Help with Astraware Fiendish puzzle

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Help with Astraware Fiendish puzzle

Postby kit_carmelite » Tue Dec 17, 2013 4:02 am

I entered this in the Simple Sudoku and when I asked for a hint, the message I got was "No hint available". When I asked for a hint in the Astraware program, it highlighted the following two cells: (row4, col 4) and (row 8, col 4). What is my next step here?

Here is the puzzle as far as I was able to progress:
9.8|7..|324
6.2|...|978
473|829|561
---+---+---
381|...|246
79.|2.1|835
52.|.8.|719
---+---+---
139|452|687
865|...|492
247|..8|153

Here is the puzzle with pencil marks:

{9} {15} {8} {7} {16} {56} {3} {2} {4}
{6} {15} {2} {135} {134} {345} {9} {7} {8}
{4} {7} {3} {8} {2} {9} {5} {6} {1}
{3} {8} {1} {59} {79} {57} {2} {4} {6}
{7} {9} {46} {2} {46} {1} {8} {3} {5}
{5} {2} {46} {36} {8} {346} {7} {1} {9}
{1} {3} {9} {4} {5} {2} {6} {8} {7}
{8} {6} {5} {13} {137} {37} {4} {9} {2}
{2} {4} {7} {69} {69} {8} {1} {5} {3}
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Re: Help with Astraware Fiendish puzzle

Postby Leren » Tue Dec 17, 2013 10:35 am

Code: Select all
*-----------------------------------------------------*
| 9    15   8     | 7    16  b56    | 3    2    4     |
| 6    15   2     |a135  134  345   | 9    7    8     |
| 4    7    3     | 8    2    9     | 5    6    1     |
|-----------------+-----------------+-----------------|
| 3    8    1     | 59   79   57    | 2    4    6     |
| 7    9    46    | 2    46   1     | 8    3    5     |
| 5    2    46    |c36   8    34-6  | 7    1    9     |
|-----------------+-----------------+-----------------|
| 1    3    9     | 4    5    2     | 6    8    7     |
| 8    6    5     |d13   137  37    | 4    9    2     |
| 2    4    7     | 69   69   8     | 1    5    3     |
*-----------------------------------------------------*

About the best next move I can see is a WXY-Z wing (in cells marked a,b,c,d) WXY = 135 and Z=6 : If r6c6 = 6 then r1c6 = 5, r6c4 = 3 and r8c4 = 1, so r2c4 is empty :( . Therefore r6c6 <> 6.

A few elementary moves will then get you to here

Code: Select all
*-----------------------------------------------------*
| 9    5    8     | 7    1    6     | 3    2    4     |
| 6    1    2     | 35   34  a3-45  | 9    7    8     |
| 4    7    3     | 8    2    9     | 5    6    1     |
|-----------------+-----------------+-----------------|
| 3    8    1     | 59   79   57    | 2    4    6     |
| 7    9    46    | 2    46   1     | 8    3    5     |
| 5    2    46    | 36   8    34    | 7    1    9     |
|-----------------+-----------------+-----------------|
| 1    3    9     | 4    5    2     | 6    8    7     |
| 8    6    5     | 1    37   37    | 4    9    2     |
| 2    4    7     | 69   69   8     | 1    5    3     |
*-----------------------------------------------------*

At this point r2c6 must be 3. The reason being that if it isn't 3 then every unsolved digit would appear in a row, column and box exactly twice with all the unsolved cells having 2 digits.

For example 3 would appear in Row 2 twice, Column 4 twice and Box 2 twice and so on for the other unsolved digits. This is a situation, called BUG, that cannot lead to a valid solution.
(BUG stands for Bi-value Universal Grave). The situation in the diagram is BUG+1 or BUG +1 extra digit, which must be true to avoid the BUG situation.

Setting r2c6 = 3 should lead to an elementary conclusion.

Hope this helps.

Leren
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Re: Help with Astraware Fiendish puzzle

Postby ArkieTech » Tue Dec 17, 2013 12:43 pm

Code: Select all
 *--------------------------------------------------*
 | 9    15   8    | 7    16   56   | 3    2    4    |
 | 6    15   2    | 135  134  345  | 9    7    8    |
 | 4    7    3    | 8    2    9    | 5    6    1    |
 |----------------+----------------+----------------|
 | 3    8    1    |a59   79  b57   | 2    4    6    |
 | 7    9    46   | 2    46   1    | 8    3    5    |
 | 5    2    46   |a36   8    346  | 7    1    9    |
 |----------------+----------------+----------------|
 | 1    3    9    | 4    5    2    | 6    8    7    |
 | 8    6    5    | 13   137 b37   | 4    9    2    |
 | 2    4    7    |a69   69   8    | 1    5    3    |
 *--------------------------------------------------*


if r6c4 is not 3 then r4c4 is 5 making r4c6 not 5 and r8c6 a 3
therefore r6c6 cannot be 3 leaving only singles to solve the puzzle

(3=5)r469c4-(5=3)r48c6 => -3r6c6; ste

Hope this helps
dan
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Re: Help with Astraware Fiendish puzzle

Postby daj95376 » Tue Dec 17, 2013 5:36 pm

I'm not familiar with the Astraware program, but the only reason that I can find to justify highlighting r4c4 and r8c4 is to include Aligned Pair Exclusion (APE) as a solving technique. In that case, Leren's WXYZ-Wing is similar ... if not equivalent.

