A Tricky One

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A Tricky One

Postby Yogi » Sat May 21, 2016 12:39 am

Pat has pulled me up for assuming that all of Nick70's list of 851 puzzles of a given pattern were Mild because the few that I had done were a walk-over.
He challenged me with 1...5.......2...3...4...6...9...3...6...7...5...1...7...1...2...3...9.......6...1 which is right out of my comfort zone. :oops:
I certainly atempted it, and after proving r7c9 = 3 because r9c7 can't be 3 (it eventually forces an inconsistency) I came to 1.3.5.......2...3...4.3.6...9...3...61..7.3.53..1...7...1...2.3.3..19......362..1

Any ideas on how to attack this?
Yogi
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Re: A Tricky One

Postby Leren » Sat May 21, 2016 1:48 am

The simple answer to your question is don't bother trying to solve this puzzle - it's solvable but not by any human friendly methods.

You can reduce the puzzle to this state using reasonably human friendly methods.

Code: Select all
*--------------------------------------------------------------*
| 1     2786  3      | 46789 5     4678   | 4789  248   24789  |
| 578   5678  69     | 2     489   14678  | 15    3     478    |
| 5789  2578  4      | 789   3     178    | 6     15    2789   |
|--------------------+--------------------+--------------------|
| 24578 9     2578   | 56    248   3      | 148   12468 2468   |
| 6     1     28     | 489   7     48     | 3     2489  5      |
| 3     458   258    | 1     2489  56     | 489   7     24689  |
|--------------------+--------------------+--------------------|
| 45789 4568  1      | 4578  48    4578   | 2     69    3      |
| 2458  3     25678  | 4578  1     9      | 4578  4568  4678   |
| 4578  4578  5789   | 3     6     2      | 45789 458   1      |
*--------------------------------------------------------------*

The next elimination requires some sort of complex Forcing chain - a long sequence of gobbledegook that is virtually meaningless to a human - but proves the elimination.

I checked this with both my solver and Hodoku - I used 10 forcing chain eliminations and Hodoku required 17.

Leren

PS Here is just a part of Hodoku's solution path - make sure you commit all this to memory :D

Forcing Chain Verity => r1c2<>6 r6c3=2 r5c3<>2 r5c8=2 r5c8<>9 r7c8=9 r7c8<>6 r7c2=6 r1c2<>6 r6c5=2 r6c5<>9 r2c5=9 r2c3<>9 r2c3=6 r1c2<>6 r6c9=2 r6c9<>6 r6c6=6 r2c6<>6 r1c46=6 r1c2<>6
Forcing Chain Verity => r1c4<>9 r6c3=2 r5c3<>2 r5c8=2 r5c8<>9 r5c4=9 r1c4<>9 r6c5=2 r6c5<>9 r2c5=9 r1c4<>9 r6c9=2 r6c9<>6 r6c6=6 r1c6<>6 r1c4=6 r1c4<>9
Forcing Chain Verity => r7c2<>5 r6c3=2 r5c3<>2 r5c8=2 r5c8<>9 r7c8=9 r7c8<>6 r7c2=6 r7c2<>5 r6c5=2 r6c5<>9 r2c5=9 r2c3<>9 r2c3=6 r2c2<>6 r7c2=6 r7c2<>5 r6c9=2 r6c9<>6 r6c6=6 r6c6<>5 r7c6=5 r7c2<>5
Forcing Net Contradiction in r4c4 => r8c1=2 r8c1<>2 r4c1=2 (r4c1<>5) r4c1<>7 r4c3=7 r4c3<>5 r4c4=5 r8c1<>2 r8c3=2 (r5c3<>2 r5c3=8 r5c6<>8 r5c6=4 r1c6<>4) (r5c3<>2 r5c3=8 r5c6<>8 r5c6=4 r2c6<>4) r8c3<>6 r2c3=6 r2c3<>9 r2c5=9 r2c5<>4 r2c9=4 (r1c7<>4) (r1c8<>4) r1c9<>4 r1c4=4 r1c4<>6 r4c4=6
Forcing Net Verity => r1c8<>4 r2c5=4 (r7c5<>4 r7c5=8 r4c5<>8 r4c5=2 r4c8<>2) r2c5<>9 r6c5=9 r5c4<>9 r5c8=9 r5c8<>2 r1c8=2 r1c8<>4 r2c6=4 (r5c6<>4 r5c6=8 r5c3<>8 r5c3=2 r5c8<>2) r2c6<>1 r2c7=1 r4c7<>1 r4c8=1 r4c8<>2 r1c8=2 r1c8<>4 r2c9=4 r1c8<> 4
Forcing Net Contradiction in r9c8 => r1c9<>2 r1c9=2 (r1c8<>2 r1c8=8 r1c2<>8 r1c2=7 r1c6<>7) r1c9<>9 r6c9=9 (r5c8<>9 r5c4=9 r5c4<>4) r6c9<>6 r6c6=6 r1c6<>6 r1c6=4 r5c6<>4 r5c8=4 r9c8<>4 r1c9=2 (r3c9<>2 r3c2=2 r3c2<>5) r1c9<>9 r6c9=9 r5c8<>9 r5c4=9 r3c4<>9 r3c1=9 r3c1<>5 r3c8=5 r9c8<>5 r1c9=2 r1c8<>2 r1c8=8 r9c8<>8
Forcing Net Contradiction in r3 => r1c9<>8 r1c9=8 r1c9<>9 r6c9=9 r5c8<>9 r5c4=9 r3c4<>9 r3c1=9 r3c1<>5 r1c9=8 r1c8<>8 r1c8=2 r3c9<>2 r3c2=2 r3c2<>5 r1c9=8 r1c9<>9 r6c9=9 (r6c9<>2 r4c9=2 r4c9<>6) r6c9<>6 r6c6=6 r4c4<>6 r4c8=6 r4c8<>1 r3c8=1 r3c8<> 5
Forcing Net Contradiction in c7 => r2c5<>4 r2c5=4 (r1c4<>4) (r1c6<>4) r2c5<>9 r2c3=9 r9c3<>9 r9c7=9 r1c7<>9 r1c9=9 r1c9<>4 r1c7=4 r2c5=4 (r6c5<>4) (r7c5<>4 r7c5=8 r7c2<>8) r2c5<>9 (r6c5=9 r6c5<>2) r2c3=9 r2c3<>6 r2c2=6 r7c2<>6 r7c2=4 (r6c2<>4) r7c2<>6 r7c8=6 r7c8<>9 r5c8=9 r5c8<>2 r5c3=2 r6c3<>2 r6c9=2 r6c9<>4 r6c7=4

