"Potential Hardest" 3

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"Potential Hardest" 3

Postby mith » Thu Sep 17, 2020 2:23 pm

Code: Select all
+-------+-------+-------+
| . 9 8 | . . 1 | . 4 . |
| . 4 . | 9 . . | 1 . . |
| 1 . . | . 7 . | . . . |
+-------+-------+-------+
| . . 6 | . . . | . . 4 |
| . . . | . 5 . | . . . |
| 9 . . | . . 4 | 7 . . |
+-------+-------+-------+
| 8 . . | . . 9 | . . . |
| 4 . . | . . 7 | . 6 1 |
| . . . | . . . | . 3 2 |
+-------+-------+-------+
.98..1.4..4.9..1..1...7......6.....4....5....9....47..8....9...4....7.61.......32


(As a reminder, these are puzzles which are rated 11+ by SE, but fall to some advanced technique not implemented by SE. I don't think this one quite reduces to basics unless I missed something, but close.)
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Re: "Potential Hardest" 3

Postby SpAce » Thu Sep 17, 2020 4:36 pm

Step 1. Double JExocet

Code: Select all
  *                                            *         *
.---------------------------.--------------------------.-------------------------.
|  7-2356   9         8     | B2356    B236     1      | t236-5   4      m356-7  |
| T2356-7   4        M235-7 |  9       m236-8  t356-28 |  1       78-25   78-356 |
|  1       b2356     b235   |  4        7       8-2356 | T235-6  M259-8  M3569-8 |
:---------------------------+--------------------------+-------------------------:
| *2357     178-235   6     |  178-23   9      *238    | *235     18-25   4      | \235
| *237      178-23    4     |  178-236  5      *2368   | *236     189-2   89-36  | \23.6
|  9        12358     1235  |  12368    12368   4      |  7       1258    3568   |
:---------------------------+--------------------------+-------------------------:
|  8        1236      123   |  1236     1236    9      |  4       57      57     |
|  4        235       2359  |  2358     238     7      |  89      6       1      |
| *567      17-56     179-5 |  18-56    4      *568    |  89      3       2      | \..56
'---------------------------'--------------------------'-------------------------'

1.a. JE2 eliminations for both contained JExocets

    JE2:(2356) r3c23,r2c6,r1c7
Code: Select all
-8 r2c6 (target: non-base digit)
-2 r2c6 (target: digit missing from mirror)
-5 r1c7 (target: digit missing from mirror)
-7 r1c9 (mirror: non-base digit)
-8 r2c5 (mirror: non-base digit)

    JE2:(2356) r1c45,r2c1,r3c7
Code: Select all
-7 r2c1  (target: non-base digit)
-6 r3c7  (target: digit missing from mirror)
-7 r2c3  (mirror: non-base digit)
-8 r3c89 (mirror: non-base digit, locked 9)

    Note: these alone are enough to lead to step 2 with basics.
1.b. JE4 eliminations

    JE4:(2356) r3c23,r2c6,r1c7; r1c45,r2c1,r3c7
Code: Select all
-2356 r1c1,r3c6 (seen by all base cells)
-2356 r2c89     (seen by all targets)
-23   r45       (fish eliminations; known base digits locked into S-cells)
-5    r49        ...
-6    r59        ...

Step 2.

Code: Select all
.----------------.---------------.-----------------.
| 7    9     8   | 235  236  1   | 236  4     356  |
| 236  4     235 | 9    236  35  | 1    78    78   |
| 1    236   235 | 4    7    8   | 235  259   3569 |
:----------------+---------------+-----------------:
| 235  78+   6   | 17+  9    23  | 235  18+   4    |
| 23   78+   4   | 17+  5    236 | 236  18+9  89   |
| 9    235   1   | 36   8    4   | 7    25    356  |
:----------------+---------------+-----------------:
| 8    236   23  | 236  1    9   | 4    57    57   |
| 4    235   9   | 235  23   7   | 8    6     1    |
| 56   1     7   | 8    4    56  | 9    3     2    |
'----------------'---------------'-----------------'

BUG-Lite+1 (178)r45c248 => +9 r5c8; stte
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

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Re: "Potential Hardest" 3

Postby mith » Thu Sep 17, 2020 7:43 pm

Yep, that's exactly what I found.

