The New Sudoku Players' Forum

[swaatacba]

This puzzle is taken from the UK's Guardian newspaper 27 February. Here is an image for I far as I have managed - not very far.

SuDoku_GUA20170225_Block.PNG

I cannot identify a next valid step. Would be grateful for advice.

[JasonLion]

To get further you are going to need to fill in all of the pencil marks so you can look for naked tuples.

Code: Select all

...1........4.7...1..328..5..52.37..2...14.533.1875...712.3.584839542167456781..2

569    246789 3478   | 1      569    69     | 234689 23479  689   
569    2689   38     | 4      569    7      | 23689  1239   1689 
1      4679   47     | 3      2      8      | 469    479    5     
---------------------+----------------------+---------------------
69     4689   5      | 2      69     3      | 7      149    1689 
2      6789   78     | 69     1      4      | 689    5      3     
3      469    1      | 8      7      5      | 2469   249    69   
---------------------+----------------------+---------------------
7      1      2      | 69     3      69     | 5      8      4     
8      3      9      | 5      4      2      | 1      6      7     
4      5      6      | 7      8      1      | 39     39     2     


[swaatacba]

Thank you Jason. It seems that my aide memoire approach to solving Sudoku puzzles within an Excel spreadsheet needs to be refined considerably.

I have some initial ideas. They need development. before I can present the state of play in the puzzle in sufficient detail. Only then can I approach tuples, triples etc.

[Leren]

Well, I'll at least explain how a naked pair operates, as you seem to have something similar to this in your own diagram

Code: Select all

 569    246789 3478   | 1      569    69     | 234689 23479  689   
 569    2689   38     | 4      569    7      | 23689  1239   1689 
 1      4679   47     | 3      2      8      | 469    479    5     
 ---------------------+----------------------+---------------------
*69     48-69  5      | 2     *69     3      | 7      14-9   18-69 
 2      6789   78     | 69     1      4      | 689    5      3     
 3      469    1      | 8      7      5      | 2469   249    69   
 ---------------------+----------------------+---------------------
 7      1      2      | 69     3      69     | 5      8      4     
 8      3      9      | 5      4      2      | 1      6      7     
 4      5      6      | 7      8      1      | 39     39     2     

You can see that in Row 4, Columns 1 and 5 (r4c15 for short), there are only the two digits 6 and 9 (in the cells I've marked with *'s).

So the only possibilities for the eventual solution are that r4c1 is 6 and r4c5 is 9, or that r4c1 is 9 and r4c5 is 6.

Either way you can remove 6 and 9 from other cells in row 4, as I've shown to the right of the - signs in Jason's amended diagram.

If you understand that, you might also see a naked triple (569) in r1c156, so in a similar fashion you can remove 5, 6 and 9 from other cells in Row 1.

You can then see that r1c9 is 8, and then r4c9 is 1, so it looks like the puzzle is starting to fall apart.

Hope this helps, Leren

[eleven]

To get further you are going to need to fill in all of the pencil marks so you can look for naked tuples.

... or you look for hidden tuples:

Code: Select all

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

You have 148 in columns 1 and 5 (also box 5), so they cannot be in row 4 there (marked x). Only 3 empty cells are left in row 4, so they must hold the 148.

[Leren]

Code: Select all

569    26789-4 3478  | 1      569    69     | 234689 23479  689   
569    2689    38    | 4      569    7      | 23689  1239   1689 
1      679-4   47    | 3      2      8      | 469    479    5     
---------------------+----------------------+---------------------
69    *4689    5     | 2      69     3      | 7      149    1689 
2      6789    78    | 69     1      4      | 689    5      3     
3     *469     1     | 8      7      5      | 2469   249    69   
----------------------+----------------------+---------------------
7      1       2     | 69     3      69     | 5      8      4     
8      3       9     | 5      4      2      | 1      6      7     
4      5       6     | 7      8      1      | 39     39     2

Perhaps before the Tuples, we should have mentioned the Pointing Pair of 4's in r46c2 (marked with *'s in the diagram).

The two 4's in these cells are the only ones in Box 4 (that's the left hand one in the middle row of boxes). Since one of these two 4's must be true in the solution, you can eliminate 4's in Column 2 that are not in Box 4, as I've shown.

If there was another 4 in r5c2, the eliminations would still be valid, but you would be using a Pointing Triple.

Whilst this doesn't advance the puzzle too much, Pointing pairs/triples is generally regarded as the most basic of moves after Naked and Hidden Singles, so you should become familiar with this technique, even before you start on Tuples.

Leren

[swaatacba]

Thank you for all your advice. You should be aware that I work primarily in Excel and impose on myself a restriction that I should use standard Excel formulae only - i.e. no VBA or other programming language.

Designing in these restrictions is quite long winded. When I have established the basics Will come back to all your pointers.

[swaatacba]

I have now managed to create a semi-automatic version of a full data version of the state of play on the Sudoku puzzle - as shown.

Now for the difficult bit.

[Leren]

OK, you appear to have created your own version of the PM diagram's in the earlier posts and you just need to follow the advice given in them to make eliminations and solve the puzzle.

Leren

[swaatacba]

Here is a visual representation of a possible way forward. The Red ovals represent the "naked triple", The blue lines delete elements of the naked triple from other cells in the relevant dimension. The green circle represents the expected results. Is this a valid analysis?

[JasonLion]

Yes, your diagram is correct.

Note that there won't always be a digit placement right away. Occasionally, it takes more than one move to eliminate enough pencil marks to place a digit.

[swaatacba]

Thank you.

So my design may have to go through several iterations of "naked" elimination. My gut reaction is that 4 would be the absolute maximum. Any thoughts?

I think that I must also bear in mind that the "naked" eliminated values must be returned to the available values record if and when a result is achieved.

[Leren]

You've basically solved this puzzle.

You can see from your own diagram that r1c9 must be 8, so you can place it there and mark off 8's elsewhere in its row, column and box. That's called a naked single, meaning that it's the only candidate left in its cell.

Having done that you should notice that r5c7 must be 8, because it is the only 8 left in Column 7, or alternatively the only 8 left in Box 6, so you can place it there and mark it off in other cells in Row 5. That's called a hidden single, because it is "hidden" amongst other candidates in it's cell, but must be True there because it the only one left in it's row, column or box.

You then have 2 more singles : a hidden single 8 in r2c3 (only 8 in Column 3) and a naked single 7 in r5c3.

As you mark these off you will find that other naked and hidden singles will be revealed, until the puzzle is completely solved.

There is no limit to the number of these cascades of naked and hidden singles, it looks like 35 for this puzzle.

Leren

[swaatacba]

Thank you. I was aware that the barrier to solving the puzzle had been removed.

My primary interest now is in how to create an audit trail in Excel to show how I achieved the breakthrough. I should move this discussion. Is there a way of linking discussion threads?

[JasonLion]

You can put a link in a thread by enclosing the UTR in a URL command. Select the URL and then press the URL button just above the message composition window.