Stumped!

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Stumped!

Postby QiGuy » Tue Mar 31, 2015 6:30 pm

The puzzle below appeared in the Globe and Mail. I got to this point and am completely stuck. Usually an xy chain will emerge at this point -- not this time. Can anyone point me to a technique to solve this?


6 4 8 359 139 13 2 35 7
2 7 35 8 4 6 9 135 13
1 9 35 35 2 7 4 6 8
8 3 4 1 5 2 6 7 9
9 5 26 36 7 8 13 4 123 Globe and Mail Toronto Saturday March 15, 2015
7 26 1 4 36 9 5 8 23
5 8 9 2 136 134 7 13 46
34 12 26 7 8 5 13 9 46
34 16 7 369 169 134 8 2 5
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Re: Stumped!

Postby QiGuy » Tue Mar 31, 2015 6:31 pm

Also, sorry about the formatting -- it looked better in Excel.
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Re: Stumped!

Postby bat999 » Tue Mar 31, 2015 7:44 pm

...........
Last edited by bat999 on Fri Jul 17, 2015 8:20 pm, edited 1 time in total.
8-)
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Re: Stumped!

Postby Leren » Tue Mar 31, 2015 8:01 pm

Code: Select all
*--------------------------------------------------------------*
| 6     4     8      | 359   139   13     | 2     35    7      |
| 2     7     35     | 8     4     6      | 9     135   13     |
| 1     9     35     | 35    2     7      | 4     6     8      |
|--------------------+--------------------+--------------------|
| 8     3     4      | 1     5     2      | 6     7     9      |
| 9     5    b26     |c36    7     8      | 13    4     123    |
| 7     26    1      | 4     36    9      | 5     8     23     |
|--------------------+--------------------+--------------------|
| 5     8     9      | 2     136   134    | 7     13    46     |
| 34    126  a26     | 7     8     5      | 13    9     46     |
| 34    1-6   7      |d369   1369  134    | 8     2     5      |
*--------------------------------------------------------------*

In more conventional Sudoku terminology what bat was describing is a Skyscraper.

Look at the cells marked abcd.

If cell a (Row 8 Column 3 or r8c3 for short) is not 6 then r5c3 (cell b) must be 6 (only 2 6's in Column 3).

So r5c4 (cell c) is not 6. So r9c4 must be 6 (only 2 6's in Column 4).

You can reverse this logic and start by assuming r9c4 is not 6 and conclude that r8c3 is 6.

The result of all this is that at least one of r8c3 and r9c4 must be 6. They could both be 6 but they can't both be not 6.

Since r9c2 can see both cells a and d you can remove the 6 from there. That solves that cell and the puzzle solves easily after that.

Here's link to a site that discusses Skyscrapers (and a lot of other solving techniques).

http://hodoku.sourceforge.net/en/techniques.php

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Re: Stumped!

Postby QiGuy » Wed Apr 01, 2015 1:58 pm

Leren: Thanks for the solution -- but even more for the Skyscraper link, which I will examine carefully. Can't believe I haven't run into it before, but then until this puzzle I've always been able to find an xy chain that breaks the impasse. Thanks very much!
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