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Set XY_03 Puzzle 007

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daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri May 29, 2009 2:57 pm Post subject: Set XY_03 Puzzle 007

Code:

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

Play this puzzle online at the Daily Sudoku site

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sat May 30, 2009 3:37 am Post subject:

whoa.

umm, ok, I am just going for it...
blues riff in B flat... oh and... I will cue the changes...
and a 1
and a 2
and a 1, 2, 3...

here is the grid after basics.
I have marked the cells in which I am going to concentrate on.
and please note the UR on {1,2} r17c89

Code:

.------------------.------------------.------------------.
| 7 8 6 | 5 3 4 |*19 U129 U129 |
| 2 19 19 | 8 6 7 | 5 3 4 |
| 4 3 5 | 9 2 1 | 7 8 6 |
:------------------+------------------+------------------:
| 6 7 19 | 2 148 3 | 1489 149 5 |
| 5 2 8 |*14 9 6 |*14 7 3 |
| 19 4 3 | 7 18 5 | 2 6 189 |
:------------------+------------------+------------------:
|*19 5 7 | 6 14 8 | 3 U1249 U129 |
| 38 169 4 | 13 7 2 | 1689 5 189 |
| 38 *16 2 |*134 5 9 |*1468 *14 7 |
'------------------'------------------'------------------'

lets start with the UR {1,2} here...

Code:

+-------+-------+------------+
| . . . | . . . | . 129 129 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+------------+
| . . . | . . . | . 1249 129 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+------------+

if you strip away the extra 9's and 4, you get the deadly pattern on 12 easy enough to see.

lets add some candidates to show a xy-wing that can be formed with the 4 and 9's... here...

Code:

+---------+-------+------------+
| . . . | . . . | . 129 129 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+---------+-------+------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+---------+-------+------------+
| 19 . . | . . . | . 1249 129 |
| . . . | . . . | . . . |
| . 16 . | . . . | . 14 . |
+---------+-------+------------+

this is important... there is a xy-wing here, you may not know it, but you can combine the {1,9}r7c1 and {4,9}r7c89 and {1,4}r9c8 to form a xy-wing.(the reason I can use the {4,9} from two cells r7c89 is because it belongs to the UR cells, getting to that in a second.)
if this xy-wing {1,4,9} that's been created is true then the 1 in r9c2 is false.
keep the fact that the 1 in r9c2 would be false in the back of your mind.

moving on...

imagine in your mind that the xy-wing that was just created {1,4,9}r7c1, r7c89,r9c8 is all false... like this

Code:

+--------+-------+-----------+
| . . . | . . . | . 129 129 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+--------+-------+-----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+--------+-------+-----------+
| . . . | . . . | . 12 12 |
| . . . | . . . | . . . |
| . 16 . | . . . | . . . |
+--------+-------+-----------+

notice now that a Type 2 UR is created which forces 9 in either of the r1c89 cells. see that?
easy eh?

ok, going to run that in reverse to cover all harmony lines
this time the group of 9's in r1c89 are false... like this...

Code:

+---------+-------+------------+
| . . . | . . . | . 12 12 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+---------+-------+------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+---------+-------+------------+
| 19 . . | . . . | . 1249 129 |
| . . . | . . . | . . . |
| 16 . | . . . | . 14 . |
+---------+-------+------------+

as can be seen, either the 4 or the 9's have to be placed in r7c89
in other words the set {4,9} (pseudocell) r7c89 has to be true in order to avoid the deadly UR {1,2}, this is how the xy-wing is formed !!!
together with the {19} cell and the {1,4} cell, it all forms a xy-wing {1,4,9}.

so what was learned?
BINGO !!! if you were thinking strong inference, you are correct.

UR12[xy-wing(1,4,9)r7c1,r7c89,r9c8 = (9)r1c89]

I know it looks really bad. Confused

but here is why its not.

in this next grid I have added the cells that I marked in the first grid above to show the entire music score.

Code:

+----------+---------+---------------+
| . . . | . . . |B19 129 129 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------+---------+---------------+
| . . . | . . . | . . . |
| . . . |D14 . . |C14 . . |
| . . . | . . . | . . . |
+----------+---------+---------------+
|A19 . . | . . . | . 1249 129 |
| . . . | . . . | . . . |
| F38 H16. |E134 . . |G1468 A14 . |
+----------+---------+---------------+

UR12[xy-wing(1,4,9)r7c1,r7c89,r9c8 = (9)r1c89] - (9=1)r1c7 - (1)r5c7 = (1-4)r5c4 = (4-3)r9c4 = (3-8)r9c1 = (8-6)r9c7 = (6)r9c2; r9c2 <> 1

the melody flows from A's (xy-wing) to H

The words to the song sing, out loud, two things, either the xy-wing is true or the 6 is true.
so lets see what happens in either case.
xy-wing (1,4,9) => 1 in r9c2 is false
r9c2 = 6 => r9c2 <> 1
both cases show 1 to be false.
-----------

all that to leave this grid

Code:

.------------------.------------------.------------------.
| 7 8 6 | 5 3 4 | 19 129 129 |
| 2 19 19 | 8 6 7 | 5 3 4 |
| 4 3 5 | 9 2 1 | 7 8 6 |
:------------------+------------------+------------------:
| 6 7 19 | 2 148 3 | 1489 149 5 |
| 5 2 8 | 14 9 6 | 14 7 3 |
| 19 4 3 | 7 18 5 | 2 6 189 |
:------------------+------------------+------------------:
| 19 5 7 | 6 14 8 | 3 1249 129 |
| 38 19 4 | 13 7 2 | 6 5 189 |
| 38 6 2 | 134 5 9 | 148 14 7 |
'------------------'------------------'------------------'

skyscraper on 9's in row 6 and 8 to finish it.

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