## Help to solve hardest puzzles

Post the puzzle or solving technique that's causing you trouble and someone will help

### Help to solve hardest puzzles

About six months ago, two experts in hardest puzzles complained:
totuan wrote:Hi champagne,
Now, not much people considers for hardest puzzles or study how to solve them. Sometimes they spend the times to discuss about the name of technique… what a sad.

champagne wrote:Hi totuan [...],
I know at least one forum member working to-day on hard puzzles looking for unseen properties, but you are right [...] players like to play with puzzles where one elimination ends the game. Some of them can produce very complex moves to do it in once.

And David P Bird mad a very good job to detect complex structures (mainly JExocets) solving or partially solving many of the hardest puzzles. At the end, the game changed.[...]

The full quotations can be read in The hardest sudokus (new thread) here

I guess the "One trick game" played in the "Puzzles" section is the concern of the complaint and I feel like the criticism is aimed at me too.

However, I'd like to be able to solve hardest puzzles, but I don't know how to learn.
champagne refers to David P Bird's teaching documents. I know these three of them:
- Junior Exocet Compendium
- Using Multisector Locked Sets
- Domino Loops

But with these techniques, I am unable to solve some of the Weekly Unsolvable Sudokus on sudokuwiki.org site.

I need help e.g. for this one (#299)
98.76.5..7..8...9...5..9..859...6.8...4...3..........546...7.5.2...1...4......2..

Code: Select all
`+---+---+---+|980|760|500||700|800|090||005|009|008|+---+---+---+|590|006|080||004|000|300||000|000|005|+---+---+---+|460|007|050||200|010|004||000|000|200|+---+---+---+`

No logical solution has been proposed (only T&E) on sudokuwiki.org site

I need help to select the relevant techniques, and I need help to present the solutions of these advanced techniques. I hope to learn from examples. Can someone help ?

Cenoman
Cenoman

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Joined: 21 November 2016
Location: Paris, France

### Re: Help to solve hardest puzzles

Hi cenoman,

a quick answer, not checked in details

My solver solves it using the exocet pattern with

base r3c4 r3c5
target r2c2 r1c8
(no direct elimination)

Step 1 check that this is an exocet pattern for each digit
a) forces the digit in the base,
b) clear the digit in the target
c) check that you have no solution

Step 2 clear step by step non valid pairs using the exocet property

Not as easy as a standard JExocet, but it works.

EDIT I checked the first part, there is no difficulty to see that this is an exocet, all comes in a digit per digit analysis
champagne
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Location: France Brittany

### Re: Help to solve hardest puzzles

Hi All,

Code: Select all
` *-----------------------------------------------------------------------------* | 9       8       123     | 7       6       1234    | 5       1234    123     | | 7       1234    1236    | 8       2345    12345   | 146     9       1236    | | 136     1234    5       | 1234    234     9       | 1467    123467  8       | |-------------------------+-------------------------+-------------------------| | 5       9       1237    | 1234    2347    6       | 147     8       127     | | 168     127     4       | 1259    25789   1258    | 3       1267    12679   | | 1368    1237    123678  | 12349   234789  12348   | 14679   12467   5       | |-------------------------+-------------------------+-------------------------| | 4       6       1389    | 239     2389    7       | 189     5       139     | | 2       357     3789    | 3569    1       358     | 6789    367     4       | | 138     1357    13789   | 34569   34589   3458    | 2       1367    13679   | *-----------------------------------------------------------------------------*`

For this puzzle, just check for first move:
Look at Exocet (1234)[r3c45, r2c2 & r1c8] and 4’s on R1 & C2 => r1c6 & r3c2=4 then the puzzle downgrade to ER9.0

totuan
totuan

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Location: vietnam

### Re: Help to solve hardest puzzles

Hi ttt totuan,

If '4' was in the base, '4' would be in both targets, what is not possible in an exocet.
so '4' is not in the base (and not in the targets)

Right ??
champagne
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Location: France Brittany

### Re: Help to solve hardest puzzles

champagne wrote:Hi ttt totuan,

If '4' was in the base, '4' would be in both targets, what is not possible in an exocet.
so '4' is not in the base (and not in the targets)

Right ??

Yes, my Big Brother
I have no time to complete this one soon, I'll do it later.

totuan
totuan

Posts: 52
Joined: 25 May 2010
Location: vietnam

### Re: Help to solve hardest puzzles

Hi Cenoman,

I am pleased that you have been able to benefit from some of the pieces I have posted. (I have written them because the best way to make sure you properly understand something is to try to write an explanation of it!)

