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MM 1678 2-12-10

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storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Fri Feb 12, 2010 8:53 am Post subject: MM 1678 2-12-10

020090006000508009075200000081000203000000000602000040000002430100306000000070051

Code:

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

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Asellus

Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

Posted: Tue Feb 16, 2010 3:53 am Post subject:

Another lonely puzzle being neglected. This one was a tough nut to crack! Here's what I came up with.

After basics:

Code:

+-----------------+------------------+---------------+
| 38 2 38 | 47 9 47 | 5 1 6 |
| 4 1 6 | 5 3 8 | 7 2 9 |
| 9 7 5 | 2 6 1 | 3 8 4 |
+-----------------+------------------+---------------+
| 57 8 1 | 679 4 579 | 2 679 3 |
| 357 3459 3479 | 16789 2 3579 | 189 679 578 |
| 6 359 2 | 1789 18 3579 | 189 4 578 |
+-----------------+------------------+---------------+
| 578 6 789 | 189 158 2 | 4 3 78 |
| 1 45 478 | 3 58 6 | 89 79 2 |
| 2 39 389 | 489 7 49 | 6 5 1 |
+-----------------+------------------+---------------+

[1] (8)r1c1=(8-5)r7c1=(5)r8c2 - (5=8)r8c5 - (8)r7c9=(8)r8c7; r7c1<>8
This can be seen as a generalized M-Wing in b178 with pincer transport in b9.

Code:

+--------------+-----------------+---------------+
| 8 2 3 | 47 9 47 | 5 1 6 |
| 4 1 6 | 5 3 8 | 7 2 9 |
| 9 7 5 | 2 6 1 | 3 8 4 |
+--------------+-----------------+---------------+
| 57 8 1 | 679 4 579 | 2 679 3 |
| 3 459 47 | 16789 2 579 | 189 679 578 |
| 6 59 2 | 1789 18 3 | 189 4 578 |
+--------------+-----------------+---------------+
| 57 6 789 | 189 158 2 | 4 3 78 |
| 1 45 478 | 3 58 6 | 89 79 2 |
| 2 3 89 | 489 7 49 | 6 5 1 |
+--------------+-----------------+---------------+

We can now repeat this trick in a similar way with <7>s, though it's
not so immediately helpful:

[2] (7)r4c1=(7-5)r7c1=(5)r8c2 - (5=8)r8c5 - (8=9)r8c7 - (9=7)r8c8; r4c8<>7

We can also exploit the external 1=8 strong inference in c45 induced by the 18UR:

[3] (9-1)r6c7=(1)r5c7 - 18UR[(1)r5c4=(8)r8c5]r67c45 - (8=9)r8c7 - (9)r6c7; r6c7<>9

The grid now simplifies nicely for one last step.

Code:

+-------------+--------------+----------+
| 8 2 3 | 47 9 47 | 5 1 6 |
| 4 1 6 | 5 3 8 | 7 2 9 |
| 9 7 5 | 2 6 1 | 3 8 4 |
+-------------+--------------+----------+
| 57 8 1 | 6 4 57 | 2 9 3 |
| 3 459 47 | 18 2 579 | 18 6 57 |
| 6 59 2 | 79 18 3 | 18 4 57 |
+-------------+--------------+----------+
| 57 6 79 | 19 15 2 | 4 3 8 |
| 1 45 48 | 3 58 6 | 9 7 2 |
| 2 3 89 | 489 7 49 | 6 5 1 |
+-------------+--------------+----------+

[4] 579 XY-Wing in b45; r4c1<>5

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