge together. Wink No love loss to Grandmaster Ruud (my ex-co-moderator) at all.
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PostPosted: Wed Apr 16, 2008 1:01 pm    Post subject: Reply with quote

mhparker wrote:
May the magic of the Pharaohs assist you in your task: farao
Wonderful magic & hidden tunnels they have! Been trying for nearly 18 months (since UTA) to be able to use this trick to solve a puzzle. Thanks Mike! I'm tempted to call this way a hard 1.25 rating, but lets settle for easy 1.50 Cool. [edit: fixed up some clean-ups & typo's. Thanks Afmob & edit 2: thanks Andrew]

(unofficial) Assassin 98 v2

Prelims
i. n1 21(3): no 1,2,3
ii. n2 12(2): no 1,2,6
iii. n3
8(3): no 6,7,8,9
9(2): no 9
7(2): no 7,8,9
28(4): no 1,2,3
iv. n4
7(2): no 7,8,9
9(2): no 9
16(2) = {79}
v. n5 both 13(2)s: no 1,2,3
vi. n6 9(2) no 9
vii. n7 10(2) no 5

1. "45" c1: 2 outies r19c2 = h4(2) = {13}: both locked for c2
1a. no 6 or 8 in 9(2)n4
1b. no 4,6 in r5c3
1c. {1389} combo blocked from 21(4)n1
1d. 14(3)n7 = 1/3 in r9c2 but not both (cage sum won't be reached) -> no 1, 3 in r89c1

2. "45" r1: 4 innies r1c1289 = h12(4)
2a. = 12{36/45}(no 7,8,9)
2b. = [63]{12}/[41]{25} ([61]{23}/[51]{24} blocked by combo's 8(3)n3)
2c. 2 locked in r1c89 for r1 & n3
2d. no 7 in r4c7
2e. no 5 in r4c8
2f. r1c1 = {46}

step 3 deleted

4. 8(3)n3 = {125}: all locked for n3
4a. no 4,8 r4c7
4b. no 2,6 r4c8
4c. no 7 in r1c6

5. "45" c9: 2 outies r19c8 = h9(2) = [18/27/54]
5a. r9c8 = {478}
5b. 3 in c9 only in n9 in 18(4): 3 locked for n9
5c. 18(4) must have 4/7/8 & 3 = 3{168/249/267/456} ({2358} blocked: must have {235} in c9 which clashes with ALS(+1) in r12c1)
5d. 18(4) has only 1 of 4/7/8 which must be in r9c8 -> not in r789c9

6. 4, 7 & 8 in c9 only in 28(4) = {4789}(no 5,6)
6a. 9 locked for c9
6b. 18(4)n9 = 36{18/27/45}
6c. 6 locked for n9

7. "45" r19 & c19! -> 4 corners r19c19 = 180 - sum cages = 22
7a. from step 2b. r1c19 = [62/61/45/42] = 6/7/8/9
7b. -> r9c19 = 13/14/15/16
7c. -> min. r9c9 = 4
7d. max r9c9 = 6 -> min r9c1 = 7
7e. min. r9c12 = [71] = 8 -> max. r8c1 = 6

8. "45" r9: 4 innies r9c1289 = h23(4) must have 1/3 and 5/6
8a. = {1589/1679/3578}
8b. = [9185/9176] ([7385] blocked since r9c19 must = at least 13 step 7b;[8375] blocked by combo's 18(4)n9 step 6b)

9. r9c12 = [91], r8c1 = 4 (cage sum)
9a. no 5 in r6c2
9b. no 6 in r9c4

10. r1c12 = [63]
10a. no 9 in 12(2)r1

11. r67c3 = [97]
11a. no 2 in r6c2
11b. no 3 in r9c4
11c. no 4 in 13(2)r6c4

12. "45" r1: 2 innies r1c89 = 3 = {12} -> r2c9 = 5

13. r9c9 = 6
13a. no 4 in r9c4

14. "45" r9: 1 innie r9c8 = 7
14a. no 3 in r9c3
14b. no 2 in r5c7

15. "45" c9: 1 outie r1c8 = 2; r1c9 = 1
15a. no 7 in r5c7

16. r23c1 = 8 (cage sum) = {17}: both locked for c1 & n1

17. 10(2)n7 = {28}: both locked for r9
17a. 3 in r9 only in n8: locked for n8

18. "45" r5: 2 innies r5c19 = 15 = [87]
18a. no 1 in 9(2)n6

19. r4c9 = 9 (hsingle n6)
19b. no 4 in 13(2)r4c5

20. 9 in r5 only in 14(3)r4c5 = 9{14/23}(no 5,6)

