The Effortless Extremes thread

Everything about Sudoku that doesn't fit in one of the other sections

Postby RW » Mon Apr 17, 2006 7:35 pm

Thanks again guys for the puzzles. This time most puzzles passed the requirements. There was a only a few that I could solve with uniqueness reductions instead and only one basic UR:

Code: Select all
XY-chain(7)
 *-----------*
 |1..|6.3|..4|
 |.7.|2.8|.9.|
 |...|.4.|...|
 |---+---+---|
 |93.|...|.68|
 |..7|.8.|3..|
 |24.|...|.57|
 |---+---+---|
 |...|.6.|...|
 |.5.|4.2|.1.|
 |8..|9.5|..3|
 *-----------*
 
 *--------------------------------------------------------------------*
 | 1      29     259    | 6      579    3      | 257    8      4      |
 |*34     7     *34     | 2      15     8      | 56     9      156    |
 | 56     8      2569   | 17     4      179    | 257    3      125    |
 |----------------------+----------------------+----------------------|
 | 9      3      15     | 157    2      147    | 14     6      8      |
 | 56     16     7      | 15     8      49     | 3      24     29     |
 | 2      4      8      | 3      19     6      | 19     5      7      |
 |----------------------+----------------------+----------------------|
 |*34     129   -12349  | 8      6      17     | 2459   247    259    |
 | 7      5      69     | 4      3      2      | 8      1      69     |
 | 8      126    1246   | 9      17     5      | 246    247    3      |
 *--------------------------------------------------------------------*


Uniqueness rectangle + swordfish and multiple colors solves the puzzle.

The other two are not nearly as obvious, but I think these are much easier solutions than the suggested XY-chains length 9 & 10:

Code: Select all
XY-chain (9)
 *-----------*
 |.8.|2.7|.5.|
 |4..|9.6|..2|
 |...|.5.|...|
 |---+---+---|
 |15.|...|.27|
 |..7|...|9..|
 |32.|...|.86|
 |---+---+---|
 |...|.4.|...|
 |2..|6.9|..8|
 |.9.|5.3|.1.|
 *-----------*
 
 *-----------------------------------------------------------*
 | 69    8     136   | 2     13    7     | 4     5     139   |
 | 4     137   5     | 9     138   6     | 78    37    2     |
 | 79    137   2     | 1348  5     148   | 678   69    139   |
 |-------------------+-------------------+-------------------|
 | 1     5     9     | 48    6     48    | 3     2     7     |
 | 8     6     7     | 13    123   12    | 9     4     5     |
 | 3     2     4     | 7     9     5     | 1     8     6     |
 |-------------------+-------------------+-------------------|
 | 5     137   1368  | 18    4     128   | 267   69    39    |
 | 2     4     13    | 6     17    9     | 5     37    8     |
 | 67    9     68    | 5     278   3     | 267   1     4     |
 *-----------------------------------------------------------*


If r3c8=9 => r3c1=7 => r3c29=(13) => r3c46=(48) => BUG-lite in r23c2, r12c5, r13c9 => r3c8<>9

Code: Select all
XY-chain (10)
 *-----------*
 |..5|...|3..|
 |.8.|.9.|.7.|
 |6..|.2.|..1|
 |---+---+---|
 |...|6.4|...|
 |.31|...|79.|
 |...|9.1|...|
 |---+---+---|
 |5..|.8.|..2|
 |.9.|.6.|.5.|
 |..3|...|6..|
 *-----------*
 
 *--------------------------------------------------*
 | 12   12   5    | 78   4    78   | 3    6    9    |
 | 3    8    4    | 1    9    6    | 2    7    5    |
 | 6    7    9    | 3    2    5    | 48   48   1    |
 |----------------+----------------+----------------|
 | 9    5    27   | 6    37   4    | 18   123  38   |
 | 4    3    1    | 28   5    28   | 7    9    6    |
 | 78   6    278  | 9    37   1    | 5    23   4    |
 |----------------+----------------+----------------|
 | 5    14   6    | 47   8    37   | 9    13   2    |
 | 178  9    78   | 24   6    23   | 148  5    378  |
 | 278  24   3    | 5    1    9    | 6    48   78   |
 *--------------------------------------------------*


If r4c9=3 => r4c5=7 => r4c3=2 => BUG-lite in r6c13, r8c39, r9c19 => r4c9<>3

As many people already have pointed out the simpler solutions to tareks ALS-XY example, I did not put that on the list either. All other puzzles were added.

I think there is probably enough of XY-chain examples by now, but plenty of room for puzzles that require other techniques.

Ruud wrote:There must be a few examples in my Benchmark Sudoku List that you can use.

Actually, I posted the list on this forum, so it can be used as source for solving technique samples. We could join forces and complete the list with advanced solving techniques that are still missing.


Yes, that's a nice list you've got. I started this thread for manual solvers who wish to try advanced techniques, that's why I think it's good to have several examples of all techniques. As your is intended for computer-solver testing you only need one of each, but there sure is a lot of good examples in your list that could be used here as well. I'll post my reverse-BUG example to your list as it seems to be missing.

