sudoku

[Kat]

Does anyone play this numbers game?
Recently Harry showed me the rudiments and now I'm hooked because it's something I can do while waiting- thru commercials, in a waiting room, on hold on the phone, on a plane, etc. I have one with me usually and I get them online. Easy ones, tho!

I realize this fad started a few years ago but I am usually late to these things.

[kssunflower]

I play this on my cell phone occasionally, but I've never gone past the basic or easy levels.

[Kat]

I tried to advance to *Medium* but it was too hard and all the fun went away! Were you taught a system? If anyone wants to find out Harry's beginners system, ask away!

[kssunflower]

No, I'm self-taught and just bungle through it myself. Also found higher levels too difficult.

Any tips would be appreciated.

[Yooper]

I've enjoyed Sudoku for the last couple of years. I'm not sure I have a system for solving, I just begin the puzzles the same way, looking for pairs in columns, then in rows. It's pretty much process of elimination from there.

[twinsrwe]

I LOVE playing Sudoku!!! It is a favorite of mine. I have been playing Sudoku, every day, for the past 4 years. I prefer to play the game using the ‘medium’ level. Sometimes I play the ‘advanced’ level, but then always seem to go back to the ‘medium’ level.

My husband also plays Sudoku, daily. We have two electronic Sudoku games; one we keep on a stand in our bathroom, and the other I take with me to places I know I will need to wait (doctor appointments, long road trips, etc.).

Actually, it was my husband who got me started on this game. I taught myself after he told me that when the game is completed each row and indiviual square will contain all of the numbers 1-9. The system I used as a beginner was: I took each of the numbers 1-9 individually and filled in as many empty spots as I could. After awhile I developed other ways to complete game. The more times you play the game, the easier it gets. I do not suggest going into the upper levels until you feel really comfortable with the level you are on and want more of a challenge.

You’ve got my curiosity up, Kat – what is Harry's beginners system?

[Kat]

I was on a train to Charleston and this lady seated next to me (going to Savannah) showed me this beginners method. Turns out she was a 7th grade science teacher! And turns out to be the same system Harry used to teach himself and the same he showed me- I guess they each figured it out themselves.

The problem with my learning this on that train 2 years ago- was after she got off the train, I forgot what she showed me!
So, YAY Harry!

I will figure out a way to break this illustration down into sections on here- so watch this space for it!

[Yooper]

The "migraine" level puzzles require a more complex process of elimination, they usually require memorizing three-number sequences at the least. Sometimes pairs of numbers can be isolated to only two spaces, and the rest of the empty spaces in the box or row or column must be what is left of the 1-9 sequence. This can also be done with groups of three numbers. Once that is done, the corresponding row or column containing the isolated either-or space can be examined for a corresponding either-or possibility.

For instance, imagine the 5,9 pairing can be isolated to two spaces in the top row of the puzzle. The two columns containing those spaces can be checked for a 5,9 either-or space. Lets say we can find one in one column which also contains 1,2,3. Once we have all that, the rest of the blanks must contain 4,6,7,8 in some sequence and sometimes one or more of these can then be placed, or possibly isolated.

It would be far easier to explain with a diagram, the explanations get quite wordy otherwise! The most difficult puzzles can usually be worked up to a stall point, at least for me, then there is usually one, and only one, key to be found. This generally happens somewhere near the half way point, where about half of the spaces are filled. Once the key is found, the rest of the puzzle pretty well falls into place.

[Yooper]

One type of puzzle which can be vexing is the one where groups of three numbers repeat in boxes going across or up and down. Isolating either-or possibilities can be very helpful. I'll attempt a diagram, but there may be edits!

Imagine this as the middle row of boxes across a puzzle:

8 x y|* * *|* * *
* * *|5 6 8|* * *
* * *|* * *|6 a b

x,y and a,b are blanks, as are * spaces. If the rest of the puzzle allows isolation of x,y to 5,6 in some order, and isolation of a,b to 5,8 in some order, then we must have this type of three-group puzzle. The rest of the spaces in each box must contain 1,2,3,4,7,9 arranged in some manner, but a specific group of three must repeat from that point because some discrete group of three must occupy some row. Lets say d,e,f are in the row immediately below 8,x,y in the same box. Those three numbers can not then be in the row above 6,a,b, they must be in the top row of that box. That leaves j,k,l in the bottom row of the 8,x,y box and likewise the middle row of the 6,a,b box. This further isolates d,e,f to the bottom row of the middle box and j,k,l to the top row of that box.