21. 9 in n3 only in r2: locked for r2 & no 9 in r3c6
21a. r3c2 = 9 (hsingle n1)

22. r78c9 = {23}: both locked for n9

23. 21(4)n1 9{237/246/345}(no 1,8) ({1479} clashes with {47} in r6c2; {1569} blocked by r2c2)
23a. r8c2 = 8 (hsingle c2)

24. r9c34 = [28]
24a. no 5 in r6c5

25. r5c3 = 1 (hsingle n4)
25a. r5c2 = 6
25b. no 3 in 9(2)n6

Naked, hidden single and cage sums & easy stuff from here


Last edited by sudokuEd on Sat Apr 19, 2008 5:23 am; edited 2 times in total
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PostPosted: Wed Apr 16, 2008 11:27 pm    Post subject: Reply with quote

I clearly found Ed's uA98 much harder than Afmob and Mike did. After my first 23 steps I ground to a halt, did the first 19 steps for Mike's V2 and then came back to Ed's puzzle a day or two later.

sudokuEd wrote:
Solving is like a lazy tropical river with 16 bridges & many back-waters to explore.

Ed, was this meant to be a hint?

My breakthrough step 24 was effectively the same as the breakthrough used by Afmob and Mike but I saw it differently. The way they did it was clearer and more direct. I also liked Mike's step 2.

I didn't use any very difficult steps but since it took me a long time to spot the breakthrough move I'll rate uA98 as an Extremely Hard 1.25.

Here is my walkthrough. I think there are a few interesting things not used by Afmob or Mike, not just because I took much longer to find how to crack this puzzle.

Many thanks Afmob and Ed for pointing out an incorrect elimination in step 12 and providing feedback on other steps.

Prelims

a) R1C67 = {14/23}
b) R3C78 = {18/27/36/45}, no 9
c) R4C56 = {69/78}
d) R45C7 = {49/58/67}, no 1,2,3
e) R45C8 = {19/28/37/46}, no 5
f) R5C23 = {39/48/57}, no 1,2,6
g) R67C2 = {59/68}
h) R67C3 = {12}, locked for C3
i) R6C45 = {15/24}
j) R67C9 = {17/26/35}, no 4,8,9
k) R78C5 = {79}, locked for C5 and N8, clean-up: no 6,8 in R4C6, no 4,6 in R8C7
k) R8C67 = {49/58/67}, no 1,2,3
l) R9C34 = {36/45}/[72/81], no 9, no 8 in R9C4
m) R9C56 = {14/23}
n) 24(3) cage in N3 = {789}, locked for N3, clean-up: no 1,2 in R3C78
o) 21(3) cage at R6C6 = {489/579/678}, no 1,2,3
p) 21(3) cage in N7 = {489/579/678}, no 1,2,3
q) 12(4) cage at R2C6 = {1236/1245}, no 7,8,9, CPE no 1,2 in R2C45, no 5,6 in R3C6
[Ed also pointed out CPE no 1,2 in R7C4. Maybe that one shouldn’t be in Prelims because there are no immediate eliminations for the 15(4) cage at R7C4. That’s probably also a reason why it’s harder to spot.]

