Sudoku are fairly conceptually easy. Fundamentally, a sudoku puzzle consists of a 9x9 grid. Each grid must contain the numbers 1 thru 9. Furthermore, each horizontal line across the grid must contain the numbers 1 thru 9. In addition, each vertical line across the grid must contain the numbers 1 thru 9. Refer to the diagram below.
The trick to Sudoku is that the same number cannot appear in the same grid twice, along the same horizontal line twice, nor along the same vertical line twice. You need to figure out how to arrange the numbers so they stay within the bounds. Sudoku puzzles will give you some numbers to start you off, at which point you simply use your powers of deduction to figure out which number to put in each empty slot. The problem is, solving Sudoku takes a while to learn. Practice. Practice. Practice. I myself took nearly a year to achieve my "experienced" Sudoku level. Some Sudoku, however, require so much mental aptitude that I just get tired out and give up. Then again, that's what Sudoku is all about.
The point of this post is to provide tips to providing any Sudoku puzzle presented to you. This guide is based on my abilities and as such is limited to the scope of my deductive reasoning skills. Others may contribute their own tips below. Whether you're an experienced Sudoku solver or a beginner, you might learn something new from this thread.
First off, let's look at an example of a Sudoku puzzle:
That's a lot of blank space, but we need to start somewhere.
We're mostly Westerners, so like most Westerners, we read left-to-right, top-to-bottom. So the top left nanant would be a good place to start looking. We see four numbers already -- 6, 7, 8 and 9. We're missing five numbers, but as it is, we have no way of knowing where each of those missing numbers will go. So we need to look elsewhere.
Now, if you're like most beginners, you'll probably go into synaptic shock when looking at Sudoku puzzles. In total, you have 81 little squares to worry about. You need to clear your mind of that huge number. Think small. A Sudoku is ultimately a 3x3 grid, which means we can pretend there are only nine squares to worry about. Within each square is another 3x3 grid, which means only nine squares to worry about there. It's so much easier to think of everything in terms of the number nine, instead of something monstrous like 81. So how can we make use of this attribute with our current puzzle?
Don't think of the first grid as containing the numbers 6 thru 9. For now, think of it as being itself just one number. Pick one number from that large square and pretend that nanant is no longer a square. Pretend it is now that number. Let's start with 9. Imagine the top-left nanant is the number 9, simply because it has a 9 in it. Now, look around the Sudoku for any other nanant with a 9. Imagine each of those nanant as themselves being 9's. Reading left-to-right, we find that the top-middle nanant also contains a 9. If we keep looking right however, we find that there is no 9 in the top-right nanant. Our Sudoku won't be complete unless every nanant is 9. We need to try to make that top-right nanant a 9.
Your first step in solving a Sudoku is to pick a number. It is always best to start with 1 then count up. After you have counted up to 9 and found any 9's possible, start from 1 again and repeat this process until you fail to reveal any new numbers.
Wouldn't it be nice to make things even smaller? Instead of thinking in terms of nine nanants, how about just three things? Each nanant contains a 3x3 grid of squares. The term three-by-three means there are three rows and three columns. Now, in this step of our Sudoku-solving, we need to find a commonality between each nanant. What do they have in common that we can utilize in order to make each nanant the same value? Do our three nanants across the top share the same up-and-down columns? Of course not. What they do share are the same rows. What is the first rule about rows in Sudoku?
Each row must contain only one of each number.
So let's look at our two nanants a little more closely. Since we are only concerned with rows for now, simply break each nanant down into rows. Which rows contain a 9? In the top-left nanant, we have a 9 in the bottom row. In the top-middle quadrant, we have a 9 in the top row. That means the only row without a 9 in it is the middle row. Now let's look at the top-right nanant. Because there are already 9's in the top and bottom rows for these three nanants, we need to find blank squares along the middle row in the top-right nanant. Fortunately for us, there is only one. We can can therefore assume that blank square contains a 9.
Unfortunately, at this time we cannot find find anymore 9's. We have no choice but to move on to another number.