Leren
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Re: A Tricky One

Postby JC Van Hay » Sat May 21, 2016 6:20 pm

1. r5c2=r8c5=1, r9c6=2
2. HP(15-24789)r2c7.r3c8; HP(56-48)r4c4.r6c6

3. Solving the loop Swordfish{3C159} -> -{3r37c4, 3r6c37} :
[6r1c4=6r4c4-6r6c6=(6-3)r6c9=3r7c9-3r7c5=3r3c5]-3r1c4; 6 singles

4. Solving the loop Jellyfish{9R57C35} -> -{9r1c8, 9r2c19, 9r9c18} :
9r5c8 -> 0 solution via Pointing{7r8c79} -> -7r8c4, Skyscraper{4C59} ->-4r8c4, r8c4=8; r5c4=9 and 6 singles

5. L4C1 : hub cell for the digits 2, 4, 7 :
(28=5)r56c3-(5=6)r6c6-Wing(6r1c6=(6-4)r1c4=4r12c6-(4=8)r5c6)-(8=2)r5c2 -> -{8r1c6, 2r4c13, 2r6c2, 2r8c3}; r8c1=2

6. Jellyfish {6R258C5} -> -{4r19c8, 4r46c9}
7. Loop to be solved later 5r3c8=(5-2)r3c2=2r3c9-(2=8)r1c8-(8=5)r9c8 -> -{(78)r3c2, 2r1c9, 8r458c8, 5r8c8}
8. [(6=4)r8c8-4r5c8=4r5c6-4r12c6=(4-6)r1c4=6r4c4]-6r4c8=6r8c8; Claiming{4r45c8} -> -4r46c4

9. Solving the 8 from the 2 solutions of R5 :
a. L2-Wing[2r4c5=2r4c89-2r5c8=(2-8)r5c3=8r5c6]-8r4c5
b. [(8=1)r4c7-(1=5)r2c7-5r8c7=XWing(5r8c34,5r4c134)-(5=28)r56c3]-8r4c13=8r4c79-8r6c79; 2 singles [digit 9 solved]
c. [(8=1)r4c7-(1=248)r145c8]-8r1c7
d. [6r1c4=6r1c6-(6=5)r6c6-(5=28)r56c3-8r8c3=Kite(8r8c479,8r91c8)]-8r1c4
e. [Skyscraper(8r29c1,8r19c8)=8r7c1-8r7c5=8r6c5-(8=4)r5c6-(4=28)r51c8]-8r1c2.r2c9; stte
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Re: A Tricky One

Postby Yogi » Sat May 21, 2016 11:27 pm

I like that comment from Leren and JC has illustrated the truth of it.

Maybe we need a new rating - NHP for Not Humanly Possible. Or not reasonably so, anyway.

I suppose it's all relative for the geniuses, but for me it begs the question of why we do the puzzles we choose to do.