1. Killer pair 1,2 in R6C3 and R6C45, locked for R6, clean-up: no 6,7 in R7C9

2. 25(4) cage at R2C3 = {2689/3589/3679/4579/4678} (cannot be {1789} because R2C345 = {789} clashes with R2C9), no 1

3. 21(3) cage at R6C6 = {489/579/678}
3a. 5 of {579} must be in R7C6 -> no 5 in R6C6 + R7C7

4. 45 rule on C1 2 outies R19C2 = 10 = [19/28/37]/{46}, no 5, no 7,8,9 in R1C2

5. 45 rule on R9 2 outies R8C19 = 8 = [53/62/71], R8C1 = {567}, R8C9 = {123}

6. 21(3) cage in N7 = {579/678} (cannot be {489} because R8C1 only contains 5,6,7), no 4, 7 locked for N7, clean-up: no 6 in R1C2 (step 4), no 2 in R9C4

[This is how I did step 7. For a much better way see after the step.]
7. Hidden killer quad 1,2,3,4 in R1C1, R1C2, R1C345 and R1C67 -> R1C1 + R1C345 must contain one of 1,2,3,4
7a. Hidden killer triple 7,8,9 in R1C1, R1C345 and R1C89 -> R1C1 + R1C345 must contain one of 7,8,9
7b. R1C345 = {169/259/268/358/367/457} (cannot be {178} which contains both 7 and 8, cannot be {349} which contains both 3 and 4)
7c. Killer quad 1,2,3,4 in R1C2, R1C345 and R1C67, locked for R1
7d. Killer triple 7,8,9 in R1C345 and R1C89, locked for R1
7e. -> R1C1 = {56}
[The much better way is hidden killer pair 5,6 in R1C1 and R1C345 for R1 -> R1C1 = {56}, R1C345 must contain 5 or 6 because R1C345 cannot be {556}.]

8. 45 rule on R6789 2 innies R67C1 = 10 = [46/64/73/82/91], no 5, no 3 in R6C1, no 8,9 in R7C1
8a. R45C1 = 7 = {16/25/34}, no 7,8,9
8b. 3 in R6 locked in R6C789, locked for N6, clean-up: no 7 in R45C8

9. 45 rule on C12 2 innies R58C2 = 1 outie R4C3
9a. Min R58C2 = 4 -> min R4C3 = 4
9b. Max R4C3 = 9 -> max R58C2 = 9, no 9, no 8 in R8C2, clean-up: no 3 in R5C3

10. 45 rule on C12 2 outies R45C3 = 1 innie R8C2 + 12, max R45C3 = 17 -> max R8C2 = 5

11. R5C456 = {138/156/237/246} (cannot be {129/147/345} which clash with R6C45), no 9

12. 45 rule in C6789 3 innies R459C6 = 14 = {149/167/239/257/347} (cannot be {158/248/356} because R4C6 only contains 7,9), no 6,8
12a. 7 of {167/257/347} must be in R4C6 -> no 7 in R5C6

13. R46C6 = {79} (hidden pair in C6), locked for N5

14. 45 rule on N5 2 innies R4C4 + R6C6 = 12 = [39/57]

15. 8 in C6 locked in R78C6, locked for N8

16. 15(3) cage at R3C3 = {159/258/348/357} (cannot be {168/249/267} because R4C4 only contains 3,5, cannot be {456} which clashes with R3C78), no 6
16a. 1 of {159} must be in R3C4 -> no 9 in R3C4

17. 9 in R3 locked in R3C123, locked for N1
17a. R1C345 (step 7b) = {169/259/268/358/367/457}
17b. 9 of {169} must be in R1C4 -> no 1 in R1C4

18. 25(4) cage at R2C3 (step 2) = {2689/3589/3679/4579/4678}
18a. 9 of {2689/3589/3679/4579} must be in R2C4 -> no 3,5 in R2C4
18b. 4 of {4678} must be in R23C5 (7 must be in R2C34 and R23C5 = {68} clashes with R4C5), no 4 in R2C4 (4 can still be in R2C3 for {4579})

19. 45 rule on R123 3 outies R4C234 = 1 innie R3C9 + 9
19a. Max R3C9 = 6 -> max R4C234 = 15, min R4C34 = 7 -> max R4C2 = 8

