Vortex Killer

Our weekly <a href="http://www.sudocue.net/weeklykiller.php">Killer Sudokus</a> should not be taken too lightly. Don't turn your back on them.
mhparker
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Vortex Killer

Post by mhparker »

Hi folks,

One could have been forgiven for thinking that concept Killers have all but died out on this forum. Until now.

Introducing the...


Vortex Killer (Est. rating: 1.75)

The 4-way rotational symmetry of this puzzle makes one feel dizzy just by looking at it. Miss a few critical tricks (especially a quick first placement), and it will suck you in. Mercilessly. But, gain a foothold, and you'll be able to clamber out relatively unscathed.


Image

3x3:d:k:4096:3073:3073:4099:4099:4869:4869:4869:5128:7177:4096:3073:3073:2829:2829:4869:5128:4369:7177:7177:4096:2325:2325:2829:5128:4369:4369:7177:3868:3868:6942:2325:6942:3105:4369:3619:804:3868:3878:3878:6942:3105:3105:4907:3619:804:5678:3878:6942:3889:6942:4907:4907:5429:5678:5678:3128:3641:3889:3889:2876:5429:5429:5678:3128:5697:3641:3641:6212:6212:2876:5429:3128:5697:5697:5697:2892:2892:6212:6212:2876:

Notes:
  • It's a Killer-X, where no repeated digits are allowed on either diagonal.
  • The four corner nonets each contain a 3-cell cage aligned on the corresponding puzzle diagonal. The central nonet contains a 5-cell X-shaped cage.
Ready to take it for a spin?
Cheers,
Mike
CathyW
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Post by CathyW »

Tempting - especially as I'm still stuck on the A66V1.5!

Got the first placement but looks like the rest is going to be a struggle. :?
mhparker
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Post by mhparker »

CathyW wrote:Tempting - especially as I'm still stuck on the A66V1.5!

Got the first placement but looks like the rest is going to be a struggle. :?
OK, Cathy, here's a Lite version to get you warmed up for the Real Thing. Still can't promise you'll be able to do it all in one lunch break, though! :)


Vortex Lite (Est. rating: 1.25)

Image

3x3:d:k:3840:4865:4865:2051:2051:4613:4613:4613:3080:5385:3840:4865:4865:5133:5133:4613:3080:7185:5385:5385:3840:3605:3605:5133:3080:7185:7185:5385:3612:3612:5918:3605:5918:2849:7185:2851:1828:3612:5414:5414:5918:2849:2849:3883:2851:1828:4398:5414:5918:4913:5918:3883:3883:3893:4398:4398:4408:3897:4913:4913:5692:3893:3893:4398:4408:3905:3897:3897:3396:3396:5692:3893:4408:3905:3905:3905:3916:3916:3396:3396:5692:
Cheers,
Mike
CathyW
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Post by CathyW »

Thanks :D

Will give this one a go before going back (for the last time before I give up!) to the A66V1.5.
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Post by Ruud »

I will leave it to others to post a walkthru, but the Vortex Lite was very enjoyable. Good work, Mike!

Did anyone notice that the outies of all the corner nonets of the original Vortex add up to 11? Is there a secret message hidden in this puzzle?

Ruud
Para
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Post by Para »

Ruud wrote:I will leave it to others to post a walkthru, but the Vortex Lite was very enjoyable. Good work, Mike!

Did anyone notice that the outies of all the corner nonets of the original Vortex add up to 11? Is there a secret message hidden in this puzzle?

Ruud
There must be. Did you also notice it was posted at exactly 11 minutes past 2, 4 hidden 11(2) cages -> both 11-2, strange right?. And 11 is 2 1's and 1 + 1 = 2. Can't be a coincidence. Must be some mind control thing. And the vortex title, and the vortex pattern and Mike talking about sucking us in. Must be some alien mind control thing. Who are you working for Mike?
Tell us!!!! :shock: :shock: :? :? :roll: :roll:

Para

ps. Anyone seen my pills?
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Post by Andrew »

Ruud wrote:Did anyone notice that the outies of all the corner nonets of the original Vortex add up to 11? Is there a secret message hidden in this puzzle?
Para wrote:There must be. Did you also notice it was posted at exactly 11 minutes past 2, 4 hidden 11(2) cages -> both 11-2, strange right?. And 11 is 2 1's and 1 + 1 = 2.
That depends on what time zone you are set to for this forum. I'm set to GMT-8 hours and with that the puzzle was posted at 11 minutes past 4 (a.m.). That still makes a coincidence with 4 and 11! :wink:

Although I haven't yet started either version, because I'm still nibbling away at A66V1.5, I had noticed the initial placement and that those outies adding to 11. I thought it was just Mike either trying to make things hard for us or that he didn't like 1s and wanted to get rid of them. Normally 9(2), 10(2) and 11(2) are initially the least useful 2-cell cages because they only eliminate 1 candidate. In the case of non-aligned outies, then 10(2) is the least useful because there are NO initial eliminations.