There is a 5-cell XY-Chain that also cracks the puzzle.

Code: Select all
 +-----------------------------------------------------+
 |  9    15   8    |  7    16   56   |  3    2    4    |
 |  6    15   2    |  135  134  345  |  9    7    8    |
 |  4    7    3    |  8    2    9    |  5    6    1    |
 |-----------------+-----------------+-----------------|
 |  3    8    1    | c59   79  d57   |  2    4    6    |
 |  7    9    46   |  2    46   1    |  8    3    5    |
 |  5    2    46   | a36   8    46-3 |  7    1    9    |
 |-----------------+-----------------+-----------------|
 |  1    3    9    |  4    5    2    |  6    8    7    |
 |  8    6    5    |  1-3  137 e37   |  4    9    2    |
 |  2    4    7    | b69   69   8    |  1    5    3    |
 +-----------------------------------------------------+
 # 25 eliminations remain

 (3=6)r6c4 - (6=9)r9c4 - (9=5)r4c4 - (5=7)r4c6 - (7=3)r8c6  =>  r6c6,r8c4<>3

However, I'm kind of partial to the Unique Rectangle eliminations that advance the puzzle to an XY-Wing or BUG+1 to crack it.

There are strong links on <1> in [c4] and [r8]. There's also a strong link on <3> in [c5].

Code: Select all
 +-----------------------------------------------------+
 |  9    15   8    |  7    16   56   |  3    2    4    |
 |  6   #15   2    | *135 *134  345  |  9    7    8    |
 |  4    7    3    |  8    2    9    |  5    6    1    |
 |-----------------+-----------------+-----------------|
 |  3    8    1    |  59   79   57   |  2    4    6    |
 |  7    9    46   |  2    46   1    |  8    3    5    |
 |  5    2    46   |  36   8    346  |  7    1    9    |
 |-----------------+-----------------+-----------------|
 |  1    3    9    |  4    5    2    |  6    8    7    |
 |  8    6    5    | *13  *137  37   |  4    9    2    |
 |  2    4    7    |  69   69   8    |  1    5    3    |
 +-----------------------------------------------------+
 # 25 eliminations remain

 r28c45  <13> UR via s-link              <> 1    r2c4
 r28c45  <13> UR via s-link + r2c2       <> 1    r2c5
 r28c45  <13> UR via s-link              <> 3    r8c4
 r28c45  <13> UR via s-link              <> 1    r8c5
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Re: Help with Astraware Fiendish puzzle

Postby daj95376 » Tue Dec 17, 2013 6:02 pm

_

For those who understand DPs, does the following pattern represent a DP?

Code: Select all
 +------------------------------------------------------+
 |  9   *15   8    |  7   *16   *56   |  3    2    4    |
 |  6   *15   2    |  135 *14+3 *45+3 |  9    7    8    |
 |  4    7    3    |  8    2     9    |  5    6    1    |
 |-----------------+------------------+-----------------|
 |  3    8    1    |  59   79    57   |  2    4    6    |
 |  7    9   *46   |  2   *46    1    |  8    3    5    |
 |  5    2   *46   |  36   8    *46+3 |  7    1    9    |
 |-----------------+------------------+-----------------|
 |  1    3    9    |  4    5     2    |  6    8    7    |
 |  8    6    5    |  13   137   37   |  4    9    2    |
 |  2    4    7    |  69   69    8    |  1    5    3    |
 +------------------------------------------------------+
 # 25 eliminations remain

I get the DP candidates to reduce as follows:

Code: Select all
 r5c3=4 ... non-(*) cells reduced to same values
 *-----------------------------------------*
 | 9  *5   8   | 7  *1  *6   | 3   2   4   |
 | 6  *1   2   | 3  *4  *5   | 9   7   8   |
 | 4   7   3   | 8   2   9   | 5   6   1   |
 |-------------+-------------+-------------|
 | 3   8   1   | 59  79  7   | 2   4   6   |
 | 7   9  *4   | 2  *6   1   | 8   3   5   |
 | 5   2  *6   | 3   8  *4   | 7   1   9   |
 |-------------+-------------+-------------|
 | 1   3   9   | 4   5   2   | 6   8   7   |
 | 8   6   5   | 13  37  37  | 4   9   2   |
 | 2   4   7   | 69  9   8   | 1   5   3   |
 *-----------------------------------------*