20. 15(4) cage at R7C4 = {1239/1248/1356/2346}
20a. 3,5 of {1356} must be in R8C234 (R8C234 cannot be {136/156} which clash with R8C19) -> no 5 in R7C4 (3 can still be in R7C4 for other combinations)
[Ed: Still missing CPE no 1,2 in R7C4]

21. 45 rule on R89 2 outies R7C45 = 1 innie R8C8 + 7
21a. R7C45 cannot total 14,16 -> no 7,9 in R8C8

22. 45 rule on C9 4 innies R1289C9 = 25 = {1789/2689/3589} (cannot be {3679} which clashes with R67C9, cannot be {4579/4678} because R8C9 only contains 1,2,3), no 4, 8,9 locked for C9
22a. R8C9 = {123} -> no 1,2,3 in R9C9

23. 4 in C9 locked in R345C9 = {147/246/345}, no 8
23a. 3 of {345} must be in R3C9 -> no 5 in R3C9

[At this stage I spotted Hidden killer quint 5,6,7,8,9 in R9C12, R9C34 and R9C789 -> R9C789 must contain two of 5,6,7,8,9 but it only eliminated one combination from 18(4) cage in N9.]

24. R12389C1 must contain at least two of 5,6,7 because R18C1 only contain 5,6,7
24a. 45 rule on C1 5 innies R12389C1 = 28 = {15679/25678} (cannot be {13789/14689/23689/24589} which only contain one of 5,6,7, cannot be {24679/34579} because no 5 in R9C2 so R89C1 cannot be [79], cannot be {34678} which would make 17(4) cage at R1C1 [64]{34}), no 3,4
24b. 5,6,7 locked for C1, clean-up: no 1,2 in R45C1 (step 8a), no 3,4 in R67C1 (step 8)
[Step 24b separated out for clarity and step 25 edited.]


25. Naked pair {34} in R45C1 = {34}, locked for N4, clean-up: no 8,9 in R5C23, no 6 in R67C1 (step 8)

26. Naked pair {57} in R5C23, locked for R5 and N4, clean-up: no 6,8 in R4C7, no 9 in R7C2

27. Naked pair {12} in R7C13, locked for R7 and N7, clean-up: no 6,7 in R6C9
27a. Naked pair {35} in R67C9, locked for C9, clean-up: no 5 in R8C1 (step 5)

28. R5C456 (step 11) = {138/246}
28a. Killer pair 3,4 in R5C1 and R5C456, locked for R5, clean-up: no 9 in R4C7, no 6 in R4C8

29. 9 in R5 locked in R5C78, locked for N6, clean-up: no 1 in R5C8

30. R345C9 (step 23) = {147/246}
30a. 1 of {147} must be in R5C9 -> no 1 in R34C9

31. R4C2 + R6C3 = {12} (hidden pair in N4)

32. 6 in N4 in R4C3 or R6C2, CPE no 6 in R23C2

The original step 33 no longer worked because of the incorrect elimination in step 12. I've re-worked the remaining steps.

33. R58C2 = R4C3 (step 9)
33a. Min R58C2 = 8 -> no 6 in R4C3
33b. R4C3 = {89} -> R58C2 = [53/54] -> R5C23 = [57], clean-up: no 9 in R6C2

34. R6C2 = 6 (hidden single in N4), R7C2 = 8, clean-up: no 2,4 in R1C2 (step 4), no 6 in 21(3) cage in N7 (step 6), no 1 in R9C4
34a. R8C1 = 7, R9C12 = [59], R1C1 = 6, R1C2 = 1 (step 4), R4C2 = 2, R67C3 = [12], R7C1 = 1, R6C1 = 9 (step 8), R6C6 = 7, R4C4 = 5 (step 14), R4C3 = 8, R4C56 = [69], R78C5 = [79], R8C9 = 1 (step 5), clean-up: no 4 in R1C67, no 7 in R4C9 (step 23), no 4,6 in R8C6, no 4 in R9C34
34b. R4C9 = 4, naked pair {26} in R35C9, locked for C9
34c. R45C1 = [34], R4C7 = 7, R5C7 = 6, R4C8 = 1, R5C8 = 9, R5C9 = 2, R3C9 = 6, clean-up: no 3 in R3C78

