Hard puzzle solve without guessing. Pencil marks filled.

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Hard puzzle solve without guessing. Pencil marks filled.

Postby hiprakhar » Sat Dec 08, 2018 10:24 pm

Please give me hints to solve the following puzzle. I have already shortlisted as many candidates as possible. How can I proceed without guessing?

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Re: Hard puzzle solve without guessing. Pencil marks filled.

Postby Madolite » Tue Dec 11, 2018 2:19 am

Hint: Focus on the 48 in the top left block and ask yourself which other numbers must be true, in either situation (if c1r2 is 4, compared to c1r2 being 8).

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If there's a 4 in c1r2, then c2r1 must be 8. Therefore, c4r1 must be 4.
Similarly, if there's an 8 in c1r2, then there must be a 4 in c7r2 and a 4 in c3r3. Therefore, c4r1 must be 4 also.
In both cases, c4r1 must be 4.


^ Idk if this solves the puzzle, but it'll help a lot.
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Re: Hard puzzle solve without guessing. Pencil marks filled.

Postby SpAce » Tue Dec 11, 2018 5:01 am

Madolite's logic is correct and would solve the puzzle. However, instead of a forcing chain, I'd rather see it as an AIC:

    (8)r1c2 = (8-4)r2c1 = r2c7 - r1c9 = (4)r1c4 => -8 r1c4; stte
I'm not really sure, but I think that chain pattern might be called L2-Wing.

For another possibility (one of many), see my reply here. (And please avoid double-posts, so the replies don't get split like this.)
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Re: Hard puzzle solve without guessing. Pencil marks filled.

Postby StrmCkr » Tue Dec 11, 2018 5:47 am

001052930059136027230907051120560079960010580540090010012605793390071200000329100

Empty Rectangle: 4 in b7 (r37c5) => r3c3<>4
Code: Select all
+-----------------+---------------+-------------+
| 67    78  1     | 48  5     2   | 9    3   46 |
| 48    5   9     | 1   3     6   | 48   2   7  |
| 2     3   6-4   | 9   8(4)  7   | 468  5   1  |
+-----------------+---------------+-------------+
| 1     2   38    | 5   6     348 | 34   7   9  |
| 9     6   37    | 27  1     34  | 5    8   24 |
| 5     4   378   | 27  9     38  | 36   1   26 |
+-----------------+---------------+-------------+
| 8(4)  1   2     | 6   8(4)  5   | 7    9   3  |
| 3     9   56(4) | 48  7     1   | 2    46  58 |
| 67    78  56(4) | 3   2     9   | 1    46  58 |
+-----------------+---------------+-------------+

Code: Select all
 2- string kite
+-----------------+---------------+-------------+
| 67    78  1     | 48  5     2   | 9    3   46 |
| 48    5   9     | 1   3     6   | 48   2   7  |
| 2     3   6(4)  | 9   8-4   7   | 468  5   1  |
+-----------------+---------------+-------------+
| 1     2   38    | 5   6     348 | 34   7   9  |
| 9     6   37    | 27  1     34  | 5    8   24 |
| 5     4   378   | 27  9     38  | 36   1   26 |
+-----------------+---------------+-------------+
| 8(4)  1   2     | 6   8(4)  5   | 7    9   3  |
| 3     9   56(4) | 48  7     1   | 2    46  58 |
| 67    78  56(4) | 3   2     9   | 1    46  58 |
+-----------------+---------------+-------------+


Sashimi X-Wing: 4 c35 r37 fr8c3 fr9c3 => r7c1<>4

Code: Select all
+----------------+---------------+-------------+
| 67   78  1     | 48  5     2   | 9    3   46 |
| 48   5   9     | 1   3     6   | 48   2   7  |
| 2    3   6(4)  | 9   8(4)  7   | 468  5   1  |
+----------------+---------------+-------------+
| 1    2   38    | 5   6     348 | 34   7   9  |
| 9    6   37    | 27  1     34  | 5    8   24 |
| 5    4   378   | 27  9     38  | 36   1   26 |
+----------------+---------------+-------------+
| 8-4  1   2     | 6   8(4)  5   | 7    9   3  |
| 3    9   56(4) | 48  7     1   | 2    46  58 |
| 67   78  56(4) | 3   2     9   | 1    46  58 |
+----------------+---------------+-------------+

any one of the three is probably the easiest way to solve it.. funny that they all use the same cells :P

W-wing...
Code: Select all
+-----------------+---------------+---------------+
| 67    7(8)  1   | (48)  5   2   | 9     3   6-4 |
| 4(8)  5     9   | 1     3   6   | (48)  2   7   |
| 2     3     46  | 9     48  7   | 468   5   1   |
+-----------------+---------------+---------------+
| 1     2     38  | 5     6   348 | 34    7   9   |
| 9     6     37  | 27    1   34  | 5     8   24  |
| 5     4     378 | 27    9   38  | 36    1   26  |
+-----------------+---------------+---------------+
| 48    1     2   | 6     48  5   | 7     9   3   |
| 3     9     456 | 48    7   1   | 2     46  58  |
| 67    78    456 | 3     2   9   | 1     46  58  |
+-----------------+---------------+---------------+


or
L wing,hybrid wing, l2 wing.... all fit the bill here...
Code: Select all
+------------------+----------------+-------------+
| 67    7(8)  1    | (48)  5    2   | 9    3   46 |
| (48)  5     9    | 1     3    6   | 48   2   7  |
| 2     3     6(4) | 9     8-4  7   | 468  5   1  |
+------------------+----------------+-------------+
| 1     2     38   | 5     6    348 | 34   7   9  |
| 9     6     37   | 27    1    34  | 5    8   24 |
| 5     4     378  | 27    9    38  | 36   1   26 |
+------------------+----------------+-------------+
| 48    1     2    | 6     48   5   | 7    9   3  |
| 3     9     456  | 48    7    1   | 2    46  58 |
| 67    78    456  | 3     2    9   | 1    46  58 |
+------------------+----------------+-------------+


plus lots and lots of other harder stuff
Some do, some teach, the rest look it up.
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