Worth noting that there is also a Senior Exocet, though unlike the JE it's not sufficient to reduce to step 2 - the Double takes care of its eliminations as well. Also worth noting that SE doesn't find the BUG-Lite+1 (yzf's solver calls this an Extended Rectangle) and rates it a 8.3 after the Double Exocet.

And of course I found it nice there there is both a Swordfish and a Jellyfish in the step 2 position, because I like fishies.
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Re: "Potential Hardest" 3

Postby mith » Thu Sep 17, 2020 7:51 pm

(There are some really nice complex fish to find after the Senior Exocet, FWIW.)
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Re: "Potential Hardest" 3

Postby SpAce » Thu Sep 17, 2020 9:09 pm

mith wrote:Yep, that's exactly what I found.

Great! Did I get the JE eliminations right? Did I miss any? I tried to double-check with SudokuWiki, but it doesn't have all the JE2 eliminations I found. I bet YZF would find them all (and then some), but I still don't have it.

Also worth noting that SE doesn't find the BUG-Lite+1 (yzf's solver calls this an Extended Rectangle) and rates it a 8.3 after the Double Exocet.

Yeah, it seems surprisingly tough without the BUG-Lite. I spotted it immediately just like my step 2 yesterday, and expected it to be just as useless. I was pretty happy to see Hodoku's progress meter turn white instead. It made me think that the puzzle would have probably fallen to some other simple technique as well, but Hodoku disagreed. That was another surprise.

It's also surprising to hear that SE doesn't spot that pattern. I don't use SE, but I've thought it has more uniqueness patterns implemented than Hodoku, and this is one of the simplest. Even SudokuWiki finds it as an "Extended Unique Rectangle".

And of course I found it nice there there is both a Swordfish and a Jellyfish in the step 2 position

Yes, though I don't really count them because they're also simple X-Loops. I think there should be a way to distinguish them from the "real" fishes that can't be seen as X-Loops/Chains, because the latter are definitely tougher to spot.

because I like fishies.

I've noticed :) That's good, because they've been rarely seen here otherwise. That said, puzzles depending on lots of basic fish steps are are quite tedious for a manual solver, so I consider them more software-oriented (which is totally fine -- nothing wrong with catering to them also). Puzzles solvable in a single step (or few) with a complex or kraken fish would be more interesting (for me).
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Re: "Potential Hardest" 3

Postby mith » Thu Sep 17, 2020 10:46 pm

yzf's solver has four extra eliminations (which get cleaned up with basics anyway):

Double JExocet:
Junior Exocet:Base Cells-r3c2,r3c3;Target Cells-r1c6,r2c6,r1c7,r2c7;Cross Cells-r4c167,r5c167,r6c167,r7c167,r8c167,r9c167
Target Cells Check: r2c6<>8
Mirror Check:r2c6<>28,r1c9<>7,r1c7<>5,r2c5<>8
Junior Exocet:Base Cells-r1c4,r1c5;Target Cells-r2c1,r3c1,r2c7,r3c7;Cross Cells-r4c167,r5c167,r6c167,r7c167,r8c167,r9c167
Target Cells Check: r2c1<>7
Mirror Check:r2c1<>7,r3c8<>8,r3c9<>8,r3c7<>6,r2c3<>7
See all the target or base cells:r1c1<>2356,r3c6<>2356,r2c8<>25,r2c9<>356
True Base Cands in non-'S' cells: r4c2<>2,r4c4<>2,r4c8<>2,r5c2<>2,r5c4<>2,r5c8<>2,r4c2<>3,r4c4<>3,r5c2<>3,r5c4<>3,r5c9<>3,r4c2<>5,r4c8<>5,r9c2<>5,r9c3<>5,r9c4<>5,r5c4<>6,r5c9<>6,r9c2<>6,r9c4<>6
Three kinds true base cands share same cover house in cross lines: r4c1<>7,r4c6<>8,r5c1<>7,r5c6<>8


(I've commented on this before, but just to make it totally clear - I am nowhere near being able to comfortably spot these things manually at this point. I make heavy use of the various solvers in deciding what to post, checking for alternate paths, that sort of thing. At some point I'll take a break from generating and posting puzzles and focus on improving my solving instead.)