35. R8C6 = 8 (hidden single in C6), R8C7 = 5, R3C78 = [45], R67C9 = [53], R7C7 = 9, R7C6 = 5 (step 3)

36. 15(4) cage at R7C4 = {2346} (only remaining combination) -> R8C4 = 2, R6C45 = [42], R7C4 = 6, R78C8 = [46], R9C34 = [63]

37. R4C23 = [28] = 10 -> R23C2 = 11 = [47], R8C23 = [34]

38. R4C4 = 5 -> R3C34 = 10 = [91], R5C4 = 8

39. Naked pair {23} in R13C6, locked for C6 and N2 -> R3C5 = 8, R12C5 = [45], R2C3 = 3, R2C4 = 9 (step 2)


and the rest is naked singles


Last edited by Andrew on Sat Apr 26, 2008 7:40 am; edited 3 times in total
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PostPosted: Thu Apr 17, 2008 5:49 am    Post subject: Reply with quote

Thanks Mike for an excellent variant! Smile

After struggling with Ed's original puzzle, I felt that V2 was easier but that was probably because of what I'd learned from solving V1. Also I think there were more key moves in my V2 solution. For those reasons I'll rate V2 as an Easy 1.5 rather than a Hard 1.25.

Afmob wrote:
Note that the structure of the puzzle also allows one of JC's favorite moves: R19C19 = 28(2+2) (using overlap of R1+C1+R9+C9)

Thanks Afmob for reminding me about that type of move. It was useful for step 20. Ed made more use of it in his solution.

I wonder which, if any, of my moves SS wouldn't be able to find. Possibly step 21 although I don't know if that's a critical move. It ought to get step 15 and step 23. There must be some reason why it gave this puzzle such a high rating. Maybe it's because step 23 analyses a hidden cage?

Here is my walkthrough for V2. As with V1, I could probably have found the most important move (step 23) earlier; maybe I would have if step 2 hadn't made the initial candidate eliminations for that hidden cage.

Thanks Ed and Afmob for the feedback and pointing out my logic error.

Prelims

a) R1C67 = {39/48/57}, no 1,2,6
b) R34C7 = {18/27/36/45}, no 9
c) R34C8 = {16/25/34}, no 7,8,9
d) R4C56 = {49/58/67}, no 1,2,3
e) R5C23 = {16/25/34}, no 7,8,9
f) R5C78 = {18/27/36/45}, no 9
g) R67C2 = {18/27/36/45}, no 9
h) R67C3 = {79}, locked for C3
i) R6C45 = {49/58/67}, no 1,2,3
j) R9C34 = {28/46}/[19/37], no 5, no 1,3 in R9C4
k) R1C345 = {489/579/678}, no 1,2,3
l) 8(3) cage in N3 = {125/134}, 1 locked for N3, clean-up: no 8 in R4C7, no 6 in R4C8
m) R3456C9 = {4789/5689}, 8,9 locked for C9

1. R1C345 = {489/579/678}
1a. 5 of {579} must be in R1C3 -> no 5 in R1C45

2. Killer triple 7,8,9 in R1C345 and R1C67, locked for R1

3. 45 rule on C1 2 outies R19C2 = 4 = {13}, locked for C2, clean-up: no 4,6 in R5C3, no 6,8 in R67C2

4. 8(3) cage in N3 = {125/134}
4a. 4 of {134} must be in R1C89 (R1C89 cannot be {13} which clashes with R1C2), no 4 in R2C9

5. 45 rule on C9 2 outies R19C8 = 9 = [18/27/36]/{45}, no 1,2,3,9 in R9C8

6. 45 rule on R9 3 outies R8C1 + R78C9 = 9, no 7 in R7C9, no 7,8,9 in R8C1

7. 14(3) cage in N7 = {149/158/167/239/347/356} (cannot be {248/257} because R9C2 only contains 1,3)
7a. R9C2 = {13} -> no 1,3 in R89C1
7b. 7,9 of {149/239/347} must be in R9C1 -> no 2,4 in R9C1