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Postby RW » Mon Apr 17, 2006 7:39 pm

ocean wrote:I counted only the relevant part of the bivalue graph... ..maybe I should change my way of counting, or be more specific when reporting 'length'


I've reported the chain legths with the same way of counting that ocean uses. Should this be changed?

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Postby ronk » Mon Apr 17, 2006 8:20 pm

RW wrote:
ocean wrote:I counted only the relevant part of the bivalue graph... ..maybe I should change my way of counting, or be more specific when reporting 'length'

I've reported the chain legths with the same way of counting that ocean uses. Should this be changed?

I spent considerable time searching for those xy-chains of length 5 in Ocean's puzzles ... and finding none ... because I was searching for "loop lengths" of 5, but don't change on my account.:D

Seriously though, I don't think a chain results in an exclusion (or an inclusion) until a loop is closed. And, in the case of a discontinuity, I dislike the idea of the loop length being different than the chain length. It's just a source of confusion.
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Postby tarek » Tue Apr 18, 2006 1:07 pm

RW wrote:As many people already have pointed out the simpler solutions to tareks ALS-XY example, I did not put that on the list either. All other puzzles were added.


Are they simpler:?: , That example was one of the the simplest forms of the ALS xy rule, it has a pattern behind it, I don't think the other (although valid) alternatives were simpler........

An even simpler one was posted in the Benchmark thread

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Postby Ocean » Tue Apr 18, 2006 5:47 pm

Thanks for analyzing the puzzles. It was not surprising that some of the puzzles with long xy-chains could be solved by (simpler) alternative methods. But interesting that one of the 10-node puzzles passed the test.

ronk wrote:
RW wrote:
ocean wrote:I counted only the relevant part of the bivalue graph... ..maybe I should change my way of counting, or be more specific when reporting 'length'

I've reported the chain legths with the same way of counting that ocean uses. Should this be changed?

I spent considerable time searching for those xy-chains of length 5 in Ocean's puzzles ... and finding none ... because I was searching for "loop lengths" of 5, but don't change on my account.:D

Seriously though, I don't think a chain results in an exclusion (or an inclusion) until a loop is closed. And, in the case of a discontinuity, I dislike the idea of the loop length being different than the chain length. It's just a source of confusion.


First: I think that established terminology and conventions should be used, if possible. I'm quite new to this (the discussions), and can easily adapt.

I tried to find discussions about chain/cycle length, but didn't find much.

From the algorithmical point of view, the length of an xy-chain is irrelevant, except for priority (selecting the shortest first), counting statistics (how many possible reductions, how many different chains of each length, etc.), and classification (identify xy-wings, xy-rings, reporting length, etc). But the nodes of the bivalue graph are treated fundamentally different from the discontinuities, so it was not natural to 'count' them together. (If one needs transport of two elephants and five mice, it's not sufficient to specify 'seven animals' only.)

tarek wrote:That example was one of the the simplest forms of the ALS xy rule, it has a pattern behind it, I don't think the other (although valid) alternatives were simpler........


I agree that the ALS method can be used, but then the simplest ALS should be preferred:
Eliminating 5 from r9c8(ALS-XY A=12 in r2c1 B=159 in r2c4,r2c8 C=25 in r1c9 x=1 y=2 z=5)

Since the als-method is new to me, I showed the 'equivalent' xy-chain, but of course it doesn't matter which method is used. There are just two points: One less cell building the 'chain' or 'sets', and one less elimination needed. (As a side comment: I think every xy-chain of this length can also be expressed as ALS.)
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Postby ronk » Tue Apr 18, 2006 6:44 pm

Ocean wrote:I tried to find discussions about chain/cycle length, but didn't find much.

From the algorithmical point of view, the length of an xy-chain is irrelevant, (...) But the nodes of the bivalue graph are treated fundamentally different from the discontinuities, so it was not natural to 'count' them together. (If one needs transport of two elephants and five mice, it's not sufficient to specify 'seven animals' only.)

From Jeff's Forcing chains: Terminology and Definition thread.

Jeff wrote:xy-chain or y-cycle - a chain, consists of all bivalue cells except at a discontinuity, that makes pure weak inferences to yield deduction(s). An xy-chain can be of any length. It can be continuous or discontinuous. The following patterns are subsets of xy-chains:
  • xy-ring - a continuous xy-chain of length 4.
  • xy-wing - a discontinuous xy-chain of length 4.

If you think usage of "length" on a definitions thread is incorrect, you should chime in there.
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Postby RW » Tue Apr 18, 2006 8:23 pm

ronk wrote:From Jeff's Forcing chains: Terminology and Definition thread.


As the terminology and definition thread supports your argument, I'll change the numbers in the list.

Ocean wrote:But interesting that one of the 10-node puzzles passed the test.