Mike's diagram is even more a Vortex when one colours the cages, which I always do.
mhparker
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Post by mhparker »

Ruud wrote:Did anyone notice that the outies of all the corner nonets of the original Vortex add up to 11? Is there a secret message hidden in this puzzle?
Funny you should say that. In Germany, where I've been living for the last 17 years, the long run-up to Carneval, where the normally orderly and methodical Germans start dressing up, flirting around, and generally going wild, officially begins at exactly eleven minutes past eleven on the eleventh day of the eleventh month.

So maybe (at least for me) the silly season has just begun! :jocolor: :bounce: :clown: :joker:
Cheers,
Mike
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Post by CathyW »

Ruud wrote:I will leave it to others to post a walkthru, but the Vortex Lite was very enjoyable. Good work, Mike!

Did anyone notice that the outies of all the corner nonets of the original Vortex add up to 11? Is there a secret message hidden in this puzzle?

Ruud
I guess that honour should fall to me but not having a good day. I've gone wrong somewhere and will have to start over tomorrow. :x

I had noticed the outies of the corner nonets in the original puzzle. That's why I knew it would be difficult!!
Para
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Post by Para »

Andrew wrote:
Ruud wrote:Did anyone notice that the outies of all the corner nonets of the original Vortex add up to 11? Is there a secret message hidden in this puzzle?
Para wrote:There must be. Did you also notice it was posted at exactly 11 minutes past 2, 4 hidden 11(2) cages -> both 11-2, strange right?. And 11 is 2 1's and 1 + 1 = 2.
That depends on what time zone you are set to for this forum. I'm set to GMT-8 hours and with that the puzzle was posted at 11 minutes past 4 (a.m.). That still makes a coincidence with 4 and 11! :wink:
Details, details. Only the ones that support our theory matter to conspiracy theorists. And Germany time is the same as mine.

Para
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Post by CathyW »

Vortex Lite - with thanks to Para for helping me see step 36:

Prelims:

a) 8(2) N2 = {17/26/35}
b) 20(3) N2: no 1,2
c) 28(4) @ r2c9 = {4789/5689} -> r12c8 <> 8,9
d) 7(2) N4 = {16/25/34}
e) 21(3) @ r5c3 = {489/579/678}
f) 11(3) @ r4c7: no 9
g) 11(2) @ r4c9 = {29/38/47/56}
h) 19(3) @ r6c5: no 1
i) 15(2) r9c56 = {69/78}
j) 22(3) N9 = {589/679} -> 9 n/e N9 and D\
k) 13(4) @ r8c6 = {1237/1246/1345} must have 1 -> r8c9 <> 1


1. Outies D\: r4c6 + r6c4 = 15 = {69/78}

2. Outies D/: r4c4 + r6c6 = 7 = {16/25/34}
-> r5c5 = 23 - 15 - 7 = 1
-> r4c4, r6c6 <> 6, r6c1 <> 6, r1c4 <> 7
-> 12(3) = {237/246/345} (no 8,9)

3. Outies N1: r2c4 + r4c1 = 10 = {19/28/37/46/55}

4. Outies N3: r1c6 + r4c8 = 13 = {49/58/67}

5. Outies N7: r6c2 + r9c4 = 4 = {13/22}

6. Outies N9: r8c6 + r6c9 = 5 = {14/23}

7. Outies r123: r4c158 = 20 - > r4c1 <> 1,2; r4c5 <> 2 -> r2c4 <> 8,9

8. Outies r789: r6c259 = 13 Max from r6c29 = 3+4 = 7 -> r6c5 min 6

9. Outies c123: r259c4 = 11 -> r5c4 <> 9 Min from r59c4 = 4+1 = 5 -> r2c4 max 6 -> r4c1 min 4

10. Outies c789: r158c6 = 10 = {127/136/145/235} (r1c6 <> 8,9) -> r4c8 <> 45
Min from r18c6 = 4+1 = 5 -> r5c6 max 5
Combos: [451/523/532/541/631/721] -> r8c6 <> 4 -> r6c9 <> 1