8. R9C567 = {129/147/156/237/246/345} (cannot be {138} which clashes with R9C2), no 8

9. R8C1 + R78C9 = 9 (step 6)
9a. Min R8C1 = 2 -> max R78C9 = 7, no 7 in R8C9

10. 45 rule on C12 1 innie R8C2 = 2 outies R45C3 + 4
10a. Min R45C3 = 3 -> min R8C2 = 7
10b. Max R8C2 = 9 -> max R45C3 = 5, no 5,6,8, clean-up: no 2 in R5C2

11. 45 rule on R5 2 innies R5C19 = 15 = {69/78}

12. 45 rule on C89 1 innie R2C8 = 2 outies R56C7 + 2
12a. Min R56C7 = 3 -> min R2C8 = 5
12b. Max R2C8 = 9 -> max R56C7 = 7, no 7,8,9, clean-up: no 1,2 in R5C8

13. 45 rule on R1234 3 innies R4C1 + R34C9 = 15
13a. Min R34C9 = 11 (from 28(4) cage combinations) -> max R4C1 = 4
13b. Min R4C1 = 1 -> max R34C9 = 14 -> min R56C9 = 14, no 4 in R6C9

14. 45 rule on N5 2 innies R4C4 + R6C6 = 5 = {14/23}

15. Combined cage R4C56 + R6C45 = 26 = {4589/4679/5678}
15a. R5C456 = {149/158/239} (cannot be {167} which clashes with R5C19, cannot be {248/257/347/356} which clash with combined cage R4C56 + R6C45), no 6,7
15b. Killer pair 8,9 in R5C19 and R5C456, locked for R5, clean-up: no 1 in R5C7

16. 17(3) cage at R3C3 = {269/278/359/368/458/467} (cannot be {179} because 7,9 only in R3C4), no 1, clean-up: no 4 in R6C6 (step 14)
16a. R4C4 = {234} -> no 2,3,4 in R3C34

17. 16(3) cage at R6C6 = {169/178/259/268/349/358/367} (cannot be {457} because R6C6 only contains 1,2,3)
17a. R6C6 = {123} -> no 1,2,3 in R7C67

18. Hidden killer pair 8,9 in R234C2 and R8C2 for C2 -> R234C2 must contain at least one of 8,9
18a. 21(4) cage at R2C2 = {1569/2379/2469/2478/2568/3459/3468} (cannot be {1389} because 1,3 only in R4C3, cannot be {1479/1578} which clash with R67C2, cannot be {3567} which doesn’t contain 8 or 9)
18b. Hidden killer pair 8,9 in R234C2 and R8C2 for C2 -> R8C2 = {89}

19. 17(4) cage at R7C4 = {1259/1268/1349/1358/2348} (cannot be {1367/1457/2357/2456} because R8C2 only contains 8,9), no 7
19a. R8C2 = {89} -> no 8,9 in R7C4 + R8C34

20. 45 rule on R19C19 overlaps, R19C19 = 22
20a. Max R1C19 = 11 -> min R9C19 = 11, no 1 in R9C9

21. 1 can only be in R9C12 if 9 is also there because 9 cannot be in R9C34 or R9C567 unless 1 is in the same cage. However, as Ed has pointed out to me, 9 can be in R9C1 when 1 is in R9C567 so the converse doesn’t apply.
21a.
14(3) cage in N7 (step 7) = {149/239/347/356} (cannot be {158/167} because they only contain one of 1,9), no 2,8

22. 45 rule on C89 2 innies R25C8 = 1 outie R6C7 + 11
22a. Max R25C8 = 16 -> max R6C7 = 5

23. 45 rule on R1 4 innies R1C1289 = 12 = {1236/1245}
23a. {1236} can only be [6312/6321] (cannot be [6123/6132] because 8(3) cage in N3 cannot be {23}3)
23b. {1245} can only be [4125/4152] (cannot be [2145/2154] because R1C89 cannot be more than 7, cannot be [5124/5142] because 8(3) cage in N3 cannot be {24}2)
23c. R1C1 = {46}, R1C12 = [41/63], R1C89 = {12/25}, clean-up: no 5,6 in R9C8 (step 5)
23d. 8(3) cage in N3 = {125} (only remaining combination), locked for N3, 2 locked in R1C89, locked for R1 -> no 2 in R2C9, clean-up: no 7 in R1C6, no 4,7 in R4C7, no 2,5 in R4C8