It is impossible to solve the toughest puzzles without stretching the acceptability criteria for the solving methods used. However, many of the relaxed methods make solving the easier problems trivial, and that takes the challenge out of them. That is the reason why I have been trying to find approaches that keep to the principles as closely as possible.

Note I am not saying that assumptive, branched, trial and error, and brute force methods are wrong. I have just been trying to contain them in 'recognisable patterns' and keep to ones that can be notated for others to follow.

I use a spreadsheet helper to take the drudgery out of the simple tasks. This makes it quite easy to develop colouring schemes to help recognise different situations (such as JExocets) and that also influences the areas I try to explore.

David PB
.
David P Bird
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### Re: Help to solve hardest puzzles

totuan wrote:
Yes, my Big Brother
I have no time to complete this one soon, I'll do it later.

totuan

I had a quick look, with the remaining situation rated 9.0, you can hesitate between "using exocet properties" or using more classical moves.

In exocet mode, the best step seems to prove that the pair 12 is not valid, leaving digit "3" forced (in base and targets), then to apply classical moves
champagne
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Location: France Brittany

### Re: Help to solve hardest puzzles

Hi cenoman and ttt,

abi came to give once again nice steps to solve this puzzle
here above, a full solution for the hard steps

the original puzzle is rated 10.8 by Sudoku Explainer

Code: Select all
`9    8    123    |7     6      1234  |5     1234   123   7    1234 1236   |8     2345   12345 |146   9      1236  136  1234 5      |1234  234    9     |1467  123467 8     --------------------------------------------------------5    9    1237   |1234  2347   6     |147   8      127   168  127  4      |1259  25789  1258  |3     1267   12679 1368 1237 123678 |12349 234789 12348 |14679 12467  5     --------------------------------------------------------4    6    1389   |239   2389   7     |189   5      139   2    357  3789   |3569  1      358   |6789  367    4     138  1357 13789  |34569 34589  3458  |2     1367   13679 `

First step is to identify the exocet r3c45; r1c8;r2c2

then, "ttt"s step on the digit 4. As digit 4 in the base forces digit 4 in both targets, digit 4 can not be in the base

The puzzle is now rated 9.0 with the following pm

Code: Select all
`9    8    123    |7     6     4    |5    123   123   7    123  1236   |8     235   1235 |4    9     1236  136  4    5      |123   23    9    |167  12367 8     ----------------------------------------------------5    9    1237   |1234  2347  6    |17   8     127   168  127  4      |1259  25789 1258 |3    1267  12679 1368 1237 123678 |1239  23789 1238 |1679 4     5     ----------------------------------------------------4    6    1389   |239   2389  7    |189  5     139   2    357  3789   |3569  1     358  |6789 367   4     138  1357 13789  |34569 34589 358  |2    1367  13679 `

Now a nice step proposed by "abi"

If 6r2c3 is true then
a) the exocet base can not be 13 locked by r3c1
b) for other possibilities 12 and 23
b.1) the cell r3c1 has the third digit
b.2) the 2 other digits are in cells r1c8;r2c2 (exocet)
and the cell r1c3 is empty.

so r2c3 is false, r3c1 is true

the puzzle is now rated 7.8 and after basic moves, we end somewhere here

Code: Select all
`9   8    123   |7    6     4    |5  123  13  7   123  123   |8    235   1235 |4  9    6   6   4    5     |123  23    9    |17 1237 8   --------------------------------------------5   9    1237  |4    237   6    |17 8    127 18  127  4     |1259 25789 125  |3  6    127 138 1237 6     |123  2378  123  |9  4    5   --------------------------------------------4   6    139   |239  239   7    |8  5    139 2   357  3789  |359  1     358  |6  37   4   13  1357 13789 |6    4     358  |2  137  179`

with an ALS r5c269

abi again proposes a single move to finish

1r5c1 - (~1r5c269) = 5rc6 - 5r89c6 = 5r8c4 _ 9r8c4 = 9r8c3 _ 8r9c3 = 8r9c6 - 8r9c7 = 3r9c7 - 3r9c1 = 1r9c1 - 1r5c1

after ~1r5c1 stte
champagne
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### Re: Help to solve hardest puzzles

Many thanks Champagne, totuan and David !
Many thanks also to abi, if ever she reads on this thread (champagne "translation" has been useful) !