Look for the number you have chosen anywhere. Then look in the nanants to the left and right or top and bottom of each nanant that contains that number. If you find two nanants along the same row or column with the number, make note of which sub-rows and sub-columns do not have the number. If only one empty square could possibly be that number, it is for sure that number. Otherwise, make a note in all the blank squares that could potentially be that number.
Let's go back to the first square and pick another number. This time, we'll pick 6, which lies in the top row, middle column. If we look in the top-right nanant, we do indeed find another 6, which lies in the middle row, right column. Since we're looking left-to-right in this case, the columns won't help us. So again, consider the rows that have 6's. The top row is taken care of, as is the middle row. That means the bottom row in the top-middle nanant will have a 6 somewhere. Unfortunately, there are three possibilities. In this case, we need to look in each of the three sub-columns for any 6's. We find one 6 in the bottom-middle nanant in the right column. We can therefore rule out any 6 in that column. However, that still leaves us with two possibilities. What do we do now?
Before you give up and move on to another number, this is something else to look for. In this case, we know that any blank square in the right sub-column cannot be a 6. That applies to not only the top-middle nanant in this case, but the center nanant as well. Take a look at the center nanant. Imagine the right sub-column is full of X's. You can't put a 6 where there's an X. But wait a minute! If the right sub-column is full and the middle sub-column is full, that means only the left sub-column in that center nanat could have a 6. If we were to put a 6 in that left sub-column, then there's no way our left-column in the top-middle nanant could be a 6. That means the middle sub-column is the 6. We just solved another number!
If a nanant contains a number in a sub-row or sub-column, it prevents all nanants from having that number in that sub-row or sub-column. If you can rule out a sub-row or sub-column from two nanants, then the number will be in that sub-row or sub-column in the only other nanant.
Continuing along with these two basic strategies, we can fill in some more numbers. Our Sudoku is looking a little better, but we still have a long way to go.
Check it out! By simply ruling out sub-rows and sub-columns at a very basic leve, we've already filled in one complete nanant. Only eight more to go! With this many numbers now known, we can start looking at the sub-rows and sub-columns themselves. Since we know each sub-row and each sub-column will contain the entire sequence from 1 to 9, we can start ruling out false numbers. In some cases, this ties in with ruling out sub-rows or sub-columns, but that's not always the case.
Let's start with the top sub-row. The only numbers we're missing from it are 1 and 2. However, if we look down those two blank columns, we find a 2 in another nanant. That means the blank square in that column cannot be a 2. If it's not a 2, it must be a 1, since that's the only other number we're missing. If the left blank is a 1, the right blank must be a 2. That's two more squares out of the way! From this we can see that the middle-left nanant will have a 2 somewhere in the middle sub-column, but at the moment we have no way of knowing in which row. We'll be able to figure that out eventually.
When you're no longer able to rule out sub-rows and sub-columns, solve for each individual sub-row and sub-column. Figure out which numbers are missing, then try to narrow down which of the blanks those numbers will go in. For each blank you cannot fill in this way, make a note of what the possible numbers are.
Sometimes you will miss a number that, after finding it, will make you wonder, "How could I possibly have missed that?" Don't worry. This happens to a lot of Sudoku players. By alternating tactics, you refocus your attention. In this case, we overlooked the location of the 2 in the top-center nanant. However, when we looked at the second sub-row and noticed it needed a 2 somewhere in the top-middle nanant, we were forced to look down each sub-column. Immediately the location of the 2 became obvious. In essence, Sudoku helps you learn to think globally -- it helps you mature mentally.
Never forget, each nanant must contain 1 thru 9 and only one of each number; each sub-row must contain 1 thru 9 and only one of each number; each sub-column must contain 1 thru 9 and only one of each number.
