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All Hail Danny (4)

 
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Mogulmeister



Joined: 03 May 2007
Posts: 963

PostPosted: Thu Oct 21, 2021 1:10 pm    Post subject: All Hail Danny (4) Reply with quote

Code:
+-----------------------+
 | . 8 . | . . 9 | 4 1 . |
 | 4 3 . | 6 . 1 | . . 9 |
 | . . . | . . 4 | . . 6 |
 |-------+-------+-------|
 | . 7 . | 9 . 3 | . . . |
 | . . . | . 8 . | . . 1 |
 | 3 4 8 | 1 . . | 9 . . |
 |-------+-------+-------|
 | 8 . . | . . 2 | 6 . 5 |
 | 6 . . | . . . | . . . |
 | . 1 7 | . 9 . | 8 . . |
 +-----------------------+
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dongrave



Joined: 06 Mar 2014
Posts: 450

PostPosted: Fri Oct 22, 2021 4:07 pm    Post subject: Reply with quote

Thanks for the puzzle Mohulmeister! Here's the grid after basics:

Code:
+--------------+--------------+-----------------+
| 7   8    6   | 235  235 9   | 4    1     23   |
| 4   3    25  | 6    27  1   | 257  8     9    |
| 19  25   19  | 8    237 4   | 2357 2357  6    |
+--------------+--------------+-----------------+
| 125 7    125 | 9    46  3   | 25   46    8    |
| 259 6    259 | 24   8   57  | 2357 23457 1    |
| 3   4    8   | 1    26  57  | 9    2567  27   |
+--------------+--------------+-----------------+
| 8   9    34  | 347  1   2   | 6    37    5    |
| 6   25   34  | 3457 345 8   | 1    9     2347 |
| 25  1    7   | 345  9   6   | 8    23    234  |
+--------------+--------------+-----------------+


Then I used chain that started with a 2 in r2c3 that visited almost every unsolved cell! Ha!
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Mogulmeister



Joined: 03 May 2007
Posts: 963

PostPosted: Fri Oct 22, 2021 9:24 pm    Post subject: Reply with quote

Well done dongrave!

Was it a relative of this one ?

-2r1c4=r5c4-r6c5=r6c89-(2=5)r4c7-(5)r56c8=r3c8-r3c2=r8c2-r8c5=r1c5 means r1c4<>5 and r1c5<>2
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Mogulmeister



Joined: 03 May 2007
Posts: 963

PostPosted: Sat Oct 23, 2021 9:38 am    Post subject: Reply with quote

There is also an interesting situation when we start with a 7 (not 5) in r6c6

(5=7)r6c6-(7=2)r6c9-(2=5)r4c7-(5)r6c8

So when we remove 5 from r6c6 and follow the chain above, the 5 in r6c8 is also removed leaving no 5's in row 6. So r6c6 is not 7 but must equal 5.
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Mogulmeister



Joined: 03 May 2007
Posts: 963

PostPosted: Sat Oct 23, 2021 9:59 am    Post subject: Reply with quote

Problem is, it doesn't make much of a dent in the puzzle!
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Clement



Joined: 24 Apr 2006
Posts: 1062
Location: Dar es Salaam Tanzania

PostPosted: Sat Oct 23, 2021 10:15 am    Post subject: All Hail Danny (4) Reply with quote

I have to settle for three steps
Code:

+------------------+---------------------+------------------------+
| 7      8     6   |b235      b235    9  | 4       1        c23   |
| 4      3    i25  | 6        a27     1  |j25-7    8         9    |
| 19    h25    19  | 8         237    4  | 2357    2357      6    |
+------------------+---------------------+------------------------+
| 125    7     125 | 9         46     3  | 25      46        8    |
| 259    6     259 | 24        8      57 | 2357    23457     1    |
| 3      4     8   | 1         26     57 | 9       2567     d27   |
+------------------+---------------------+------------------------+
| 8      9     34  | 347       1      2  | 6       37        5    |
| 6     g25    34  | 3457      345    8  | 1       9        d2347 |
|f25     1     7   | 345       9      6  | 8      e23       d234  |
+------------------+---------------------+------------------------+

Step 1: (7=2)r2c5 – r1c45 = r1c9 – (2=74|3)r689c9 – (3=2)r9c8 – (2=5)r9c1 – r8c2 = r3c2 – r2c3 = (5)r2c7 => - 7r2c7
Code:

+--------------------+---------------------+-----------------------+
| 7       8      6   | 235      235     9  | 4      1         23   |
| 4       3     d25  | 6        7       1  |e25     8         9    |
| 19     c25     19  | 8        23      4  | 37     2357      6    |
+------------+-------------+---------------+
| 125     7      125 | 9        46      3  | f25    46        8    |
| 259     6      259 | 24       8       57 | 37     23457     1    |
| 3       4      8   | 1        26      57 | 9      2567      7-2  |
+--------------------+---------------------+-----------------------+
| 8       9      34  | 347      1       2  | 6      37        5    |
| 6      b25     34  | 3457     345     8  | 1      9        a2347 |
| 25      1      7   | 345      9       6  | 8      23        234  |
+--------------------+---------------------+-----------------------+

Step 2: (2)r8c9 = r8c2 – r3c2 = r2c3 – r2c7 = (2)r4c7 => - 2r6c9
Code:




+--------------------+-------------------+----------------------+
| 7       8      6   | 235     235     9 | 4      1         23  |
| 4       3      25  | 6       7       1 | 25     8         9   |
| 19     b25     19  | 8       23      4 | 7      c235      6   |
+--------------------+-------------------+----------------------+
| 125     7      125 | 9       46      3 | 25      46       8   |
| 259     6      259 |e24      8       7 | 3      d245      1   |
| 3       4      8   | 1       26      5 | 9       26       7   |
+--------------------+-------------------+----------------------+
| 8       9      34  |f34       1      2 | 6       7        5   |
| 6      a25     34  | 7       g34-5   8 | 1       9        234 |
| 25      1      7   |f345      9      6 | 8       23       234 |
+--------------------+-------------------+----------------------+

Step 3: (5)r8c2 = r3c2 – r3c8 = (5-4)r5c8 = r5c4 – r79c4 = (4)r8c5 => - 5r8c5; stte
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Mogulmeister



Joined: 03 May 2007
Posts: 963

PostPosted: Sat Oct 23, 2021 10:53 am    Post subject: Reply with quote

Very Nice Clement
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dongrave



Joined: 06 Mar 2014
Posts: 450

PostPosted: Sat Oct 23, 2021 12:25 pm    Post subject: Reply with quote

Mogulmeister wrote:
Well done dongrave!

Was it a relative of this one ?

-2r1c4=r5c4-r6c5=r6c89-(2=5)r4c7-(5)r56c8=r3c8-r3c2=r8c2-r8c5=r1c5 means r1c4<>5 and r1c5<>2


Thanks Mogulmeister! No, yours is much simpler. Mine started with a 2 in r2c3 and went around the grid and ended up with a 7 in both r7c4 and r7c8!

Nice puzzle Mogulmeister! wow! Great job Clement!
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dongrave



Joined: 06 Mar 2014
Posts: 450

PostPosted: Sat Oct 23, 2021 4:48 pm    Post subject: Reply with quote

I found a slightly shorter chain than my original one.

2*r2c3-(2=7)r2c5-(27=5)r2c7-(5=2)r4c7-(2=1|5)r4c13-(2*5=9)r5c3-(59=2)r5c1-[(2=4*)r5c4 -(2=5)r9c1]-(4*5=3)r9c4-(34*=7)r7c4-r8c4=r8c9-(7=2)r6c9-(2=6)r6c5-(6=4)r4c5 contradiction (i.e. 4r5c4, 4r4c5) => r2c3<> 2; stte. Whew!
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Mogulmeister



Joined: 03 May 2007
Posts: 963

PostPosted: Sun Oct 24, 2021 10:25 am    Post subject: Reply with quote

So here’s a sideways look.

There’s an ANP <25> at r2c5 and r2c7.

If ANP is TRUE (5=27)r2c57 then R2c3 < > 2 and puzzle is solved.

-OR-

If ANP is FALSE (27=5)r2c57 then

(27=5)r2c57-(5=2)r4c7-(2=15)r4c13-(5=29)r5c13-(2=4)r5c4

R5c4 = 4 and puzzle is solved

You could extend this chain further, which will eventually produce contradictions in block 1 (two 2's) showing that r2c7 < > 5


Last edited by Mogulmeister on Sun Oct 24, 2021 1:00 pm; edited 7 times in total
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Mogulmeister



Joined: 03 May 2007
Posts: 963

PostPosted: Sun Oct 24, 2021 10:27 am    Post subject: Reply with quote

dongrave wrote:
I found a slightly shorter chain than my original one.

2*r2c3-(2=7)r2c5-(27=5)r2c7-(5=2)r4c7-(2=1|5)r4c13-(2*5=9)r5c3-(59=2)r5c1-[(2=4*)r5c4 -(2=5)r9c1]-(4*5=3)r9c4-(34*=7)r7c4-r8c4=r8c9-(7=2)r6c9-(2=6)r6c5-(6=4)r4c5 contradiction (i.e. 4r5c4, 4r4c5) => r2c3<> 2; stte. Whew!


Whew! Shorter ? Amazing chain! Two contradictory 4's in block 5.
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TomC



Joined: 30 Oct 2020
Posts: 143
Location: Wales

PostPosted: Sun Oct 24, 2021 1:51 pm    Post subject: Reply with quote

After basics
Code:

+------------+--------------+-----------------+
| 7   8  6   | 235  235  9  | 4    1     23   |
| 4   3  25  | 6    27   1  | 257  8     9    |
| 19  25 19  | 8    237  4  | 2357 2357  6    |
+------------+--------------+-----------------+
| 125 7  125 | 9    46   3  | 25   46    8    |
| 259 6  259 | 24   8    57 | 2357 23457 1    |
| 3   4  8   | 1    26   57 | 9    2567  27   |
+------------+--------------+-----------------+
| 8   9  34  | 347  1    2  | 6    37    5    |
| 6   25 34  | 3457 3457 8  | 1    9     2347 |
| 25  1  7   | 345  9    6  | 8    23    234  |
+------------+--------------+-----------------+

Play this puzzle online at the Daily Sudoku site

One way to simplify this puzzle is to notice that if r1c9 =2 then using box 2 and 9 you would end up with no 2's in row 6

Still not solved but much easier

edit basics fixed (I hope!)


Last edited by TomC on Sun Oct 24, 2021 2:36 pm; edited 2 times in total
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Mogulmeister



Joined: 03 May 2007
Posts: 963

PostPosted: Sun Oct 24, 2021 2:07 pm    Post subject: Reply with quote

Nice one Tom. Agreed.
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