Code: Select all
 r5c3=6 ... non-(*) cells reduced to same values
 *-----------------------------------------*
 | 9  *1   8   | 7  *6  *5   | 3   2   4   |
 | 6  *5   2   | 3  *1  *4   | 9   7   8   |
 | 4   7   3   | 8   2   9   | 5   6   1   |
 |-------------+-------------+-------------|
 | 3   8   1   | 59  79  7   | 2   4   6   |
 | 7   9  *6   | 2  *4   1   | 8   3   5   |
 | 5   2  *4   | 3   8  *6   | 7   1   9   |
 |-------------+-------------+-------------|
 | 1   3   9   | 4   5   2   | 6   8   7   |
 | 8   6   5   | 13  37  37  | 4   9   2   |
 | 2   4   7   | 69  9   8   | 1   5   3   |
 *-----------------------------------------*
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Re: Help with Astraware Fiendish puzzle

Postby ronk » Tue Dec 17, 2013 11:39 pm

daj95376 wrote:... does the following pattern represent a DP?

Code: Select all
 +------------------------------------------------------+
 |  9   *15   8    |  7   *16   *56   |  3    2    4    |
 |  6   *15   2    |  135 *14+3 *45+3 |  9    7    8    |
 |  4    7    3    |  8    2     9    |  5    6    1    |
 |-----------------+------------------+-----------------|
 |  3    8    1    |  59   79    57   |  2    4    6    |
 |  7    9   *46   |  2   *46    1    |  8    3    5    |
 |  5    2   *46   |  36   8    *46+3 |  7    1    9    |
 |-----------------+------------------+-----------------|
 |  1    3    9    |  4    5     2    |  6    8    7    |
 |  8    6    5    |  13   137   37   |  4    9    2    |
 |  2    4    7    |  69   69    8    |  1    5    3    |
 +------------------------------------------------------+

It does. Each digit of the pattern appears exactly twice in its row, column and box, or appears not at all.
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Re: Help with Astraware Fiendish puzzle

Postby Luke » Thu Dec 26, 2013 9:30 pm

daj95376 wrote:For those who understand DPs, does the following pattern represent a DP?

Code: Select all
 +------------------------------------------------------+
 |  9   *15   8    |  7   *16   *56   |  3    2    4    |
 |  6   *15   2    |  135 *14+3 *45+3 |  9    7    8    |
 |  4    7    3    |  8    2     9    |  5    6    1    |
 |-----------------+------------------+-----------------|
 |  3    8    1    |  59   79    57   |  2    4    6    |
 |  7    9   *46   |  2   *46    1    |  8    3    5    |
 |  5    2   *46   |  36   8    *46+3 |  7    1    9    |
 |-----------------+------------------+-----------------|
 |  1    3    9    |  4    5     2    |  6    8    7    |
 |  8    6    5    |  13   137   37   |  4    9    2    |
 |  2    4    7    |  69   69    8    |  1    5    3    |
 +------------------------------------------------------+

Really nice, Danny, a fantastic spot there! Already in my notebook. This is an excellent example of an overlooked and rarely identified BUG-Lite. This pattern is classified here as a "Type 9 Unavoidable set of size 8."

Code: Select all
-----------
12.|4..|...
34.|1..|...
...|...|...
-----------
23.|
...|
...|

I find it interesting to note how much of the original work done on deadly patterns seemed to come not from manual solvers and end users, but from constructors and programmers trying to deal with the issue of unavoidable sets so their puzzles would have single solutions.

-----------

This thread also documents the very moment when the term "BUG-Lite" was conceived. I'm betting beer was involved ... 8-)
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Re: Help with Astraware Fiendish puzzle

Postby eleven » Thu Dec 26, 2013 11:17 pm

Hey, i didn't know that one, thanks.
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Re: Help with Astraware Fiendish puzzle

Postby Luke » Tue Dec 31, 2013 4:38 am

eleven, tell me this doesn't look like one of your "Burst Into Tears" MUGs reduced to bivalues.
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Re: Help with Astraware Fiendish puzzle

Postby eleven » Wed Jan 01, 2014 2:18 pm

No, it's a variation, which "goes around the corner", which is possible here, because there are only 3 MUG candidates in both columns c56.
But similar to the T6 UA i think, that puzzles, where this pattern is a big help for solving, are extremely rare (without having tried it).
The problem is, that to get such a pattern, normally the grid already is that candidate reduced, that it is easy to solve.
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