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Extreme 071019

 
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immpy



Joined: 06 May 2017
Posts: 234

PostPosted: Wed Jul 10, 2019 4:40 pm    Post subject: Extreme 071019 Reply with quote

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 . | . . . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

cheers...immp
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AjÚ Dimonios



Joined: 01 May 2017
Posts: 338
Location: Sassari Italy

PostPosted: Sun Jul 14, 2019 10:24 pm    Post subject: Reply with quote

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: 974
Location: Dar es Salaam Tanzania

PostPosted: Mon Jul 22, 2019 2:20 pm    Post subject: Extreme 071019 Reply with quote

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 |
+------------------------+---------------------+--------------------+

(9=8)r9c6 - r9c3 = r1c3 - (8=4)r1c1 - (4=7231)r8c1358 - (1=54)r6c58 - (4=29)r5c45 => - 9r7c4,r9c6; stte
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