11. Innies N5: r46c5 + r5c46 = 22 = {2569/2578/3469/3478}

12. Killer combo 13(4) @ r8c6 and 22(3) N9:
22(3) = {589/679}
13(4) = {1237/1246/1345} -> one of 5,6,7 within N9
-> 15(4) @ r6c9 <> 5 -> 15(4) = {1248/1347/2346}

13. O-I N2: r1c6 + r2c4 - r4c5 = 3

14. O-I N4: r4c1 + r6c2 - r5c4 = 3

15. O-I N6: r4c8 + r6c9 - r5c6 = 8

16. O-I N8: r8c6 + r9c4 - r6c5 = -4 -> r6c5 - (r8c6+r9c4) = 4 -> r6c5 <> 6

17. HS r8c6 = 1 -> r6c9 = 4 -> r5c1 <> 3, r45c9 <> 7, r4c4 <> 3
-> If 28(4) = {4789}, r3c8 = 4 -> r3c8 <> 7

18. HS r7c9 = 1

19. r6c5 = (78) -> r4c6 + r6c4 = {69} n/e D/, N5

20. 12(3) N3 = {237/345} -> 3 n/e D/, N3 -> 17(3) N7 = {278/458} -> 8 n/e N7

21. Split 11(3) r259c4 = [182/173/452/542] -> r2c4 <> 2,3,6 -> r4c1 <> 4,7,8

22. 11(3) @ r4c7 = {128/137/146/236/245}
Combo analysis: r5c6 <> 5 -> r1c6 <> 4, r4c7 <> 7,8
-> r4c8 <> 9

23. 9 locked to 28(4) within N3 -> r12c7 <> 9
-> 9 locked to r1c23 n/e N1 -> 19(4) = 9{127/136/145/235} -> r1c23, r2c3 <> 8

24. 8 locked to r1c17 -> r7c7 <> 8

25. Killer combo: r7c8+r8c9 = {28/37}, 22(3) N9 = {589/679} -> r8c7, r9c78 <> 7

26. Grouped Turbot (1): r1c8 = r6c8 - r6c1 = r23c1 -> r1c23 <> 1

27. Grouped Turbot (8): r1c1 = r1c7 - r23c9 = r34c8 -> r8c8 <> 8 -> r9c9 <> 5

28. Combo analysis split 20(3) r4c158 -> r4c1 <> 6 -> r2c4 <> 4
-> split 11(3) r259c4 = [182/173/542] -> r5c4 <> 5

29. Grouped x-wing: 8 locked to r7c8, r89c9 in N9; 8 locked to 28(4) within c89
-> r45c9, r56c8 <> 8 -> r45c9 <> 3

30. If 28(4) = {4789} r4c8 = 7 -> r23c9 <> 7 (Can't have both 47 within N3 since 12(3) must have one of 4,7)

31. Killer combo: 11(2) r45c9 = {29/56}, r23c9 (of 28(4)) = {56/58/89} ({68} not possible in r45c9 as neither 5 or 9 in r4c8) Must have one of 5,9
-> r9c9 <> 9, r1c9 <> 5

32. From step 13, r4c5 <> 7 as can’t make 10 from r1c6 + r2c4

33. 1 locked to 18(4) within N3 -> 18(4) = 1{278/458/467}
If {1458}, r1c6 = 5 -> r1c78, r2c7 <> 5

34. Grouped Turbot (9): r4c6 = r6c4 - r6c7 = r7c7 -> r7c6 <> 9 -> r7c5 <> 2,3

35. Pointing pair: 7 in either r5c4 or r6c5 -> r6c3 <> 7

So near and yet so far. Don't know why I couldn't see the next step before. :?

36. 12(3) N3 = {237} ({345} would block both options for 28(4) which must have one of 4,5 within N3.) -> 2,7 n/e N3 and D/
-> 17(3) N7 = {458} -> 4,5 n/e N7

37. Split 20(3) r4c158 = {389/479/578} ({569} not possible because r4c6 = {69} -> r4c8 <> 6
Andrew noted: r1c6 <> 7 as well

38. 17(4) @ r6c2 = {1367} (only remaining combo)
-> r6c2 = 1 -> r9c4 = 3, r9c3 = 1, r8c3+r9c2 = {29}

39. r6c5 = 8 (from O-I N8) -> r5c4 = 7 -> r2c4 = 1 -> r4c1 = 9
...