From this point, the rest of the puzzle may allow placement or isolation of d,e,f,j,k,l to at least a row in a specific box. If any of the * spaces contain numbers, that number can then be isolated to a row in the other two boxes. In this particular example, we know that either x or y must be 6, and either a or b is 8, just from the diagram.

Clear as mud, right?

[Kat]

Whew! Superhuman effort!

I was contemplating the best way to illustrate the method by scanning a puzzle and blocking it out. Over and over.
It will take time.

[Kat]

Edit here! Due to a few changes that occurred naturally once I looked everything over again while trying to illustrate the illustrations in explanation, please start over from the beginning- HERE:

Gaithers singing in the background while I'm making JPEGs.

Here's what I've done to illustrate the hints-
This first page is the one we'll work with:

[Kat]

Page 2

In this first example, we only work on the left hand section going up and down. Plz block out in your mind the other 2 sections to the right.

Now, see where the "1" is? Down at the bottom?
You start with the number '1'.
You're looking for other '1's in the next two columns to the right within the section. There aren't any. So you 'don't have enough information' to follow the '1's. You need at least a '1' in one column and a '1' in one other column to begin to decide where the third '1' will go.

Go now to the number '2'.

You have a '2' in the middle row and a '2' in the far right row.
You will need to look for a place for a '2' in the far left row- in the top box- because the middle box has a '2' and the bottom box has a '2'.

(Each box of nine squares will not yet be considered as ready to be filled for quite a while yet- so don't be distracted by the boxes of nine squares. Just be thinking of up-and-down rows and their relationships with each other.)

We have 2 possible places for a '2' so I put a penciled small '2' there to remind me later. See circles where a '2' could possibly go.

Next check for '3's. (I only used circles, triangles and squares to bring attention to the numbers we are looking at on each pass.)

I've put '3's in a square.

See each '3' in a square. See the empty square in the left lower box? That is where the '3' we need will go.

Look at '4's next. I put those in a triangle. Look for the 4's in triangles.

There is a '4' in the left column, in the lower box of nine, a '4' in the right column in the middle box of nine, and so we look for a '4' in the middle column, in the top box.
We can put a '4' there (see empty triangle, middle square, top line of three in the top box).

Next go to '5's, then '6's, then '7's, then '8's then '9's.

Note: There are no '5's in this section, so skip '5' as there 'is not enough information.'
There's only one '6' so 'not enough information.'
There is only one '7' so 'not enough information.'
There are two '8's so you can place an '8' but since I've blocked your view to the right, you can't see where the '8' fits in relationship to a row that already has an '8'.
Ditto for '9's. (We will see that later when I uncover the rest of the puzzle.)

But see where the '9' fits?
Since there is a '9' in the right column, and another '9' in the middle column, we look to place a '9' in the far left column. It has to be the middle box area because the lower box has it's '9' and the upper box has it's '9'.

[Kat]

The middle section, still looking up-and-down

But first, you can see why that '8' goes there in the first section we worked on- the middle box is where an '8' can go, in the middle column.

Second you can see why the '9' goes there (referring to the first section we worked on)- there is a '9' already on the lower line in the middle box going vertical- you can only have one each of the numbers 1 thru 9 in any line vertical or horizontal.

Now the middle section we start with '1' looking up-and-down. Concentrate only on the middle section.

A. There is only one '1' so there's 'not enough information.'
B. There is only one '2' so there is 'not enough information.'
C. There is a '3' in the right column in the upper box and a '3' in the middle column of the lower box. So we can possibly place a '3' in one of two empty squares in the far left column.

We look to the sides to see if there is already a '3' in that whole line vertically. There is one '3' in that middle row that will run vertically, so we, by default, find the only other empty place for a '3' is the top row in that left column.

We put a '3' there (see empty triangle).

[Now: plz note! If there was already a '3' in that row vertically either to the right or left, then we have made a mistake somewhere and it's best to start over as soon as you find a mistake. Otherwise you may get to the end with only one square box left to fill and find it's all wrong and that is very frustrating, but also very elegant. Numbers are very elegant, I think. I suggest pencil, unless your printer has lots of ink!]

