Help with solution needed.

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Help with solution needed.

Postby User16 » Thu Mar 26, 2015 11:19 am

Hello again. I have generally been able to solve sudoku puzzles with tips I have learned from here and further reading online. But this one has me stumped and I don't think I can "see" it any more. I have looked for patterns of numbers across rows/columns that remove numbers from other cells, and for cells where both numbers result in the same number further along the chain, but nothing. It seems to be really clean (minimum candidates all making sense within rows, columns and regions).

The program is again the TicBits sudoku app for iOS, expert level, the screen print is form sudoku-solutions.com - which could offer no hints, or partial solution, but said the puzzle was valid with one solution.

Many thanks!
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Re: Help with solution needed.

Postby JasonLion » Thu Mar 26, 2015 12:23 pm

I see a finned X-Wing in there, some basic moves, and then a BUG+1 to finish it off.
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Re: Help with solution needed.

Postby SteveG48 » Thu Mar 26, 2015 2:50 pm

Alternately, there are a number of choices of simple colorings/turbot fish/skyscrapers that will finish off the 6's. Then the 3's and 5's go easily and it's clear sailing.
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Re: Help with solution needed.

Postby Leren » Thu Mar 26, 2015 8:11 pm

A couple of Skyscrapers should finish off the puzzle. In case you are not familiar with this technique here's how it works.

Code: Select all
*--------------------------------------------------------------*
| 2     7     1      | 4    b356   8      | 9     35   a356    |
| 8     35    35     | 9     1     26     | 2-6   7     4      |
| 4     6     9      | 37    235   2357   | 235   8     1      |
|--------------------+--------------------+--------------------|
| 7     9     6      | 2     8     1      | 35    4     35     |
| 3     1     4      | 5     7     9      | 8     6     2      |
| 5     2     8      | 36    4     36     | 7     1     9      |
|--------------------+--------------------+--------------------|
| 6     8     35     | 1     9     357    | 4     2     357    |
| 1     35    2      | 78   c356   4      |d356   9     78     |
| 9     4     7      | 368   2356  2356   | 1     35    358-6  |
*--------------------------------------------------------------*

The diagram shows your puzzle position. Look at the cells marked abcd. If Cell a (Row 1 Column 9 or r1c9 for short) is not 6 then r1c5 (Cell b) is 6 (only 2 6's in Row 1).

So r8c5 (Cell b) is not 6, so r8c7 (Cell d) is 6 (only 2 6's in Row 8).

You can reverse this argument and follow the cells in order dcba to show that if r8c7 is not 6 then r1c9 is 6.

The conclusion is that at least one of r1c9 and r8c7 must be 6. They might both be 6 but they can't both be not 6.

Since the 6's in r2c7 and r9c9 can see both of these cells you can remove 6 from both of them.

Doing this and a few more basic moves should get you to here:

Code: Select all
*--------------------------------------------------------------*
| 2     7     1      | 4     5-3   8      | 9    d35    6      |
| 8     35    35     | 9     1     6      | 2     7     4      |
| 4     6     9      |a37    2     57     | 5-3   8     1      |
|--------------------+--------------------+--------------------|
| 7     9     6      | 2     8     1      | 35    4     35     |
| 3     1     4      | 5     7     9      | 8     6     2      |
| 5     2     8      | 6     4     3      | 7     1     9      |
|--------------------+--------------------+--------------------|
| 6     8     35     | 1     9     57     | 4     2     37     |
| 1     35    2      | 78    35    4      | 6     9     78     |
| 9     4     7      |b38    6     2      | 1    c35    358    |
*--------------------------------------------------------------*

There is another Skyscraper in 3's in Cells r3c4, r9c4, r9c8 and r1c8 which removes 3 from r1c5 and r3c7.

The puzzle will solve easily after that.

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Re: Help with solution needed.

Postby User16 » Fri Mar 27, 2015 1:00 pm

Thank you all very much! I had somehow remained refreshingly free of the skyscraper method. I was used to looking for more direct relationships (basic swordfish and x-wing) and just didn't see these inferences.

Leren, I had fun following your examples, thank you. I got to the second stage as you did, excepting r7c9 which I still had candidates 357 and not 37 as you showed (which didn't seem to make any difference), and then it unravelled nicely. I am going to have to practice spotting these patterns; the type of search wasn't that much different to what I was trying but I didn't get there on my own. I will look up some of these bugs and fishes too!

Hopefully even longer until I have to call for help again!

Thanks again.
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