The New Sudoku Players' Forum

[JCell]

Hi,

Fairly new to this but am stuck with this one and have some questions.

I have enterered 18 numbers into this puzzle. Now am at the point where it doesn't seem like there are any cells which have only one possible number as a solution.

Shouldn't a puzzle always have at least one cell that has only one number that can be correctly placed in that cell? Otherwise it seems like finding the solution becomes try each of the two or more possibilities and see which ultimately works.

In this case, for example, the center cell in row 1 can now be a 1 or 5. It seems overly laborious to have to pursue both possibilities separately to see which one actually works. Any help?

Thanks,

JCell

[PaulIQ164]

In fact there are various other techniques that might work even if every cell has two or more possibilities. Most obviously, check the missing numbers in each row, column and 3x3 box, there might be only one place a certain number can go (e.g., "the 8 in this row can only be in this cell" as poopsed to "this box can only be an 8"). Then, if the puzzle is hard enough, there might be more advanced tactics still, but they're much more satisfying if you work them out for yourself.

[JCell]

In fact there are various other techniques that might work even if every cell has two or more possibilities. Most obviously, check the missing numbers in each row, column and 3x3 box, there might be only one place a certain number can go (e.g., "the 8 in this row can only be in this cell" as poopsed to "this box can only be an 8"). Then, if the puzzle is hard enough, there might be more advanced tactics still, but they're much more satisfying if you work them out for yourself.

Hey Paul,

Thanks for your answer. I have tried every thing I can think of as far as techniques go, but still don't see a single cell that reduces to one and only one logical answer. Has that ever happened to you? Any other ideas?

Also is there a way to post my solution so far so that others can try and figure out what the next logical cell to fill is?

JCell

[Karyobin]

Right, what you might consider is the following:

Let's say that you've got a row and in this row the possibilities for each of the nine cells are as follows:

{1,2} {3} {7,8,9} {1,2} {1,4,7} {5} {6} {2,7} {4,7,8,9} (By the way, the bold ones are just cells in which you already know the number.)

Now, notice that cells 1 and 4 only have the options {1,2} in them. This means that if these two cells can only contain these two numbers, then these two numbers must be in these two cells. Which therefore means that these two numbers can't be anywhere else. So, look at cell 8. This could only be 2 or 7, but we've just worked out that, in fact, 2 can't be there! So, it must be a 7. If you follow that, you can do the same to cell 5. This cell looks like it could be {1,4,7} but we've just proved it can't actually be a 1, and after the last step, we now know it can't be a 7 either - so it must be a 4. And so on...

This method is known as naked pairs (I think!) and if you follow what I've just said, you can probably see how it would also work with three numbers and three cells, and still higher numbers.

As Paul said, it is fun to work out the higher strategies for yourself, but if you like you could do a lot worse than read the following two sites for some explanations:

http://www.angusj.com/sudoku/hints.php

and

http://www.simes.clara.co.uk/programs/sudoku.htm

By the way, as to posting the grids, I'm sorry to say I don't know - I just type in things like:

2 * * 4 * 1 * * 7

for each line, and so on.

[Doyle]

That particular Wash Post puzzle doesn't crack until you identify a set of three triples, in three cells of a box (not three cells in a row or in a column, the example posted above was for a row, but the principle applies also to columns and to boxes). It might be hard for a new solver to notice these triples, because they are in the form 123, 123, 12 (not the actual numbers). That is, one of the cells is missing one number of the triple, but they still represent "naked triples". Once you've identified these three cells, you can eliminate those three numbers from all other cells in that box, which leads to finding "naked pairs" in a row that intersects that box, which leads to further eliminations and then to finding some unique numbers for other cells. Not an easy train of deductions for a new solver, but not trial and error. (Caveat: there may be an easier route to the solution, but that's the way I did it.)

[Karyobin]

Oh yeah! Bearing in mind the original post, I bet he got all of that! *Sniggers*

P.S. Quite right, works for columns and boxes as well - forgot to mention that.

[JCell]

Thanks Karyobin. So far I have read two or three lines of your post and my mind has expanded. I'm putting new numbers up and see the world has another dimension. I'll try to take this as a hint and see how far I can go before I read further!

JCell

[nj3h]

Can someone please post the original puzzle being referenced in the message traffic.

Thanks,
nj3h

[PaulIQ164]

I just noticed that in my first post in this topic I inadvertantly coined a new word: "poopsed". It was obviously meant to be "opposed", but I think I'll leave it as it's clearly great.

[Doyle]

Don't yet know how to use the "Code", this is hand-entered:

*** 2** 4**
**1 *9* *7*
*** *84 *3*

**8 9** ***
*42 *** 39*
*** **2 6**

*9* 83* ***
*7* *4* 5**
**4 **1 ***

[JCell]

Karyobin, yes, that's all it took--the first few lines of your response to me to get me there. Still took some doing, but that was basically the thing I didn't see. I think part of the problem for me was that I was, trying to solve the problems by inspection, without using "pencil marks" as much as possible; thus I was minimizing this "pencil mark" info as only being good for sort of a brute force accounting approach, when actually it is more subtle information that must be considered with care!

Thanks,

JCell

[JCell]

Can someone please post the original puzzle being referenced in the message traffic.

Thanks,
nj3h

One way to see it is to go to solutions, select Washington Post and enter 24197. Of course that shows the solved puzzle, but the original numbers are hi-lited. It got hairy for me on about the 19th move.

JCell

[Karyobin]

JCell - congrats. There's a whole lot more where that came from. Just check out the sites I gave you.

Paul - Top word. I noticed it straight away.

Goodbye poople.

[The Central Scrutinizer]

...
Let's say that you've got a row and in this row the possibilities for each of the nine cells are as follows:

{1,2} {3} {7,8,9} {1,2} {1,4,7} {5} {6} {2,7} {4,7,8,9} (By the way, the bold ones are just cells in which you already know the number.)

Now, notice that cells 1 and 4 only have the options {1,2} in them. This means that if these two cells can only contain these two numbers, then these two numbers must be in these two cells. Which therefore means that these two numbers can't be anywhere else. So, look at cell 8. This could only be 2 or 7, but we've just worked out that, in fact, 2 can't be there! So, it must be a 7. If you follow that, you can do the same to cell 5. This cell looks like it could be {1,4,7} but we've just proved it can't actually be a 1, and after the last step, we now know it can't be a 7 either - so it must be a 4. And so on...

This method is known as naked pairs (I think!) and if you follow what I've just said, you can probably see how it would also work with three numbers and three cells, and still higher numbers.

Thank you for the very well stated definition. I only signed up today and I’m seeing a lot of terms that I should learn. ‘X-Wing’ and ‘Naked Pairs’ are at the top of the list.

I used the Naked Pair strategy this morning to break today’s puzzle without even knowing it had a name. I had {1 8} {1 8} seemingly everywhere and one little square on the opposite end of the row that was a {1 3 8} possibility. Once I realized that the 3 could only go one place, it unlocked the whole puzzle like an avalanche. I couldn’t fill in the numbers fast enough. God I love that feeling!

[Karyobin]

Not a problem, thanks for the appreciation. If you want to read some descriptions of X-wings, you could do a lot worse that look at:

http://www.angusj.com/sudoku/hints.php

and

http://www.simes.clara.co.uk/programs/sudoku.htm

for some descriptions. Best not to get to excited about Swordfish though. In my opinion these were identified as a mathematical extension of the X-wing, (rather than a structure in their own right) and though they're just as useful, they're sadly quite rare. Equally powerful candidate structures have been developed since; also derivatives, but far more common.