Personally, I find basic fish a lot when I solve, but I'm usually solving electronically with some way to highlight all instances of a digit and full pencilmarks - manually solving on paper, not so much. In that context, I often spot fish before I see a hidden pair (say), just because it stands out visually to me. Many of the "fish puzzles" I've generated also rely on specific geometries in the givens, which make (most of) the fish much easier to spot straight away. But yeah, I'm sure they're tedious sometimes too. :)

I really need to come up with a good system for categorizing my puzzles though, maybe spoilered so those who want to know whether it's a one-stepper/tedious school of fish/whatever else can and those who like the variety can stay surprised. (Regardless, hopefully it's still a good variety of things!)
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Re: "Potential Hardest" 3

Postby SpAce » Fri Sep 18, 2020 12:22 am

mith wrote:yzf's solver has four extra eliminations (which get cleaned up with basics anyway):

Three kinds true base cands share same cover house in cross lines: r4c1<>7,r4c6<>8,r5c1<>7,r5c6<>8

Ok, thanks! I suspected as much. Those are of course valid, though a bit redundant, taking both naked and hidden eliminations at once. I'm just wondering why it doesn't list -7r9c1 and -8r9c6 as well, as those cells get locked too. We have four true base candidates and eight S-cells, which means that each S-cell gets filled with a base candidate (2x4).

(As a side note, I really hate that style of listing eliminations. I find it very slow to read quickly compared to the -7 r4c1 (or -7r4c1) style. For yzf: I would recommend adding the latter as an option. And white space too.)

I've commented on this before, but just to make it totally clear - I am nowhere near being able to comfortably spot these things manually at this point.

Who is? This one was easy because it was in the "default" spot. Btw, can you give a hint about the SExocet? (Btw, I don't think it can be shortened to two letters because 'SE' is reserved. Perhaps three first letters? 8-) ) I briefly tried to find it, but didn't succeed. Which base cells is it using? (You can put it in a hidden comment if others don't want to see a spoiler at this point.)

I make heavy use of the various solvers in deciding what to post, checking for alternate paths, that sort of thing

And we appreciate. These are quality puzzles, and somewhat different from what we've been used to. It's good to leave the comfort zone every now and then.

At some point I'll take a break from generating and posting puzzles and focus on improving my solving instead.

Probably a good idea (as long as someone keeps posting puzzles!). I'm pretty sure those activities have a positive feedback cycle. Unfortunately I don't know anything about creating puzzles, which probably limits my solving skills a bit. I think it would help with spotting things like complex uniqueness patterns, symmetries, and how the givens can hint to what patterns might be available, etc. It would be awesome if someone wrote a crash course on puzzle generation, especially with those kinds of perspectives included.

Personally, I find basic fish a lot when I solve, but I'm usually solving electronically with some way to highlight all instances of a digit and full pencilmarks - manually solving on paper, not so much.

Yes, it's definitely easier with digit filtering. Still I rarely spot "real" fishes unless they're very obvious, because I usually move on to chaining right after checking for uniqueness patterns.

In that context, I often spot fish before I see a hidden pair (say), just because it stands out visually to me.

Interesting. Even with digit filtering non-chain fishes rarely stand out very easily to me, although I've improved a bit lately (your puzzles have helped). As for hidden pairs, most of them are actually easier to see without candidates. With pencil marks I usually see their naked counterparts first, even if the latter are much bigger.
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Re: "Potential Hardest" 3

Postby mith » Fri Sep 18, 2020 12:42 am

The Senior Exocet yzf's solver gives has base cells:

Hidden Text: Show
r2c89 - kinda fun arrangement, comparing the base cells from the Double.
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Re: "Potential Hardest" 3

Postby SpAce » Fri Sep 18, 2020 2:29 am

Thanks for the hint! I never would have found that one without it, the exotic digit count being the smallest of reasons. A very interesting one, if I got it right. Then again, I think there's an easier way to get the same result with a JE2 in the same cells. Both below.

SExocet: Show
Code: Select all
  *                                     *        *
.----------------------.-----------------------.------------------------.
| *23567  9       8    | 2356    236     1     |  2356   4       3567   |
|  23567  4       2357 | 9       2368    23568 |  1     b78-25  b78-356 |
|  1      2356    235  | 4       7      *23568 |  2356   2589    35689  |
:----------------------+-----------------------+------------------------:
| *2357   123578  6    | 12378   9      *238   | *235    1258    4      | \235.
| *237    12378   4    | 123678  5      *2368  | *236    1289    3689   | \23.6
|  9      12358   1235 | 12368   12368   4     |  7      1258    3568   |
:----------------------+-----------------------+------------------------:
| t8      1236    123  | 1236    1236    9     |  4      57      57     |
|  4      235     2359 | 2358    238    t7     |  89     6       1      |
| *567    1567    1579 | 1568    4      *568   |  89     3       2      | \..56
'----------------------'-----------------------'------------------------'

SExocet:(235678) r2c89,r7c1,r8c6 => +78 r2c89

(78 are true in the targets -> true in the base cells.)

