Extreme** 6/15/17

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Extreme** 6/15/17

Postby nedBlake » Thu Jun 15, 2017 1:54 am

Code: Select all
  *-----------*
  |9.7|.4.|...|
  |..5|...|1..|
  |...|..3|.29|
  |---+---+---|
  |6..|37.|...|
  |...|1..|8..|
  |.3.|...|29.|
  |---+---+---|
  |..1|..9|..2|
  |.5.|8.7|...|
  |...|...|.15|
  *-----------*


4 Medusa chains, 1 causing contradiction
nedBlake
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Re: Extreme** 6/15/17

Postby Leren » Thu Jun 15, 2017 4:03 am

Tougher than a daily. My solution used 5 moves : An L3 Wing, a M wing, a W wing, a H2 wing and a 2nd W Wing.

Hodoku's solution used 1 UR, an XY chain, a Sue de Coq, a 2nd XY chain, 1 Empty Rectangle, an AIC and a W Wing.

Andrew Stuart's solver used 3 XY chains, 1 UR, 2 APE 1 X Wing and 1 Simple coloring.

Leren
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Re: Extreme** 6/15/17

Postby Leren » Thu Jun 15, 2017 7:30 am

Hi Ned, try this easy puzzle

Code: Select all
*-----------*
|..4|..6|..2|
|.1.|.8.|4..|
|5..|4..|.8.|
|-----------|
|..5|...|..9|
|.9.|.1.|.5.|
|7..|...|3..|
|-----------|
|.5.|..3|..6|
|..9|.4.|.2.|
|2..|8..|7..|
*-----------*

Apart from singles and 1 pointing pair, only one non-basic move is required to solve it.

Leren
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Re: Extreme** 6/15/17

Postby eleven » Thu Jun 15, 2017 12:07 pm

Back to Ned's:
Code: Select all
 *-----------------------------------------------------------------*
 |  9     268    7      |  256   4      1    |  356    356   368   |
 |  3     2468   5      |  9    a2-68 ha68   |  1      7   hb468   |
 | f48    1      68     |  7   ba568    3    |gc456    2     9     |
 |----------------------+--------------------+---------------------|
 |  6     89     289    |  3     7      28   |  45     45    1     |
 |  5     7      24     |  1     9      24   |  8      36    36    |
 |  1     3      48     |  46   a68     5    |  2      9     7     |
 |----------------------+--------------------+---------------------|
 | e47    46     1      |  456  a356    9    | e367    8     2     |
 |  2     5      369    |  8     1      7    |  3469   346   346   |
 |  478   4689   3689   |  246   236    46   |  3679   1     5     |
 *-----------------------------------------------------------------*

Uses (2=*3)r2367c5 (no 2 in r2c5 implies 3r7c5)
(2=68)r2c56-(68=45)r2c9,r3c5-(4|5=6)r3c7-*(3|6=7)r7c7-(7=4)r7c1-r3c1=r3c7-(4=68)r2c69 => -68r2c5

Then:
Code: Select all
 *----------------------------------------------------------------*
 |  9     2      7      | c5-6   4     1    |  356    356   8     |
 |  3     48-6   5      |  9     2    a68   |  1      7     46    |
 |  48    1      68     |  7     568   3    |  456    2     9     |
 |----------------------+-------------------+---------------------|
 |  6     89     289    |  3     7    a28   |  45     45    1     |
 |  5     7      24     |  1     9    a24   |  8      36    36    |
 |  1     3      48     | b46    68    5    |  2      9     7     |
 |----------------------+-------------------+---------------------|
 |  47   d46     1      | c456   356   9    |  367    8     2     |
 |  2     5      369    |  8     1     7    |  3469   346   346   |
 |  478   4689   3689   |  2     36    46   |  3679   1     5     |
 *----------------------------------------------------------------*

(6=4)r245c6-(4=6)r6c4-(6=4)r17c4-(4=6)r7c2 => -6r1c4,r2c2; stte
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Re: Extreme** 6/15/17

Postby nedBlake » Thu Jun 15, 2017 5:29 pm

Thanks for the nice "Easy"geometrical puzzle, Leren
Imported it into my App. The Grader found hardly anything beyond a couple of intersection-related strategies and a triple, then gave up with a Extreme**** rating (meaning it couldn't solve it). I expect I couldn't either. Exported it to Andrew Stuarts solver and am now sure I couldn't.
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Re: Extreme** 6/15/17

Postby Leren » Thu Jun 15, 2017 8:51 pm

Hi Ned. This puzzle has a special property that makes it easy to solve. This was discovered about ten years ago and as far as I know, only investigated on this site. I wonder if any of the old timers can recognize the trick.

Leren
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Re: Extreme** 6/15/17

Postby eleven » Thu Jun 15, 2017 10:54 pm

Oh yes, it is digit symmetric at the main diagonal, with number mapping 11,22,33,45,67,89. (E.g. all given 4's have a 5 mirrored like 4r1c3-5r3c1, 4r3c4-5r4c3 etc.)
Then in the solution all digits must be mirrored the same way.
This means that only 1,2,3 can be in the main diagonal, and r1c1=3,r3c3=2,r6c6=2,r4c4=3,r7c7=1,r9c9=3.
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