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Can you spot the next move?

 
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TerenceF



Joined: 21 Dec 2007
Posts: 26
Location: Takapuna, NZ

PostPosted: Fri Oct 13, 2017 6:25 am    Post subject: Can you spot the next move? Reply with quote

From one of the newspapers a week or so ago
Code:

+--------------+-------------+--------------+
| 19   3   59  | 7    6  8   | 4  25  125   |
| 146  8   46  | 2    5  9   | 36 7   136   |
| 7    56  2   | 4    3  1   | 9  8   56    |
+--------------+-------------+--------------+
| 48   1   3   | 58   9  7   | 2  6   458   |
| 5    26  468 | 368  1  246 | 38 9   7     |
| 2468 9   7   | 3568 28 246 | 1  345 3458  |
+--------------+-------------+--------------+
| 2389 7   1   | 68   4  26  | 5  23  2389  |
| 2368 4   68  | 9    28 5   | 7  1   2368  |
| 2689 256 59  | 1    7  3   | 68 24  24689 |
+--------------+-------------+--------------+

Play this puzzle online at the Daily Sudoku site
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ZeroAssoluto



Joined: 05 Feb 2017
Posts: 542
Location: Rimini, Italy

PostPosted: Fri Oct 13, 2017 8:01 am    Post subject: Reply with quote

Hi TerenceF,

there are various possibilities as a next move to clean the scheme;

Skyscraper with number 8 in r58c3,r68c5 and -8 in r5c4,r6c1
or
Skyscraper with number 8 in r58c3,r59c7 and -8 in r8c9,r9c1
or
XY-Chain r3c2-5-r3c9-6-r2c7-3-r5c7-8-r9c7 and -6 in r9c2

none are resolved but allow you to proceed to the end

Ciao Gianni
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

PostPosted: Fri Oct 13, 2017 9:21 am    Post subject: Reply with quote

1. Sudoku rule : a candidate for a digit d missing from all the valid solutions of the digit d is excluded.
Code:
+----------------------+-----------------+--------------------+
| 19       3     59    | 7     6     8   | 4     25   125     |
| 146      8     46    | 2     5     9   | 36    7    136     |
| 7        5(6)  2     | 4     3     1   | 9     8    5(6)    |
+----------------------+-----------------+--------------------+
| 48       1     3     | 58    9     7   | 2     6    458     |
| 5        26    46(8) | 36-8  1     246 | 3(8)  9    7       |
| 246-8    9     7     | 3568  2(8)  246 | 1     345  3458    |
+----------------------+-----------------+--------------------+
| 2389     7     1     | 68    4     26  | 5     23   239-8   |
| 238(6)   4     (68)  | 9     2(8)  5   | 7     1    23-8(6) |
| 269(-8)  25-6  59    | 1     7     3   | 6(8)  24   2469(8) |
+----------------------+-----------------+--------------------+
Here, this can only happen for the digits 2, 6 and 8 (Keith's principle).
After inspection and interpretation in terms of patterns :
{6R38} -> -{6r9c2}
{8C35} -> -{8r5c4, 8r6c1}
{8C37} -> -{8r9c8, 8r9c1}
{8R9} -> -{8r7c9}
2. The constraint {8r4c1, 8r5c7} excluding the set {8r4c9, 8r5c3} is derived from the 2 solutions of R3C27; stte
Code:
+------------------+---------------+------------------+
| 19      3   59   | 7     6   8   | 4     25   125   |
| 146     8   46   | 2     5   9   | 6(3)  7    16(3) |
| 7       56  2    | 4     3   1   | 9     8    56    |
+------------------+---------------+------------------+
| 4(8)    1   3    | 58    9   7   | 2     6    45-8  |
| 5       26  46-8 | (36)  1   246 | (38)  9    7     |
| 246     9   7    | 3568  28  246 | 1     345  3458  |
+------------------+---------------+------------------+
| 239(8)  7   1    | (68)  4   26  | 5     23   239   |
| 26(38)  4   68   | 9     28  5   | 7     1    26(3) |
| 269     25  59   | 1     7   3   | 68    24   24689 |
+------------------+---------------+------------------+
Interpretations of an optimized path:
a. Either r5c7=8; or r5c7=r2c9=r8c1=3 and r5c4=6, r7c4=8, r4c1=8
b.
Code:
8r5c7 3r5c7
         3r2c7 3r2c9
               3r8c9 3r8c1
         3r5c4             6r5c4
                           6r7c4 8r7c4
                     8r8c1       8r7c1 8r4c1
c. 8r4c1=*[(3=68)r57c4-8r7c1=*(8-3)r8c1=3r8c9-3r2c9=3r2c7]-(3=8)r5c7
d. ...
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Aj Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy

PostPosted: Fri Oct 13, 2017 2:12 pm    Post subject: Reply with quote

Hi everyone


Solution in four steps


Code:

+----------------+-------------+--------------+
| 19    3   59   | 7    6  8   | 4  25  125   |
| 146   8   46   | 2    5  9   | 36 7   136   |
| 7     56  2    | 4    3  1   | 9  8   56    |
+----------------+-------------+--------------+
| 48    1   3    | 58   9  7   | 2  6   458   |
| 5     26  468  | 368  1  246 | 38 9   7     |
| 2468  9   7    | 3568 28 246 | 1  345 3458  |
+----------------+-------------+--------------+
| 23689 7   1    | 68   4  26  | 5  23  23689 |
| 2368  4   68   | 9    28 5   | 7  1   2368  |
| 2689  256 5689 | 1    7  3   | 68 24  24689 |
+----------------+-------------+--------------+

Play this puzzle online at the Daily Sudoku site


[(6)R5C6-(6=2)R7C6-(2=8)R8C5-(8)R8C3 and (6-4)R5C6=(4)R5C3-(4=6)R2C3-(6)R8C3]=>contradition R8C3==>-6R5C6.

[(6-4)R2C1=(4)R2C3-(4)R5C3; (6)R2C1-(6=3)R2C7-(3=8)R5C7-(8)R5C3 and (6)R2C1-(6)R3C2=(6)R3C9-(6)R89C9=(6)R9C7-(6)R9C2=(6)R5C2-(6)R5C3; contradition R5C3==>-6R2C1.

[(5-4)R4C9=(4)R4C1-(4=1)R2C1-(1)R1C1 and (5)R4C9-(5)R3C9=(5)R3C2-(5=9)R1C3-(9)R1C1]=>contradition R1C1==>-5R4C9.

[(6)R5C4-(6)R5C3; (6-8)R5C4; (6-3)R5C4=(3-8)R5C7=(8)R5C3-(8=4)R4C1 ;(6)R5C4-(6=8)R7C4-(8)R7C1;(6-3)R5C4=(3)R5C7-(3)R6C8=(3)R6C8-(3)R6C1=(3-8)R8C1
and (6-3)R5C4=(3-8)R5C7=(8)R9C7-(8)R9C13=(8)R8C3-(8=4)R5C3]=>contradition two singles 4 in box 4=>-6R5C4=>stte.

Ciao a Tutti

Paolo
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immpy



Joined: 06 May 2017
Posts: 345

PostPosted: Fri Oct 13, 2017 9:09 pm    Post subject: Reply with quote

A truly beautiful and very challenging scheme. I lost track of my steps when I was about 6 deep! A skyscraper or two, multiple empty rectangles, an XY-Wing (flightless)+1, and I think I ended with a W-Wing. I think there was more that I am forgetting in between.
Apologies for not jotting all of this down step by step.
Thank you for posting this most challenging and ultimately rewarding puzzle.

Keeping my pencil sharp, and my eraser handy....

immpy
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