JExocet: Show
Code: Select all
  *                                        *         *
.------------------------.-------------------------.------------------------.
| t7-2356  9       m8    | 2356     236     1      |  2356   4       3567   |
|  23567   4        2357 | 9        2368    23568  |  1     b78-25  b78-356 |
|  1       2356     235  | 4       m7      t8-2356 |  2356   2589    35689  |
:------------------------+-------------------------+------------------------:
| *2357    123578   6    | 12378    9      *238    | *235    1258    4      | \235.
| *237     12378    4    | 123678   5      *2368   | *236    1289    3689   | \23.6
|  9       12358    1235 | 12368    12368   4      |  7      1258    3568   |
:------------------------+-------------------------+------------------------:
|  8       1236     123  | 1236     1236    9      |  4      57      57     |
|  4       235      2359 | 2358     238     7      |  89     6       1      |
| *567     1567     1579 | 1568     4      *568    |  89     3       2      | \..56
'------------------------'-------------------------'------------------------'

JE2:(235678) r2c89,r1c1,r3c6 => +78 r2c89, +7 r1c1, +8 r3c6

(78 are the only base candidates with valid mirrors -> true in the base and the targets.)

Let me know if I screwed up. I didn't spend much time double-checking.
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

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Re: "Potential Hardest" 3

Postby mith » Fri Sep 18, 2020 2:36 am

That's not what yzf's solver has. I have too much benadryl in my system right now to make sense of whether it's correct or not. :)
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Re: "Potential Hardest" 3

Postby SpAce » Fri Sep 18, 2020 2:43 am

mith wrote:That's not what yzf's solver has. I have too much benadryl in my system right now to make sense of whether it's correct or not. :)

Ok, thanks for letting me know! It's perfectly possible that I screwed up. Then again, it would be kind of fun if I didn't, as I've never seen those kinds of variants. Perhaps I'll try again later and see if I find something else that might resemble YZF's result.

(Probably not, though. I think I'm done with this puzzle :) Someone else can try to find the expected SExocet. I do want to know the answer eventually!)
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Re: "Potential Hardest" 3

Postby SpAce » Fri Sep 18, 2020 8:16 pm

Hi mith,

Do you have a verdict? :) Could you also post or pm the SExocet YZF found?
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Re: "Potential Hardest" 3

Postby mith » Fri Sep 18, 2020 9:10 pm

If there's something wrong with yours, I'm not seeing it. For whatever little that is worth. :)

yzf's has target cells:

Hidden Text: Show
r3c6, 7r6c7, force a 7 in the base cells and eliminating from r1c9 and r2c12


After singles, there are four complex fish that make eliminations on the base cells, if you want to look for them. I thought a couple make particularly nice patterns.
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Re: "Potential Hardest" 3

Postby SpAce » Sat Sep 19, 2020 3:47 am

mith wrote:If there's something wrong with yours, I'm not seeing it. For whatever little that is worth. :)

Well, let's hope it's valid, as it's a pretty interesting variant! Or I think so.

yzf's has target cells:

Thanks! So I actually had the same idea, but I just went all-in with it. In fact, it appears that mine is a bit better (assuming it's correct), because it fixes both base digits. Then again, I think the YZF variant would give the other one too as a follow-up inference:

details: Show
r3c6, 7r6c7, force a 7 in the base cells and eliminating from r1c9 and r2c12

That places 7 in r1c1, which leaves 8 as the only possibility for target r3c6 because none of the other digits have a mirror in r1c123. Right?

After singles, there are four complex fish that make eliminations on the base cells, if you want to look for them.

Thanks for the tip! I did let Hodoku look for them :) (Btw, it pays off to let it take the X-Wing (1) first. Otherwise it lists about 500 fishes.) Frankens are the most difficult (practically impossible) fish type for me to spot, especially finned ones. Mutants are usually easier because they're often findable as grouped chains.

I thought a couple make particularly nice patterns.

Indeed! Good for practicing purposes too, though I don't think it will much help me.
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