I'm presently missing time to assimilate your posts. I'll do it later.
Regards.
Cenoman
Cenoman

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Location: Paris, France

### Re: Help to solve hardest puzzles

champagne wrote: you can hesitate between "using exocet properties" or using more classical moves.

Yes, but abi did it soon (on “using exocet properties”) so I’m lazy to find others way

The original puzzle ER10.8
Code: Select all
` *-----------------------------------------------------------------------------* | 9       8       123     | 7       6       1234    | 5       1234    123     | | 7       1234    1236    | 8       2345    12345   | 146     9       1236    | | 136     1234    5       | 1234    234     9       | 1467    123467  8       | |-------------------------+-------------------------+-------------------------| | 5       9       1237    | 1234    2347    6       | 147     8       127     | | 168     127     4       | 1259    25789   1258    | 3       1267    12679   | | 1368    1237    123678  | 12349   234789  12348   | 14679   12467   5       | |-------------------------+-------------------------+-------------------------| | 4       6       1389    | 239     2389    7       | 189     5       139     | | 2       357     3789    | 3569    1       358     | 6789    367     4       | | 138     1357    13789   | 34569   34589   3458    | 2       1367    13679   | *-----------------------------------------------------------------------------*`

Thanks for the puzzle, I re-present abi’s steps as diagram.

01: Exocet(1234)[r3c45,r1c8 & r2c2]
02: (4)r1c6=Exocet(1234)[r3c45,r1c8 & r2c2][(4)r1c8-(4)r2c2]=(4)r3c2 => r3c45, r2c2, r1c8<>4, some singles

03: abi’s move, present as diagram: => r3c1=6 and some singles

Code: Select all
`Exocet(123)[r3c45,r1c8 & r2c2] ||(13)r3c45-(13=6)r3c1*     -----------------------                         ||                      |                       |   (12)[r3c45,r1c8 & r2c2]----(12=3)r1c3----        |            ||                                      |       | ||                       --------------(3)r3c1=(1)r3c1=(6)r3c1*                         ||                      |                       |                ||                      |                       |(23)[r3c45,r1c8 & r2c2]---(23=1)r1c3-------------`

04: abi’s move, present as diagram: => r5c1<>1, stte

Code: Select all
`(3)r9c6-(3=1)r9c1* ||(5)r9c6------------------------------------(5=127)r5c269* ||                                     |(8)r9c6-r9c3=(8-9)r8c3=(9-5)r8c4=r89c5--`

Note: this puzzle as an example on using Almost-Exocet to attack hardest puzzles.

totuan
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Location: vietnam

### Re: Help to solve hardest puzzles

champagne wrote:Step 1 check that this is an exocet pattern for each digit
a) forces the digit in the base,
b) clear the digit in the target
c) check that you have no solution

Is this the normal process to characterize the exocet pattern ?
It seems to be what some would call an assumptive step...
abi seems to propose a process based on chains, that I have not yet successfully caught.

So I have a question to experts: is there a summary document of the exocet pattern (I mean the larger one, beyond the JExocet) ?

totuan wrote:Note: this puzzle as an example on using Almost-Exocet to attack hardest puzzles.

Why this one is it "almost" ? Which character is in excess to a full exocet pattern ?

Regards.
Cenoman
Cenoman

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Joined: 21 November 2016
Location: Paris, France

### Re: Help to solve hardest puzzles

Cenoman wrote:
champagne wrote:Step 1 check that this is an exocet pattern for each digit
a) forces the digit in the base,
b) clear the digit in the target
c) check that you have no solution

Is this the normal process to characterize the exocet pattern ?
It seems to be what some would call an assumptive step...
abi seems to propose a process based on chains, that I have not yet successfully caught.

So I have a question to experts: is there a summary document of the exocet pattern (I mean the larger one, beyond the JExocet) ?

totuan wrote:Note: this puzzle as an example on using Almost-Exocet to attack hardest puzzles.

Why this one is it "almost" ? Which character is in excess to a full exocet pattern ?

Regards.

The original summary of the exocet pattern is
here
Later David did a lot of work on Jexocets, a subset of the exocets family, that one can detect just out of the given.

