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immpy
Joined: 06 May 2017
Posts: 574
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 Posted: Wed Jul 10, 2019 4:40 pm Post subject: Extreme 071019 |
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Hello all, enjoy the puzzle...
| Code: |
+-------+-------+-------+
| . . . | 3 9 . | 1 . . |
| . . . | . 8 1 | . 4 . |
| . 3 . | . . 2 | 5 . 7 |
+-------+-------+-------+
| . 8 6 | . . . | 4 9 . |
| 5 . . | . . . | . 7 8 |
| . 7 . | . . . | . . 2 |
+-------+-------+-------+
| . . 1 | . . 4 | . . . |
| . . . | 6 . 5 | 8 . . |
| 3 . . | . 1 . | . . . |
+-------+-------+-------+
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Play this puzzle online at the Daily Sudoku site
cheers...immp |
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Ajò Dimonios
Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
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| Posted: Sun Jul 14, 2019 10:24 pm Post subject: |
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Hi everyone
After basics
| Code: |
+--------------+-------------+------------+
| 48 45 58 | 3 9 7 | 1 2 6 |
| 67 26 27 | 5 8 1 | 9 4 3 |
| 1 3 9 | 4 6 2 | 5 8 7 |
+--------------+-------------+------------+
| 2 8 6 | 17 57 3 | 4 9 15 |
| 5 1 34 | 29 24 69 | 36 7 8 |
| 9 7 34 | 18 45 68 | 36 15 2 |
+--------------+-------------+------------+
| 678 2569 1 | 2789 237 4 | 27 356 59 |
| 47 249 27 | 6 237 5 | 8 13 149 |
| 3 24569 58 | 2789 1 89 | 27 56 459 |
+--------------+-------------+------------+
|
Play this puzzle online at the Daily Sudoku site
One step after basics.
Forcing chains:
If we put R4C5 = 5 (backdoor), using only the basic technique, we easily reach the solution that has in R1C1 the candidate 8. But even if we put R4C5 = 7 we find that the candidate in R1C1 is always 8
(7-5)R4C5=(5-1)R4C9=1R8C9-(49)R8C9=9 R8C2-4R8C2=4R8C1-(4=8)R1C1.
Whatever the candidate in R4C5 (5 or 7) 8 in R1C1 is always true.
The consequence of this is that in R1C1 the only valid candidate is 8. Setting R1C1 = 8 the solution is easily obtained using only the basic technique. In this way, in addition to having found the solution, the uniqueness is also demonstrated.
In this scheme there are 36 Backdoors on a total of 96 possible candidates:
(R1C1=8,R1C2=4,R1C3=5,R2C1=7,R2C2=6,R2C3=2,R4C4=7,R4C5=5,
R4C9=1,R5C3=4;R5C4=9,R5C5=2,R5C6=6,R5C7=3,R6C3=3,R6C4=1,
R6C5=4,R6C6=8,R6C7=6,R6C8=5,R7C1=6,R7C2=9,R7C4=8,R7C5=7,
R7C8=3,R7C9=5,R8C1=4,R8C2=2,R8C3=7,R8C5=3,R8C8=1,R8C9=9,
R9C2=5,R9C3=8,R9C4=2,R9C6=9).
Ciao a Tutti
Paolo |
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Clement
Joined: 24 Apr 2006
Posts: 1113
Location: Dar es Salaam Tanzania
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| Posted: Mon Jul 22, 2019 2:20 pm Post subject: Extreme 071019 |
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| Code: |
+------------------------+---------------------+--------------------+
|d48 45 c58 | 3 9 7 | 1 2 6 |
| 67 26 27 | 5 8 1 | 9 4 3 |
| 1 3 9 | 4 6 2 | 5 8 7 |
+------------------------+---------------------+--------------------+
| 2 8 6 | 17 57 3 | 4 9 15 |
| 5 1 34 |g29 g24 6-9| 36 7 8 |
| 9 7 34 | 18 f45 68 | 36 f15 2 |
+------------------------+---------------------+--------------------+
| 678 2569 1 | 278-9 237 4 | 27 356 59 |
|e47 249 e27 | 6 e237 5 | 8 e13 149 |
| 3 24569 b58 | 2789 1 a89 | 27 56 459 |
+------------------------+---------------------+--------------------+
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(9=8)r9c6 - r9c3 = r1c3 - (8=4)r1c1 - (4=7231)r8c1358 - (1=54)r6c58 - (4=29)r5c45 => - 9r7c4,r9c6; stte |
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