Help? Is a guess required?

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Help? Is a guess required?

Postby judebarnes » Tue Jan 20, 2015 12:28 am

We are debating whether some sudoku's require a guess as part of the technique, in very difficult puzzles? Or are ALL sudoku's supposed to be solvable w/ logic (and no hacking or guesswork)?
As examples, .. see 3 puzzles below. I plugged all three into sudokuhints.com and it said it was stuck. Is the website not smart enough, and there actually is a technique or advanced technique for the next step??

PUZZLE 1 OF 3:
----642-3,
-4---89-6,
--6-5-4-7,
6-38--745,
45-6-3821,
---54-639,
2-143-5-8,
7-41-5362,

PUZZLE 2 OF 3
14-9--73-,
763-148--,
--2-3-461,
-37--16--,
-5----14-,
--1---25-,
81--4-9--,
3291--5-4,
-74--931-,

PUZZLE 3 OF 3:
--25---98,
49--2---5,
3-59--2--,
864312759,
153798-2-,
927654831,
2-1--59-3,
----3-582,
53-2--1--,
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Re: Help? Is a guess required?

Postby JasonLion » Tue Jan 20, 2015 4:48 pm

Yes, it is certainly possible to solve any Sudoku puzzle without guessing, though at the very hardest level a puzzle might take an expert days and a non-expert would not be able to solve it.

The puzzles you posted are not especially difficult. Well, the first puzzle isn't valid, it appears to be missing a row. The second puzzle can be solved with an XY-Wing plus some simpler techniques. The third puzzle is even simpler, requiring a single Skyscraper/Finned X-Wing plus singles.
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Re: Help? Is a guess required?

Postby Leren » Tue Jan 20, 2015 9:01 pm

Code: Select all
*--------------------------------------------------------------*
| 67    17    2      | 5     467   1367   | 346   9     8      |
| 4     9    b68     |a18    2     1367   | 36    167   5      |
| 3     178   5      | 9    *467-8 167    | 2     1467  467    |
|--------------------+--------------------+--------------------|
| 8     6     4      | 3     1     2      | 7     5     9      |
| 1     5     3      | 7     9     8      | 46    2     46     |
| 9     2     7      | 6     5     4      | 8     3     1      |
|--------------------+--------------------+--------------------|
| 2     478   1      |*4-8   678   5      | 9     67    3      |
| 67    47    69     | 14    3     1679   | 5     8     2      |
| 5     3    c689    | 2    d678   679    | 1     467   467    |
*--------------------------------------------------------------*

Here is the way to get further in puzzle 3 without guessing. A couple of simple moves have removed the 4's from row 7 column 5 (shortened to r7c5), r9c5 and r7c8.

Hopefully you'll know how to do this and in any case it doesn't affect what follows.

Now here's the important part : Look at the cell's I've marked a, b, c and d. Notice that they all contain 8's and that a and b contain the only two 8's in Row 2 and c and d contain the only two 8's in Row 9.

Now suppose r2c4 (cell a) is not 8. Then, since there are two 8's in Row 2, r2c3 (cell b) must be 8. That means that r9c3 (cell c) is not 8. Since there two 8's in Row 9, r9c5 (cell d) must be 8.

You can reverse this argument, assume r9c5 is not 8 and follow the cells in the order dcba to show that if r9c5 is not 8 then r2c4 must be 8.

All of this means that at least one of r2c4 and r9c5 must be 8. (They might both be 8 but they can't both be not 8.)

Now look at r3c5 and r7c4 (I've marked them with a * in the diagram. They can both see (ie share a row, column or box with) cells a and d. Since at least one of a and d must be 8 then r3c5 and r7c4 can't be 8.

In particular this solves r7c4 to 4 and r1c4 to 8 (since there are only two 8's in Box 2 or Column 4) and the puzzle solves easily after that. As Jason said this solving technique is called a Skyscraper.

Hope this helps, Leren
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