This one in very close to a Jexocet,but likely not in the specification of David.

a) forces the digit in the base,
b) clear the digit in the target
c) check that you have no solution

is as assumptive as any clearing rule, not less, not more.
point c) is usually an easy step done on the pm of the digit
.
champagne
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### Re: Help to solve hardest puzzles

Cenoman wrote:
totuan wrote:Note: this puzzle as an example on using Almost-Exocet to attack hardest puzzles.

Why this one is it "almost" ? Which character is in excess to a full exocet pattern ?

Code: Select all
` *-----------------------------------------------------------------------------* | /       /       /       | /       /       axxx    | /       abcd    /       | | /       abcd    /       | /       /       /       | /       /       /       | | /       axxx    /       | abcd    abcd    /       | /       /       /       | |-------------------------+-------------------------+-------------------------| | /       axxx    axxx    | /       /       /       | /       /       /       | | /       /       /       | /       /       /       | /       /       /       |`

I meant: to attack hardest puzzles we need to seek as much as possible the link between the cells, candidates..., so we can extend the concept on the second move above (4’s on exocet).

For example – see above grid:
01- Exocet(abcd)[r3c45,r1c8 & r2c2]
02- If r4c3=a => r4c2<>a => r3c45, r1c8 & r2c2<>a
………
Based on Exocet(abcd)[r3c45,r1c8 & r2c2] we have a link between r4c3 & [r3c45, r1c8 & r2c2]

My English is too bad, so hope that you can understand my concept.
P/s: you can see sort explanation of Exocet here by me (ttt ) and eleven – not too hard and long...

totuan
totuan

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Location: vietnam

### Re: Help to solve hardest puzzles

After the first step (Exocet (1234)[r3c45, r2c2 & r1c8], eliminitaion of 4r3c45, r2c2, r1c8) it was suggested to end the remaining ER9.0 with "more classical moves"

Here an attempt to do so (FWIW):
Code: Select all
` +-------------------------+-------------------------+-------------------------+ |  9      8      123      |  7       6       4      |  5      123     123     |  |  7      123    1236     |  8       235     1235   |  4      9       1236    |  |  136    4      5        |  123     23      9      |  167    12367   8       |  +-------------------------+-------------------------+-------------------------+ |  5      9      1237     |  1234    2347    6      |  17     8       127     |  |  168    127    4        |  1259    25789   1258   |  3      1267    12679   |  |  1368   1237   123678   |  1239    23789   1238   |  1679   4       5       |  +-------------------------+-------------------------+-------------------------+ |  4      6      1389     |  239     2389    7      |  189    5       139     |  |  2      357    3789     |  3569    1       358    |  6789   367     4       |  |  138    1357   13789    |  34569   34589   358    |  2      1367    13679   |  +-------------------------+-------------------------+-------------------------+`

2. Kraken column (6)r259c9 =>-17r6c7
||(6)r2c9 - (6=17)r34c7
||(6-9)r5c9 = (9)r6c7
||(6-7)r9c9 = r45c9* - (7=1)r4c7

3. Almost X-wing(2)r47c45
(2)r4c3 - r1c3 = r1c89
XW(2)r47c45 - r3c45 = r3c8
(2)r4c9
=> -2 r2c9

4. Finned jellyfish(1)r1347\c3479 + fins r13c8
=> -1 r2c9

Code: Select all
` +-------------------------+-------------------------+-------------------------+ |  9      8      123      |  7       6       4      |  5      123     123     |  |  7      123    1236     |  8       235     1235   |  4      9       36      |  |  136    4      5        |  123     23      9      |  167    12367   8       |  +-------------------------+-------------------------+-------------------------+ |  5      9      1237     |  134     2347    6      |  17     8       127     |  |  168    127    4        |  1259    25789   1258   |  3      1267    12679   |  |  1368   1237   123678   |  1239    23789   1238   |  69     4       5       |  +-------------------------+-------------------------+-------------------------+ |  4      6      1389     |  239     2389    7      |  189    5       139     |  |  2      357    3789     |  3569    1       358    |  6789   367     4       |  |  138    1357   13789    |  34569   34589   358    |  2      1367    13679   |  +-------------------------+-------------------------+-------------------------+`

5. (3)r1c3 = r1c89 - (3=6)r2c9 - r2c3 = (6)r3c1 => -3 r3c1

6. Kraken cell (1239)r6c4 => -3 r3c8
(1)r6c4 - (1=23)r3c45
(2)r6c4 - r56c6 = r2c6 - (2=3)r3c5
(3)r6c4 - r4c45 = r4c3 - r1c3 = (3)r1c89
(9)r6c4 - (9=6)r6c7 - r6c3 = r2c3 - (6=3)r2c9