Relatively straightforward from here with cage combos and singles.
Phew! :)
I'll leave Mike's original Vortex for the Masters!

Now off to follow Para's WT for the A66 V1.5 before tomorrow's A67!
Last edited by CathyW on Thu Sep 13, 2007 8:28 pm, edited 3 times in total.
mhparker
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Post by mhparker »

Great stuff Cathy! :D

Like your grouped X-Wing and your chains (steps 26, 27 and 34) especially. BTW, the chains are not CPE, but instead are Turbot fishes (2 strong links at each end with a weak link in the middle)! (Note: What most of us call CPE is what you refer to as "pointing cells".)

But...

Come on guys, the Vortex Lite is really no more difficult than a typical Assassin! Less than 3 hours to go until A67! Surely someone can knock this one on the head by then!

Maybe a marks pic will help (grid state after Cathy's step 35):

Code: Select all

.-----------.-----------------------.-----------------------.-----------------------------------.-----------.
| 2345678   | 2345679     2345679   | 12356       23567     | 567         124678      12467     | 237       |
&#58;-----------+-----------.           '-----------.-----------'-----------.           .-----------+-----------&#58;
| 12345678  | 2345678   | 1234567     15        | 3456789     3456789   | 124678    | 23457     | 5689      |
|           '-----------+-----------.-----------'-----------.           &#58;-----------+-----------'           |
| 12345678    12345678  | 2345678   | 123456789   23456789  | 3456789   | 23457     | 45689       5689      |
|           .-----------'-----------+-----------.           &#58;-----------+-----------&#58;           .-----------&#58;
| 59        | 123456789   123456789 | 245       | 3458      | 69        | 12356     | 678       | 2569      |
&#58;-----------&#58;           .-----------'-----------+-----------+-----------'           &#58;-----------&#58;           |
| 2456      | 23456789  | 456789      478       | 1         | 234         235678    | 235679    | 2569      |
|           &#58;-----------&#58;           .-----------+-----------+-----------.-----------'           &#58;-----------&#58;
| 12356     | 12        | 5689      | 69        | 78        | 235       | 12356789    1235679   | 4         |
&#58;-----------'           &#58;-----------+-----------&#58;           '-----------+-----------.-----------'           |
| 2345679     2345679   | 24578     | 23456789  | 456789      2345678   | 5679      | 2378        1         |
|           .-----------+-----------&#58;           '-----------.-----------'-----------+-----------.           |
| 2345679   | 24578     | 2345679   | 23456789    23456789  | 1           23456     | 5679      | 2378      |
&#58;-----------+-----------'           '-----------.-----------'-----------.           '-----------+-----------&#58;
| 24578     | 12345679    12345679    23        | 6789        6789      | 23456       23456     | 678       |
'-----------'-----------------------------------'-----------------------'-----------------------'-----------'
Cheers,
Mike
Para
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Post by Para »

Hey Mike

I already send Cathy a hint so she can finish it. I solved both. Just no walk-throughs. But still busy tweaking, so will get to a Walk-through when i am done with that.

greetings

Para
CathyW
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Post by CathyW »

Thanks Mike - and again to Para. I finished it with Para's tips and have edited steps to read Grouped Turbot instead of CPE, although aren't the eliminations in common peer cells of the start and finish of the Turbot Chain? Did I get the notation correct? In previous WTs these type of steps have been described in terms of If (a) then (c), if (b) then (c), either case (c).
mhparker
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Post by mhparker »

Hi Cathy,

To answer your questions:
CathyW wrote:...aren't the eliminations in common peer cells of the start and finish of the Turbot Chain?
True, but the emphasis is on the type of chain in this case.
CathyW wrote:Did I get the notation correct?
Yes.
CathyW wrote:In previous WTs these type of steps have been described in terms of If (a) then (c), if (b) then (c), either case (c).
Actually, it's a bit different to the way you stated it. Traditionally, people unfamiliar with AICs and Nice Loops will write something like:
  • if (a) then ... (b)
  • if (a) then ... not (b) => Contradiction!
  • Conclusion: (a) cannot be true
What's happening is this: One can consider the cell(s) being acted on as an additional node, joined to each end of the AIC by two weak links, thus transforming the chain into a Nice Loop. Because these two weak links are contiguous, the alternating nature of the AIC is broken, so the loop is discontinuous.

Many people intuitively prefer this loop approach (even though they may be unaware that it's a Nice Loop), because they find it more natural to start on a true premise than on a false premise, as is the case with AICs.

