The New Sudoku Players' Forum

by **amjones** » Sat Oct 20, 2007 1:38 pm

Hello, fellow SuDoKu addicts, my first post. I'm stuck on puzzle #32 in the referenced book by Will Shortz. Here's the original:

Code: Select all: .-----.-----.-----. |. . 2|7 . 6|. . .| |. . 4|. . 8|7 . .| |. 7 .|1 . .|. 2 6| :----- ----- -----: |4 1 .|. 8 .|3 . 7| |. . .|4 . 7|. . .| |2 . 7|. 9 .|. 8 4| :----- ----- -----: |3 2 .|. . 4|. 9 .| |. . 5|2 . .|4 . .| |. . .|8 . 9|2 . .| '-----'-----'-----'

Here's where I get stuck:

Code: Select all: -------------+--------------+----------------- 15 38 2 | 7 35 6 | 158 4 9 156 56 4 | 9 2 8 | 7 135 135 9 7 38 | 1 4 35 | 58 2 6 -------------+--------------+----------------- 4 1 9 | 56 8 2 | 3 56 7 568 38 368 | 4 156 7 | 9 156 2 2 56 7 | 3 9 15 | 156 8 4 -------------+--------------+----------------- 3 2 168 | 56 7 4 | 156 9 158 678 9 5 | 2 136 13 | 4 1367 138 67 4 16 | 8 1356 9 | 2 13567 135 -------------+--------------+-----------------

by **wintder** » Sat Oct 20, 2007 2:04 pm

Welcome to the forums!

Edited to add: My bad, the first skyscraper is not correct, as daj points out.

There are 2 skyscrapers, also known as sashimi x-wings, available from your position.

Code: Select all: -------------+--------------+----------------- 15 38 2 | 7 35 6 | 158 4 9 156 56 4 | 9 2 8 | 7 135 135 9 7 38 | 1 4 35 | 58 2 6 -------------+--------------+----------------- 4 1 9 |*56 8 2 | 3 *56 7 568 38 368 | 4 156 7 | 9 156 2 2 56 7 | 3 9 15 | 15-6 8 4 -------------+--------------+----------------- 3 2 168 |*56 7 4 |*156 9 158 678 9 5 | 2 136 13 | 4 137-6 138 67 4 16 | 8 1356 9 | 2 1357-6 135 -------------+--------------+----------------- -------------+--------------+----------------- 15 38 2 | 7 35 6 | 158 4 9 156 56 4 | 9 2 8 | 7 135 135 9 7 38 | 1 4 35 | 58 2 6 -------------+--------------+----------------- 4 1 9 |*56 8 2 | 3 5-6 7 568 38 368 | 4 156 7 | 9 156 2 2 56 7 | 3 9 15 |*156 8 4 -------------+--------------+----------------- 3 2 168 |*56 7 4 |*156 9 158 678 9 5 | 2 136 13 | 4 1367 138 67 4 16 | 8 1356 9 | 2 13567 135 -------------+--------------+-----------------

by **daj95376** » Sat Oct 20, 2007 6:31 pm

wintder wrote:BTW, it is quite "legal" to take ALL these eliminations at once.

I suggest that you review cell [r7c3] and recheck your first Skyscraper.

by **amjones** » Mon Oct 22, 2007 3:07 pm

Thanks for the help! Unfortunately I'm not familiar with a skyscraper. I looked at the explanation on sudopedia and I must be dense, I don't get it. I'm googling for other explanations on the net that might make sense to a simple mind like mine!

by **udosuk** » Mon Oct 22, 2007 3:53 pm

amjones, see if the following link is more easy to understand:

http://www.sudopedia.org/wiki/Turbot_Fish

As for your puzzle:

Code: Select all: *--------------------------------------------------------------------* | 15 38 2 | 7 35 6 | 158 4 9 | | 156 56 4 | 9 2 8 | 7 135 135 | | 9 7 38 | 1 4 35 | 58 2 6 | |----------------------+----------------------+----------------------| | 4 1 9 |*56 8 2 | 3 -56 7 | | 568 38 368 | 4 156 7 | 9 156 2 | | 2 56 7 | 3 9 15 |*156 8 4 | |----------------------+----------------------+----------------------| | 3 2 168 |*56 7 4 |*156 9 158 | | 678 9 5 | 2 136 13 | 4 1367 138 | | 67 4 16 | 8 1356 9 | 2 13567 135 | *--------------------------------------------------------------------* . . . | / . . | / . . . . . | / . . | / . . . . . | / . . | / . . -----------+-----------+----------- . . . | A6 . . | / x6 . . . . | / . . | / . . . . . | / . . | B6 . . -----------+-----------+----------- . . . | C6 . . | D6 . . . . . | / . . | / . . . . . | / . . | / . . / = cells without 6 on c4 & c7

You have to notice that cells A & C above are the only cells possible to hold 6 on c4, while cells B & D are the only cells possible to hold 6 on c7.

Now consider what will happen if the cell marked with "x" happens to be a 6:

Cells A & B will not be able to hold 6 (same row and box with "x" respectively).

But then both C & D must hold 6 now (from c4 & c7 respectively).

Now we will have two 6s on r7, which violates the rule of Sudoku!

Therefore by contradiction the cell marked with "x" must not hold 6, and we can eliminate 6 from it. :idea:

Straightly after this move, we'll see r4c8 must be 5, so r4c4 must be 6, r7c4 must be 5.

Now r67c7 forms a naked pair of {16} on c7. Thus we reach this state:

Code: Select all: *-----------------------------------------------------------* | 15 38 2 | 7 35 6 | 58 4 9 | | 156 56 4 | 9 2 8 | 7 13 135 | | 9 7 38 | 1 4 35 | 58 2 6 | |-------------------+-------------------+-------------------| | 4 1 9 | 6 8 2 | 3 5 7 | | 568 38 -368 | 4 15 7 | 9 16 2 | | 2 *56 7 | 3 9 15 |*16 8 4 | |-------------------+-------------------+-------------------| | 3 2 *168 | 5 7 4 |*16 9 18 | | 678 9 5 | 2 136 13 | 4 1367 138 | | 67 4 16 | 8 136 9 | 2 1367 135 | *-----------------------------------------------------------* *-----------------------------------------------------------* | 15 38 2 | 7 35 6 | 58 4 9 | | 156 56 4 | 9 2 8 | 7 13 135 | | 9 7 38 | 1 4 35 | 58 2 6 | |-------------------+-------------------+-------------------| | 4 1 9 | 6 8 2 | 3 5 7 | | 568 38 368 | 4 15 7 | 9 16 2 | | 2 56 7 | 3 9 *15 |*16 8 4 | |-------------------+-------------------+-------------------| | 3 2 168 | 5 7 4 |*16 9 18 | | 678 9 5 | 2 136 *13 | 4 -1367 -138 | | 67 4 16 | 8 136 9 | 2 1367 135 | *-----------------------------------------------------------*

There are 2 similiar moves here which will enable you to eliminate 6 from r5c3 and 1 from r8c89.

I will leave you to work out the details yourself.

BTW this technique is called "turbot fish" in general.

"Skyscraper" is just a name for this particular type of "turbot fish".

Once you know the mechanics names are not important.

by **amjones** » Mon Oct 22, 2007 4:38 pm

Thanks again!! I understand this example now. The fun part will be, finding cases myself like this in the future!

The New Sudoku Players' Forum

puzzle #32 in"the first world sudoku championship"

puzzle #32 in"the first world sudoku championship"