With 17 puzzles to test go through in a short time, I'm not very suprised.:)

tarek wrote:Are they simpler? That example was one of the the simplest forms of the ALS xy rule, it has a pattern behind it, I don't think the other (although valid) alternatives were simpler........


To be honest with you, I'm not very familiar with ALS-rules either, that's probably why the other alternatives seemed simpler. I'll have another look at the puzzle.

Regards
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Postby ronk » Tue Apr 18, 2006 8:52 pm

RW wrote:
ronk wrote:From Jeff's Forcing chains: Terminology and Definition thread.


As the terminology and definition thread supports your argument, I'll change the numbers in the list.

I'd proceed slowly with that. Jeff's POV may be in the minority ... and I learned my POV from Jeff. My prior post was intended to stimulate discussion ... not an immediate change.
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Postby Ocean » Wed Apr 19, 2006 8:01 am

RW wrote:As the terminology and definition thread supports your argument, I'll change the numbers in the list.

That's ok with me. Maybe it would be more precise to say (n)=cycle length then, instead of chain length.
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Postby nathanmcmaster » Wed Apr 19, 2006 6:06 pm

oceans right ive been reading about wat ocean just said alot
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Postby RW » Wed Apr 19, 2006 6:38 pm

ronk wrote:I'd proceed slowly with that. Jeff's POV may be in the minority ... and I learned my POV from Jeff.


As it is a well written thread with terminology explained and links to that thread can be found in almost every other thread on this forum that discusses chains, I think it's best to use Jeff's definitions. After all, they're only definitions, shouldn't change the way you solve the puzzle.

ocean wrote:Maybe it would be more precise to say (n)=cycle length then, instead of chain length.


You are absolutely right, problem fixed.

tarek wrote:That example was one of the the simplest forms of the ALS xy rule, it has a pattern behind it, I don't think the other (although valid) alternatives were simpler...


The difficultyrating on various techniques cannot be determined as it depends on the solver. When I looked at the pencilmark grid of your puzzle:

Code: Select all
*-----------------------------------------------*
| 8    12   9   | 13   5    6   | 4    37   237 |
|*12   6    3   | 19   7    4   | 8    59  ^25  |
| 7    5    4   | 39   8    2   | 6    39   1   |
|---------------+---------------+---------------|
| 3    4    5   | 7    2    1   | 9    6    8   |
| 9    8    1   | 4    6    3   |-57   2   ^57  |
| 6    7    2   | 5    9    8   | 3    1    4   |
|---------------+---------------+---------------|
| 4    3    7   | 6    1    5   | 2    8    9   |
|%15   19   8   | 2    3    79  |%57   4    6   |
| 25   29   6   | 8    4    79  | 1    357 -357 |
*-----------------------------------------------*


it took me about 2 seconds to see that r8c7<>5 (UR in r19c89 two steps ahead), because uniqueness rectangles usually are the first reductions I spot. Ocean solved the puzzle by using a chain and Ron used the BUG-principle. I cannot say that any of these would be easier than your solution, I think the problem is that there is too many different paths to the solution. I'd rather have puzzles on the list where there isn't too many altenative ways to get through the bottleneck.

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Postby fermat » Wed Jun 21, 2006 5:58 am

I'd like to add some. I'll start with this one to see if it passes the test.

It takes a skyscraper to solve, but otherwise is easy.

Code: Select all
3 . . | . . 8 | 4 7 .
. 1 . | . 4 . | . . 9
. . 2 | . . 5 | 8 6 .
---------------------
1 . . | 8 . . | . . .
. . . | . 3 . | . . .
. . . | . . 2 | . . 4
---------------------
. 3 4 | 2 . . | 1 . .
5 . . | . 1 . | . 9 .
. 6 1 | 3 . . | . . 2
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Postby fermat » Wed Jun 21, 2006 6:10 am

Here is another. It needs a two-string kite.

Code: Select all
1 . . | . . . | . 7 .
. 2 4 | . 8 . | . 6 5
. 9 . | . . 2 | . . .
---------------------
. . . | . . 9 | 8 . .
. 4 . | . 7 . | . 5 .
. . 6 | 8 . . | . . .
---------------------
. . . | 2 . . | . 8 .
9 7 . | . 5 . | 3 1 .
. 5 . | . . . | . . 9
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Postby gsf » Wed Jun 21, 2006 7:04 am

this one solves with hidden singles, a size 5 x cycle, and a size 11 xy cycle
Code: Select all
. 1 .  8 . .  4 . 3
5 . .  4 7 .  . . .
8 . 4  . 1 9  . . .

. . .  . . .  8 2 5
7 . .  . . .  . . 9
6 5 8  . . .  . . .

. . .  9 3 .  5 . 2
. . .  . 2 7  . . 4
3 . 6  . . 1  . 8 .
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Postby ronk » Wed Jun 21, 2006 10:59 am

gsf wrote:this one solves with hidden singles, a size 5 x cycle, and a size 11 xy cycle

It solves ... with hidden singles, a size 5 x-cycle (aka x-wing), and a size 4 y-cycle (aka xy-wing) too.
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