Because the loop is discontinuous, if one starts at the discontinuity (the cell(s) being acted on), and works one's way around the loop back to the start, one ends up with a contradiction. The chain proves that if X is true, then X must be false. The result being that X is false.

However, instead of working their way around the loop, back to the start, it's unfortunately common practice in walkthroughs for people to start at the discontinuity and branch out in both directions, meeting up in the middle of the loop somewhere. Whilst this will also prove a contradiction, it's considered less elegant than doing a complete cycle of the loop in one direction.

If you find yourself in this "either/or" situation, it's worth spending a couple of minutes to "normalize" the loop to standard form to just go in one direction. This is always possible.

As an example, consider your contradiction move in your Assassin 59 WT:
25. Split 6(2) r3c46:
If [24] -> r1c7 = 2 -> CONFLICT: No place for 2 in N1
Marks pic:

Code: Select all

.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 12346789    12346789  | 1234        56789     | 5678      | 1234        123       | 345789      345789    |
&#58;-----------------------'-----------.           |           |           .-----------'-----------------------&#58;
| 3456789     3456789     345678    | 123567    | 5678      | 1234      | 3456789     123456789   123456789 |
&#58;-----------------------.-----------&#58;           &#58;-----------&#58;           &#58;-----------.-----------------------&#58;
| 12345678    12345678  | 456789    | 25        | 789       | 14        | 12346789  | 123456789   123456789 |
&#58;-----------.           |           &#58;-----------'           '-----------&#58;           |           .-----------&#58;
| 2345678   | 3456789   | 456789    | 12356789    1234789     1235679   | 12346789  | 12345689  | 23456789  |
|           '-----------'-----------+-----------------------------------+-----------'-----------'           |
| 12345678    12345678    12345678  | 12356789    1234789     1235679   | 3456789     123456789   123456789 |
|           .-----------.-----------+-----------------------------------+-----------.-----------.           |
| 12345678  | 345679    | 4789      | 2356789     1234789     235679    | 2467      | 123567    | 12345678  |
&#58;-----------'           |           &#58;-----------.           .-----------&#58;           |           '-----------&#58;
| 1234568     1234568   | 3458      | 79        | 123       | 79        | 3468      | 1234568     1234568   |
&#58;-----------------------'-----------&#58;           &#58;-----------&#58;           &#58;-----------'-----------------------&#58;
| 123456789   123456789   12345678  | 124       | 2356      | 568       | 3456789     123456789   123456789 |
&#58;-----------------------.-----------'           |           |           '-----------.-----------------------&#58;
| 456789      456789    | 5678        1234      | 2356      | 568         234       | 12346789    12346789  |
'-----------------------'-----------------------'-----------'-----------------------'-----------------------'
This is a case of what I mean by going in two directions:
  1. r3c4 = 2 -> r3c12 <> 2
  2. r3c4 = 2 -> r12c6 <> 2 => r1c7 = 2 -> r1c123 <> 2
(Note: "->" = weak link; "=>" = strong link)

However, this can be reworked. The fact that knocking 2 out of two groups of aligned cells in N1 leaves no candidate positions for 2 in N1 should alert one to the fact that there is a strong link between these groups of cells in N1 on the digit 2. We can use this strong link to make up a complete circuit, and move round the loop in a constant direction, starting from (and finishing at) r3c4 as follows:

r3c4 = 2 -> r12c6 <> 2 => r1c7 = 2 -> r1c123 <> 2 => r3c12 = 2 -> r3c4 <> 2 (contradiction)

This is a Nice Loop with two weak links at the discontinuity. To "convert" this to an AIC, we can simply strip off the two weak links at the discontinuity, so that the resulting chain starts and ends with a strong link, as follows:

r12c6 <> 2 => r1c7 = 2 -> r1c123 <> 2 => r3c12 = 2

Converting this to Eureka notation, we have the AIC:

(2)r12c6=r1c7-r1c123=r3c12

In other words, if r12c6 does not contain a 2, then r3c12 must contain a 2, so we can remove a 2 from all common peers of r12c6 and r3c12, as at least one of the ends of the chain must be true.

Note that the AIC consists of two strong links (at either end), with a weak link in the middle, and some of the nodes consist of groups of multiple cells. Therefore, your move was actually a grouped Turbot fish!

It's well worth getting into the habit of trying to "normalize" contradiction moves in this way, if for no other reason than the fact that the WT sounds more impressive and less like T&E when using the correct lingo!

Hope this post has helped and not been totally confusing!
Cheers,
Mike
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