Code: Select all
` +------------------------+-------------------------+------------------------+ |  9      8      123     |  7       6       4      |  5      123    123     |  |  7      123    1236    |  8       25      125    |  4      9      36      |  |  16     4      5       |  123     23      9      |  167    1267   8       |  +------------------------+-------------------------+------------------------+ |  5      9      1237    |  34      2347    6      |  17     8      127     |  |  168    127    4       |  1259    25789   1258   |  3      1267   12679   |  |  1368   1237   12678   |  1239    23789   1238   |  69     4      5       |  +------------------------+-------------------------+------------------------+ |  4      6      1389    |  239     2389    7      |  189    5      139     |  |  2      357    3789    |  3569    1       358    |  6789   367    4       |  |  138    1357   13789   |  34569   34589   358    |  2      1367   13679   |  +------------------------+-------------------------+------------------------+`

7. Finned Jellyfish(3)r2347\c3459 + fin r2c2
=>-3 r1c3; 10 placements & basics

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` +-----------------------+-----------------------+--------------------+ |  9     8      12      |  7      6       4     |  5    123   13     |  |  7     123    123     |  8      25      125   |  4    9     6      |  |  6     4      5       |  123    23      9     |  17   127   8      |  +-----------------------+-----------------------+--------------------+ |  5     9      1237    |  4      237     6     |  17   8     127    |  |  18    127    4       |  1259   25789   125   |  3    6     127    |  |  138   1237   6       |  123    2378    123   |  9    4     5      |  +-----------------------+-----------------------+--------------------+ |  4     6      139     |  239    239     7     |  8    5     139    |  |  2     357    3789    |  359    1       358   |  6    37    4      |  |  13    1357   13789   |  6      4       358   |  2    137   1379   |  +-----------------------+-----------------------+--------------------+`

8. (1)r1c3 = r2c23 - r2c6 = (1-3)r3c4 = r3c5 - r4c5 = r4c3- r2c3 = (3)r2c2 => -1 r2c2; 5 placements & basics
9. (3)r6c6 = r89c6 - r7c45 = r7c3 - (3=157)r8c2.r9c12 - (7123=8)r6c1246 => -3 r6c1; singles to 81

Not sure to have given the right fish names...

No doubt, abi's way was the right way...
Cenoman
Cenoman

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### Re: Help to solve hardest puzzles

Thanks to Cenoman for asking this question and others for commenting! I've been following with great interest. I haven't tried to seriously study (J)Exocets before because it's seemed too complicated to even know when you have a valid one and when not, not to even mention the numerous variants and eliminating rules. Somehow the big picture has escaped me, and that's poison to my learning style. This discussion has possibly provided some clarity and definitely a renewed interest. This seems like a simple enough rule for me to understand and remember:

champagne wrote:Step 1 check that this is an exocet pattern for each digit:
a) force the digit in the base
b) clear the digit in the target
c) check that you have no solution

Step 2 clear step by step non valid pairs using the exocet property

That's it, huh? Cool. I don't care if a method is assumptive or not as long as it's easily understandable. Only after understanding the underlying logic I'm interested in learning specific patterns which make applying it easier. Now, some follow-up questions:

Not as easy as a standard JExocet, but it works.

What exactly makes it different from a standard JExocet? Is it because some of the digits (13) seem to require more than two cover houses in the S-cells? Like I said, I'm a total newbie to this pattern so this may be a stupid question.

Cenoman wrote:
totuan wrote:Note: this puzzle as an example on using Almost-Exocet to attack hardest puzzles.

Why this one is it "almost" ? Which character is in excess to a full exocet pattern ?

I would have the same question, and I guess it got answered already, but I'd like to double-check if I understood the answers correctly. Would it be correct to call this an Exocet but not a JExocet? In other words, is it actually an almost-JExocet but a full Exocet? (Or perhaps an almost-almost-JExocet?)

Thanks in advance. If this helps me to understand the general concept, I'll be more inclined to start studying David's detailed documents which I'm sure are an excellent source of information. (My first exposure to the pattern was on SudokuWiki, and I think it killed my motivation because it was so scatter-brained and incomplete.)
Last edited by SpAce on Sat Jul 14, 2018 8:01 pm, edited 1 time in total.
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"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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