24. 3 in C9 locked in R789C9, locked for N9
24a. 18(4) cage in N9 = {1368/2367/3456} (cannot be {2358} which clashes with R12C9)
24b. R9C8 = {478} -> no 4,7 in R789C9 (this sub-step has been simplified; I think I’d forgotten to do the step 23c clean-up when I first did this step)

25. 4,7 in C9 locked in R45C9 -> R4567C9 = {4789} (only remaining combination), no 5,6, clean-up: no 9 in R5C1 (step 11)

26. 17(4) cage in N1 = {1349/1367/1457} (cannot be {1259/1358/2357} because R1C1 only contains 4,6, cannot be {1268/2348} which clash with R1C12, cannot be {2456} because R1C2 only contains 1,3), no 2,8, 1 locked for N1
26a. R1C1 = {46} -> no 4,6 in R23C1
26b. {1367} must be [6317/6371]

27. 8 in C1 locked in R567C1 -> R4567C1 = {1278/1368/2358} (cannot be {1458} which clashes with 17(4) cage in N1), no 4,9

28. 14(3) cage in N7 (step 21a) = {149/239/356} (cannot be {347} clashes with 17(4) cage in N1), no 7

[I had to re-solve the remaining steps after Ed pointed out the incorrect elimination of {239}. Fortunately I then discoved that using step 20 together with steps 23a and 23b led to a much quicker finish than I originally had. Very Happy ]

29. R19C19 = 22 (step 20)
29a. Max R1C19 = 9 (steps 23a and 23b) -> min R9C19 = 13 -> R9C1 = 9, R9C9 = {56}, R8C2 = 8, R67C3 = [97], clean-up: no 2 in R6C2, no 4 in R6C45, no 5,6 in R8C1 (step 28), no 2 in R9C4
29b. R9C19 = 14,15 -> R1C19 = 7,8 = [61/62] -> R1C1 = 6, R1C9 = {12}, R1C2 = 3 (step 23c), R9C2 = 1, R8C1 = 4 (step 28), clean-up: no 9 in R1C67, no 9 in R5C9 (step 11), no 5 in R6C2, no 6,9 in R9C4

30. R1C89 = {12} (hidden pair in R1) -> R2C9 = 5, R9C9 = 6, R1C9 = 1 (step 20), R1C8 = 2, R9C8 = 7 (step 5), clean-up: no 2 in R5C7, no 3 in R9C3, no 4 in R9C4
30a. R9C34 = [28], R7C12 = [35], R78C9 = [23], R8C3 = 6, R6C2 = 4, R5C2 = 6, R5C3 = 1, R4C1 = 2, R4C2 = 7, R4C3 = 3, R4C4 = 4, R6C6 = 1 (step 14), R4C8 = 1, R56C1 = [85], R7C4 = 1, R8C4 = 2 (step 19), R56C9 = [78], R34C9 = [49], R3C8 = 6, R6C78 = [23], clean-up: no 8 in R1C6, no 7,8 in R3C7, no 6 in R4C56
30b. R3C7 = 3, R4C7 = 6

31. R4C4 = 4 -> R3C34 = 13 = [85], R1C6 = 4, R1C7 = 8, R2C78 = [79], R3C6 = 2, R12C3 = [54], R23C1 = [17], R23C2 = [29], R3C5 = 1, R2C6 = 3 (cage sum)


and the rest is naked singles


Last edited by Andrew on Sun Apr 27, 2008 4:14 am; edited 4 times in total
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Afmob
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PostPosted: Thu Apr 17, 2008 11:45 am    Post subject: Reply with quote