We can't solve anything else in the second sub-row, but the third sub-row brings up an important phenomenon in Sudoku. Regularly you will come across a number that can only appear in a specific set of squares. In the third sub-row, we are missing 3, 4, 5 and 7. Since the top-right nanant is already filled in that sub-row, those four numbers will be somewhere in the top-left or top-middle nanants. Look closely at the top-left nanant. It contains two of those numbers that we need for the third sub-row. Therefore, those two numbers must be in iether of the blanks in the top-middle nanant's bottom sub-row. In other words, the top-left nanant contains 3 and 4, while the top-middle contains 5 and 7. Notice anything else? One of the blanks in the top-left nanant is in a column that already contains a 4. It must therefore be a 3, which means the other blank is 4! We just completed another nanant!
Before we look at the other sub-rows, let's look at the other nanants first. Notice currently we have two filled nanants, one half-empty nanant at the top, three fairly empty ones in the middle row, one fairly empty nanant in the bottom-middle and two nearly full nanants in the bottom-left and bottom-right. Let's look at the bottom-left nanant first for a sec. It is very nearly filled. We can see that it needs only two numbers. Well, we just do the same thing we did with solving for the sub-rows. The two numbers we are missing are 1 and 9. When we check the sub-columns, we find that there is already a 9 in the same sub-column as one of the blanks. Therefore, that blank must be 1 and the other 9. That's another nanant out of the way!
Look for missing sequences in all sub-rows, sub-columns and nanants every time you make any change to the grid. Everytime you reveal a number's location, a sequence somewhere is one number closer to being complete.
With so many numbers so close together in a single sub-row down there at the very bottom, it's so tempting to skip straight to it. By all means, solve that sub-row. All it's missing is a 1 and a 7. One of the blanks lies in the same sub-column as a 7, which means that blank is a 1 and the other is a 7. Look! There's only one blank left in that nanant. The only number we're missing from it is 9, so fill in that blank. That's another nanant down. We're really moving now!
We might as well look at the next sub-row at the bottom. It needs a 5, 8 and 9. What's the first thing we do? Look at the sub-columns. Notice anything? One of the columns already contains 5 and 8. If our blank can't be 5 and if it can't be 8, then there's only one possibility. So, fill in that blank.
The rest of the sub-rows in this Sudoku so far are too incomplete to be of any further use for the time being. This would be a good time to look at the various sub-columns and try to complete their sequences. The very far left sub-column needs an 8 and 9, but unfortunately, the middle row contains no 8's or 9's yet, so that path is a dead end. Sadly, there isn't much else that can be done.
Now the hard part -- we need to try to solve all those very empty sub-rows' sequences. How in the world can we do that? We do what some Sudoku players consider cheating. I call it "taking notes."
What we need to do first is find any two numbers that do not just have two possible blanks, but that share the exact same two blanks. For example, in the top-middle nanant's middle sub-row are two blanks. Those blanks are either 1 or 4. They cannot be anything else. When you find a number that has only two possibile locations in a nanant, make a note of it. Then look for another number that has only two possible locations. If you're lucky, you'll find one.
With this puzzle, we are lucky. Two of the middle nanants lack a 7. In both of those nanants, 7 can only be in the upper- or lower-middle squares. Look around for other numbers. There just so happens to be another number that doesn't just share two blanks with 7, but two blanks in the same sub-row. That is what we are looking for. In either quadrant, the top-middle blank square could be a 2 or 7. Since those two blanks are in the same sub-row, we need to check if there are any other possible locations for 2 and 7 in that sub-row. Luckily, there aren't. Therefore, those two blanks in the top-middles are either 2 or 7. They cannot be any other number. Make a note of that.
But in the end, at this point what it all comes down to is a lucky guess for most people.
Fortunately for you, Trickster's Sudoku puzzles don't require you to solve the entire puzzle.
I hope this guide helps you in some way or another. It helped me waste hours and hours and hours of my life once again.
Oh, and for those of you that want to solve this Sudoku, it's not a valid sudoku. I made it myself then tried to solve it. I made a wild guess. I got it wrong yet my solution was still a valid sudoku. You can mess with it if you want, though. I'll post the possible answers later. If you're really jonesin' for a Sudoku puzzle, you can try the one at the bottom of this post. If you read this thread though, you could probably solve it in a heartbeat.
