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TerenceF
Joined: 21 Dec 2007
Posts: 26
Location: Takapuna, NZ
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 Posted: Fri Oct 13, 2017 6:25 am Post subject: Can you spot the next move? |
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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 |
+--------------+-------------+--------------+
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Play this puzzle online at the Daily Sudoku site |
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ZeroAssoluto
Joined: 05 Feb 2017
Posts: 942
Location: Rimini, Italy
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| Posted: Fri Oct 13, 2017 8:01 am Post subject: |
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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
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| Posted: Fri Oct 13, 2017 9:21 am Post subject: |
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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) |
+----------------------+-----------------+--------------------+
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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 |
+------------------+---------------+------------------+
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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
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c. 8r4c1=*[(3=68)r57c4-8r7c1=*(8-3)r8c1=3r8c9-3r2c9=3r2c7]-(3=8)r5c7
d. ... |
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Ajò Dimonios
Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
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| Posted: Fri Oct 13, 2017 2:12 pm Post subject: |
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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 |
+----------------+-------------+--------------+
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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=Ø=>-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=Ø=>-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=Ø=>-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: 571
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| Posted: Fri Oct 13, 2017 9:09 pm Post subject: |
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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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