Ed said that V1 could be solved in a normal (aka not hard) 1.25 way. I discovered this way of solving it with the help of Mike's step 2. And as luck has it, this was nearly the way Ed solved it, so here it is:

UA 98 Walkthrough (easier):

1. R6789
a) 3(2) = {12} locked for C3
b) 16(2) = {79} locked for C5+N8
c) Outies R9 = 8(2) = [53/62/71]
d) 21(3) @ N7 = 7{59/68} because R8C1 <> 4,8,9 -> 7 locked for N7
e) 13(2): R8C7 <> 4,6
f) 9(2): R9C4 <> 2,8
g) Killer pair (12) locked in R6C3 + 6(2) for R6
h) 8(2): R7C9 <> 6,7
i) 21(3): R6C6+R7C7 <> 5 because R7C6 <> 7,9

2. C789 !
a) Innies+Outies C9: -1 = R1C8 - R89C9 -> R9C9 <> 1,2,3,4 because R8C9 <= 3
b) 4 locked in 12(3) @ C9 -> 12(3) = 4{17/26/35} <> 8,9
c) ! Hidden Killer pair (12) in 10(2) + 12(3) for N6
-> 10(2) = {19/28} and 12(3) = 4{17/26} and R3C9 <> 1,2
d) 24(3) = {789} locked for N3
e) 9(2) <> 1,2
f) Killer pair (46) locked in 9(2) + R3C9 for R3+N3
g) 12(4) must have 4 xor 6 and it's only possible @ R2C6 -> R2C6 = (46)
h) R1C6 <> 1
i) ! Innies+Outies N69: -8 = R3C9 - R78C7; R3C9 = (46)
-> R78C7 = 12/14(2) = [48/68/75/95] -> R7C7 <> 8 and R8C7 = (58)
j) 13(2) = {58} locked for R8

3. N569
a) 13(2) @ N6 <> 5,8 because R8C7 = (58) blocks {58}
b) 3,5 locked in R6C789 for R6
c) 6(2) = {24} locked for R6+N5
d) 12(3) @ N5 = 1{38/56} -> 1 locked for R5+N5
e) Hidden pair (79) in R46C6 for C6 locked for N5; R46C6 = {79}
f) Innies N5 = 12(2) = [39/57]
g) R6C3 = 1, R7C3 = 2

4. R789
a) Outies R9 = 8(2) <> 3
b) 3 locked in 8(2) @ C9 -> 8(2) = {35} locked for C9
c) 21(3) @ N8 must have 5 xor 8 and it's only possible @ R7C6 -> R7C6 = {58}
d) Naked pair (58) locked in R78C6 for C6+N8
e) 15(4) = 23{19/46} -> R8C4 = 2
f) 5(2) = {14} locked for R9+N8
g) 9(2) = {36} locked for R9
h) Naked pair (36) locked in R79C4 for C4
i) 18(4) = {1278} -> R8C9 = 1, {278} locked for R9+N9
j) 21(3) @ N7 = {579} -> R8C1 = 7, {59} locked for N7

5. C123+R1
a) Outies C1 = 10(2) = [19] -> R1C2 = 1, R9C2 = 9
b) 5(2) = {23} locked for R1
c) 16(3) = {457} locked for R1
d) Hidden Single: R2C9 = 7 @ N3
e) 25(4) = 89{26/35}, 9 locked for R2
f) R4C4 = 5
g) 15(3) = [37/91]5

6. R6789
a) R9C1 = 5
b) Outies = 7(2) = {34} locked for C1+N4

7. Rest is singles.

Rating: 1.25. I used Hidden Killer pairs and Innies+Outies analysis.


Last edited by Afmob on Fri Apr 18, 2008 5:34 am; edited 1 time in total
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PostPosted: Thu Apr 17, 2008 5:20 pm    Post subject: Reply with quote

Quote:
Anyone want to volunteer for uA99?

Dancing Me!

I'll post uA99 on friday and later (Sunday?) a V1.5. It's quite fun to make your own Killers and it can be as challenging as solving to get the rating and uniqueness right.

Of course, if somebody else is eager to post his killer I'll wait one week though protest fast!
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