Continue by checking for two '4's, two '5's, two '6's etc. Until you finish with '9's.
Then go to the next section to the very right up-and-down.

When you finish numbers '1' thru '9' in each of the three sections going up-and-down, we will then do the same thing, only going sideways.

[Kat]

Still going-up-and-down- last column on right, isolated

Plz note- this is for beginners. I did this method/system very carefully for over twelve puzzles before I got comfortable finding more ways to do this.

[Kat]

next illustration.

This is the results page after we did all three columns up-and-down.

[Kat]

Next we examine the puzzle in sideways 'columns' I will call 'rows', each section separately, as we did the up-and-down puzzle.



There is only one '1' so there is 'not enough information.'
There is no '2' so there is not 'not enough information.'
There are already three '3's in this section, one in each row.
There are two '4's so we will look for another.

There is a '4' in the middle row; there is a '4' in the bottom row; we will look to place a '4' in the top row.

We see there is already a '4' in the first column of the second box in the middle row;
We see there is already a '4' in the first column in the far right box, in the bottom row;
We can put a '4' in the middle spot in the top row (because there is not another '4' in that whole line yet)
(When we look 'up-and-down' in the first box, in the first column, there already is a '4' in that column;
When we look 'up-and-down' in the third column of that first box, there already is a '4' in that column.)

There is only one '5' so there is 'not enough information.'
There is only one '6' so there is 'not enough information.'
There is only one '7' so there is 'not enough information.'
There is only one '8' so there is 'not enough information.'

We see there are two '9's in this section.
There is one '9' in the middle row (on the far right) in the far right box.
There is one '9' in the bottom row, in the far left box, in the far right spot.
Since these are pre-printed '9's we can be sure a '9' will go in the top row somewhere, and we look to the middle box because the far left box has a '9', and the far right box has a '9'.
We can't place the '9' yet as there is 'not enough information.

I usually pencil in a small note in the 2 spots it might go- that keeps me organized for when I next go around looking at spots for a future '9'.

[Kat]

Next: The middle section going horizontally.
(Start with the '1's, '2's,)...
-We can place a '3'
-However, we see there are two '4's: one in the top row and one in the bottom row, so we will look to place our '4' in the middle row. It will not go in the first spot in the first column because when we look at the row above, that column already has a '4'.
-There are two places possible to put our '4' but 'not enough information' so I usually pencil them in small and look at them later when the puzzle is more filled out.
-(I left out a '5' in the previous vertical assessment so you can figure out where that went on your own when you make your first pass.)
-The '8's are easy tho. There is an '8' in the top row and an '8' in the bottom row, so we know to look in the middle row.
The middle square (of nine boxes) has an '8', and the far right square (of nine boxes) has an '8' so:
Since the puzzle has pre-printed numbers already occupying two spots in that middle row of the far left square (of nine boxes ), process of elimination shows the '8' goes between the '6' and the '3' in that middle row.
-Also, you want to gain the habit of always checking the rest of the surrounding numbers, above in a row, side-to-side in a row, and within the box itself to look for a duplicate number. If you see an '8', for instance in the row above or side-to-side in your column, you know there is a mistake somewhere. Catch these early.
-And remember this is fun! So checking all around for no duplicates is part of the process.

[Kat]

I will show next what results we will have after one pass all the way thru the puzzle starting first up-and-down, and then sideways, each section.
(Remember the procedure of first '1' then '2' then '3' etc, each approach.)

[Kat]

First pass over the puzzle= results

If you find any numbers that you think should be on here, and you have a question about it, plz ask.
(ie: If you can figure it out on your own that a number is missing and are confident, you don't need to comment, thanks.)

The way I was shown, I would follow this system over and over until the numbers were filled in (unless a square of nine numbers only needed one number to fill the whole square and it was obvious, or a row or whole column was only missing one number and it was obvious. It gave me discipline to keep to the method.)

I would next start at the left looking at '1's vertically, '2's, 3's etc, thru the up-and-down columns, each section separate.
Then proceed to the horizontal (side-ways) again, sections top, middle, and bottom. Then back to the vertical etc.

[Kat]

Plz see the beginning of the illustrations and follow again. Thanks!