OK that's off-topic, so if you want to discuss it further, better start a new thread.
Yogi
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Postby Pat » Sun May 22, 2016 7:30 am

Yogi wrote:Pat has pulled me up for assuming that all of Nick70's list of 851 puzzles of a given pattern were Mild because the few that I had done were a walk-over.

yes, you stated "it seems that they are all rated as MILD" so i had to wonder where you got that

He challenged me with
1...5.......2...3...4...6...9...3...6...7...5...1...7...1...2...3...9.......6...1
which is right out of my comfort zone

also way too tough for me,
i simply offered one of his toughest



so now you can try to find your own comfort-zone,
starting perhaps somewhere in the middle of his list ?

    1...5.......7...4...6...3...3...4...5...7...2...6...5...4...9...9...1.......2...8
    [ play ]
    1...5.......7...6...4...1...3...8...5...4...7...6...9...7...4...6...3.......1...8 [ play ]
    1...5.......1...6...7...4...3...9...5...1...3...6...9...8...2...6...7.......3...1 [ play ]
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Re: A Tricky One

Postby Yogi » Mon May 23, 2016 9:28 pm

Thanx for that. I had no idea that they were listed easy to difficult. My mind-set assumed that they were all a similar rating because they were all the same pattern.
I could look at the ones you suggested, but I'm trying to fly Kites at the moment.

Yogi
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Re: A Tricky One

Postby Kozo Kataya » Fri May 27, 2016 10:24 am

How to solve A Tricky-One by "standardization" ( wonder if meaningful ? )
Thinking about sudoku's rule of [single], inter-relations of each cell with each digit is not change,
even if any row or column is moved around within mini-range.
For example, using Leren's data of A Tricky One, table A-1 of digit 3 is standardized as table A-2.
Table B-1 of digit 2 is standardized as table B-2 with same manner.
As shown marked [ *2 ], digit 2 located out of standard-position can be eliminated, then stte

Code: Select all
  table A-1                                         table A-2
   c1 c2 c3  c4 c5 c6  c7 c8 c9                       c3 c1 c2  c5 c6 c4  c8 c7 c9
  *-----------------------------*                   *-----------------------------*
r1| .  .  3 | .  .  . | .  .  . |                 r1| 3  .  . | .  .  . | .  .  . |
r2| .  .  . | .  .  . | .  3  . |                 r3| .  .  . | 3  .  . | .  .  . |
r3| .  .  . | .  3  . | .  .  . |                 r2| .  .  . | .  .  . | 3  .  . |
  |---------+---------+---------|                   |---------+---------+---------|
r4| .  .  . | .  .  3 | .  .  . |                 r6| .  3  . | .  .  . | .  .  . |
r5| .  .  . | .  .  . | 3  .  . |                 r4| .  .  . | .  3  . | .  .  . |
r6| 3  .  . | .  .  . | .  .  . |                 r5| .  .  . | .  .  . | .  3  . |
  |---------+---------+---------|                   |---------+---------+---------|
r7| .  .  . | .  .  . | .  .  3 |                 r8| .  .  3 | .  .  . | .  .  . |
r8| .  3  . | .  .  . | .  .  . |                 r9| .  .  . | .  .  3 | .  .  . |
r9| .  .  . | 3  .  . | .  .  . |                 r7| .  .  . | .  .  . | .  .  3 |
  *-----------------------------*                   *-----------------------------*

  table B-1                                         table B-2
    1  2  3   4  5  6   7  8  9                       2  3  1   4  5  6   9  8  7
  *-----------------------------*                   *-----------------------------*
1 | .  2  . | .  .  . | . *2 *2 |                 1 | 2  .  . | .  .  . |*2 *2  . |
2 | .  .  . | 2  .  . | .  .  . |                 2 | .  .  . | 2  .  . | .  .  . |
3 | . *2  . | .  .  . | .  .  2 |                 3 |*2  .  . | .  .  . | 2  .  . |
  |---------+---------+---------|                   |---------+---------+---------|
4 |*2  . *2 | .  2  . | . *2 *2 |                 6 | .  2  . | . *2  . |*2  .  . |
5 | .  . *2 | .  .  . | .  2  . |                 4 | . *2 *2 | .  2  . |*2 *2  . |
6 | .  .  2 | . *2  . | .  . *2 |                 5 | . *2  . | .  .  . | .  2  . |
  |---------+---------+---------|                   |---------+---------+---------|
7 | .  .  . | .  .  . | 2  .  . |                 8 | . *2  2 | .  .  . | .  .  . |
8 | 2  . *2 | .  .  . | .  .  . |                 9 | .  .  . | .  .  2 | .  .  . |
9 | .  .  . | .  .  2 | .  .  . |                 7 | .  .  . | .  .  . | .  .  2 |
  *-----------------------------*                   *-----------------------------*

Appreciate your comments.
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Re: A Tricky One

Postby David P Bird » Sun May 29, 2016 7:42 am

KK, you can only be sure of the position of some of your cells in your standardised (or normalised) grid and there are choices about the others. Therefore not all of your eliminations will be certain. If you only made the certain ones your method would be very similar to <templating> but this isn't considered a very elegant approach.

DPB
.
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