Advanced methods and approaches for solving Sudoku puzzles

I've been busting my b...cracking this one and so far i've only added five numbers. Now I'm stuck, and I've been using all kinds of techniques. My worst fear is that I have to start guessing. Can this really be true?

| 5 1 9 | * * * | * 8 * |
| 7 3 2 | * * * | * * 5 |
| 6 8 4 | * * 7 | * * 9 |
--------------------------
| * 6 * | * 3 1 | * * * |
| * * * | * 2 * | * * * |
| * 2 * | 8 6 * | * 5 * |
--------------------------
| 2 * * | 1 * * | * * 8 |
| * * * | * * * | 1 6 4 |
| * 4 * | * * * | * 7 2 |
akbristow

Posts: 5
Joined: 12 September 2005

### Thanks for the puzzle

| 5 1 9 | 2 4 6 | 7 8 3 |
| 7 3 2 | 9 1 8 | 6 4 5 |
| 6 8 4 | 3 5 7 | 2 1 9 |
--------------------------
| 8 6 5 | 4 3 1 | 9 2 7 |
| 4 9 1 | 7 2 5 | 8 3 6 |
| 3 2 7 | 8 6 9 | 4 5 1 |
--------------------------
| 2 5 6 | 1 7 4 | 3 9 8 |
| 9 7 3 | 5 8 2 | 1 6 4 |
| 1 4 8 | 6 9 3 | 5 7 2 |
brianbbrian

Posts: 1
Joined: 12 September 2005

For a start, what values can go in r1c5 and r4c9?
SteveF

Posts: 86
Joined: 26 March 2005

I put together a program that takes the "grudge accounting" out of the way but doesn't do any logic. It displays all the "pencil marks" for each cell. With that in mind, here's what I did to solve this one:
1. Box 5 has 459, 459, 49 in 3 different cells. That's a naked triple, therefore we can remove 4, 5, 9 from R5C4. Leaves only 7 in that cell.
2. Now 4 only appears in row 4 for col 4, we remove it from R5C6 and R6C6.
3. Box 4 has 134, 134, 13; another naked triple. We remove 1, 3 from R6C3, leaves only 7.
4. Row 1 has 236, 236, 36; yet another naked triple. We remove 2, 3, 6 from R1C7.
5. Box 6 has 34, 13, 34; yes, still one more naked triple. Remove 1, 3, 4 from the other cells in the box.
My program clears out the no-longer-valid pencil marks after each step, and there's only one per cell after step 5.
(Note that I'm new to posting so my terminology might not be right for "box" - meaning the three-row/three-column entity).

I'm finding that naked triples are very useful in solving harder puzzles.
rlangston

Posts: 4
Joined: 12 September 2005

Thanks for the very useful tips and solutions. I'm also new to the game, so when you say "naked triple" what exactly do you mean?
akbristow

Posts: 5
Joined: 12 September 2005

akbristow: a 'naked triple' is three cells in a row, column or box that between them contain only three possible candidates. This means that those specific three candidates must be in those three cells, which means you can remove those possible candidates from other cells in that row, column or cell.

E.g.

{1} {2,4} {3} {4,5,6,9} {4,7} {2,4,7} {8} {6,9} {5,6,7,9}

In the above example (where the bold entries are known) cells 2, 5 and 6 contain only the candidates 2, 4 and 7 (a naked triple). This indicates that you can remove all possible 2's, 4's and 7's from every other cell in that row, which leaves:

{1} {2,4} {3} {5,6,9} {4,7} {2,4,7} {8} {6,9} {5,6,9}

which, as you can see, now leaves two naked triples in that row. Geddit?

Karyobin

Posts: 396
Joined: 18 June 2005

Karyobin: AAHHHH!....Now I get it! Thanks a lot. This is very great help.
Actually I havn't even looked at the solution yet, for that simple reason that I wanted a technique, so I can solve it myself. It's a matter of pride and stubbornness. Again thank you Karyobin for helping me win the battle. Now I'll bust this sucker!
akbristow

Posts: 5
Joined: 12 September 2005

Well.....Not quite!
rlangston wrote: Box 5 has 459, 459, 49 in 3 different cells.. After placing all the pencilmarks in box 5 I find that both R4C4 and R5C4 has 4579 in them, leaving four cells with {4579} {4579} {459} {49}. How come R5C4 is the cell that can not have 459 and not R4C4
akbristow

Posts: 5
Joined: 12 September 2005

The naked triple is something that appears once you've pencilled in all the candidates for all the empty cells - unless you're one of those mathematical giants who can hold the whole lot in their head as they go!

Look at r4c9.
emm

Posts: 987
Joined: 02 July 2005

Then from what you have just given as the correct pencil marks, namely:

{4579} {4579} {459} {49}

...it would seem that what you have there is a naked quad, which may or may not turn out to be useful. I must confess to not having actually had a go at your particular sudoku, I merely explained what a naked triple was. Pleased you found it helpful.
Karyobin

Posts: 396
Joined: 18 June 2005

Remember that my program does the "grudge accounting", and it went ahead and determined that R4C8 had to be a 7. All other digits are either in the same row or column. So that means R4C4 can only contain 459, hence the naked triple availability.
rlangston

Posts: 4
Joined: 12 September 2005

I think you mean r4c9 not r4c8.
emm

Posts: 987
Joined: 02 July 2005

yes, sorry, R4C9.
rlangston

Posts: 4
Joined: 12 September 2005

Thanks for all the response guys. I did it Last night I cracked the bloody thing. And I learned a lot about technique doing it. Actully it wasn't the 'naked triple' in box 4 that did it. It was the very obvious {4} in R1C5. Some how I missed that cell (I must be getting old! And yes rlangston, I see now that I also missed the {7} in box 6 R4C9). After the {4} in box 2 everything was pretty much straight forward, allthough later on I did get to use a 'naked triple'.
akbristow

Posts: 5
Joined: 12 September 2005