Solve Japanese. How to solve Japanese crosswords? Instructions

Japanese crosswords (scanwords) are encoded images. The player's task and the goal of the logic game is to solve this image.

The coding goes like this. Let's say we have an image:

For each line, we count the lengths of the filled segments and write these numbers next to the corresponding strips:

Now we repeat the same operation for the columns of the scanword and write down the corresponding sets of numbers above the columns:

Now remove the image and leave only the numbers. This is a ready-made Japanese crossword puzzle:

The player's task is to restore the picture with only numbers.

General logic and tactics for solving Japanese crosswords

The logic is very simple. It is necessary to find horizontal lines or vertical columns where you can make any conclusion about which cells are filled and which are not filled. You display these inferences with notes. As you receive more and more leads, you move further and further until the scanword is fully solved.

Let's now look at some of the techniques

How to start solving a Japanese crossword puzzle

At first, the scanword is empty. So far, you only know the numbers. Let's see what you can do in this situation.

The simplest techniques: solving at a glance

As you saw, there are times when you can tell unambiguously how a row is filled. For instance:

can be filled in only one way - all cells are filled.

A slightly less obvious case:

turns out to be just as simple and unambiguous:

But such situations are not common.

Partial crossword puzzle solving at a glance

Often times, a row or column cannot be fully deciphered right away, but we can still draw some conclusions about how it is filled.

Let's consider an example:

There are three options for filling:

As you can see, in all these variants the third cell is filled in. From this we can conclude: "We do not know exactly how this row is filled, but the third cell in it is exactly filled":

A similar approach works for more complex logical problems. Example:

The following options are possible here:

and we can draw a conclusion about the four filled cells of the scanword:

We didn’t fully solve the series, but we received a lot of information. Let's now see how to use it and continue solving.

How to continue to solve the crossword puzzle using incomplete information.

So. Do you already know something, how to clarify these conclusions and get closer to a complete solution?

Let's introduce one more notation. We will denote by the symbol "✕" those positions about which we know for sure that they are not painted over.

Such information is also very valuable in guessing.

You know that something is painted over

If you already know that some cell in a row / column is painted over, then you can often conclude that some cells are definitely not painted over.

The simplest case is when there is only one strip in a row. Let's say you have a situation like this:

We already know that one cell must be painted over. And we are left with only three options:

That is, we can say with confidence that the two outermost cells on each side are definitely not painted over:

If there is more than one colored strip in a row / column, then the situation becomes more complicated, but even here it is possible to draw a conclusion.

Consider this example:

At first glance, the colored cell can be part of either of the two stripes, and we cannot say anything definite. But if you look closely, it becomes clear that the strip of two cells cannot be to the right of the filled cell. After all, then they will stick together and there will no longer be two cells in the strip. So the rightmost cell is definitely empty:

And applying the knowledge from the previous presentation, we can draw a conclusion about two more cells:

And this is already very good.

You know that something is not painted over

At the previous step, cells began to appear, about which we know for sure that they are not painted over. This information is very useful and very easy to use.

Very often you can infer that there are other empty cells. Let's consider an example:

Here all the stripes are 2 in length, which means that none of them can fit to the right of the unpainted cell. This means that the rightmost cell is not painted over.

And of course, we can draw a conclusion about two more cells, using the techniques described above (having considered all the options for the location of the colored stripes, and highlighting the cells that turn out to be painted over in any case):

We found out the color of the three squares of the scanword.

Let's consider one more logical trick.

Unfilled cells break the line / column into segments, and quite often it is possible to determine which segments are in which strips. Look at an example:

For convenience, I have marked the segments with letters of the Latin alphabet.

It is clear that segment A is empty, since a segment of four filled cells cannot fit in it. First conclusion:

Two bicellular segments cannot fit in segment D (otherwise they will "stick together"). This means that each of our three segments occupies one of the three remaining segments. We can draw the following conclusions about the first two segments:

In total, we have not made bad progress.

By combining these logical techniques, you can solve any Japanese crossword puzzle. Rather, any crossword puzzle on this site as there are unsolvable ambiguous Japanese crosswords. But all the scanwords on this site have been tested and are not only solvable, but also allow for a step-by-step solution.

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Japanese crosswords. Solution Algorithm

Now there are so many different puzzles that allow you to have fun and with interest. Among them, Japanese puzzles stand out: kakuro, sudoku and, of course, Japanese crosswords. Even as a child, I liked to solve Sudoku and I always looked at Japanese crosswords located in the same magazines with bewilderment. They were very complicated and incomprehensible to me, although I tried to understand them. Since I couldn't figure it out, I left them. And he returned to them after 10 years, when he was already at the university. There was a lot of free time during the summer holidays and I decided to try to deal with them again and this time it worked out. Since that time, they have been probably the most beloved puzzles.

Among the masters of our university there are several people who have covered this topic in their individual section [,]. Moreover, Nina Avci did it very well, telling about the general description of crosswords, the history of their origin, the general methodology and principles of solution. She also covered the features of black and white and color crosswords. However, the solution algorithm itself and the methods were not described in detail, so in this section I want to describe them formally, in a form in which they can be used to write a program for solving Japanese crosswords as a person.

Designing a programming model

In order to describe in detail the algorithm for solving Japanese crosswords, you first need to briefly describe the program model and the procedure for its operation. The Japanese crossword puzzle consists of a main field on which cells are located, which can have 3 states: filled, empty and undefined. This field is divided into rows and columns, next to which there are numbers indicating the number of cells that should be filled. Based on this, a class diagram was developed, presented in Figure 1.

Figure 1 - Class diagram

The algorithm for solving the Japanese crossword puzzle will not be applied to the entire crossword puzzle at once, but alternately for rows and columns, because in fact there are no significant differences between them. Consequently, the solution algorithm is reduced to the analysis of one line of cells and the corresponding numbers that determine the shading.

In the Nonogram class, there is a queue of line numbers for analysis. After each line analysis performed, the method returns the numbers of the modified cells so that they could be added to the queue for analysis, since when the cells were modified, some changes might appear that would advance the solution.

It should be noted that the developed program does not implement all methods of solving as a person. Only methods are implemented that work with extreme groups and empty gaps. The rest of the methods are detailed in.

The source code of the program can be obtained at.

Edge crossing method

Each numeric group in a line is analyzed and the right-most and left-most boundaries of the numeric group are found. If the difference between the right and left borders is greater than or equal to zero, then you can fill in the cells between them (inclusive). It is worth noting that, as can be seen from the figure, in the final line, the groups that intersect only with themselves are painted over, so cell 6 is not painted over, since in different positions (left and right) it belongs to different numerical groups.

Figure 2 - An example of line analysis using extreme border crossings

Method of pushing away from walls

Extreme non-empty intervals are analyzed. If there are shaded cells at a distance of a numerical group from the edge, then you can paint cells, starting with the filled one and up to the cell equal to the value of the numeric group.

If the number of filled cells is equal to the value of the number group, then the number group can be crossed out, and after the group, cross out the cell (the minimum space between the groups of cells).

Figure 3 - An example of line analysis using wall repulsion

Method Unreachable

Extreme numeric groups are analyzed. If the distance from the beginning of an undefined line fragment to the first filled cell is less than or equal to the extreme numerical group, then it is necessary cross out the cells that the number group does not reach.

It is also necessary to consider the case if there is one uncrossed group in the line. In this case, it is necessary to cross out all the cells that are further from the filled cells by the length of the number group.

As we already mentioned, all Japanese crosswords on our site have a single solution. Most have 100% solvability using the algorithms discussed below.

When solving some, you will have to act by the selection method. For such crosswords, the percentage of solvability is below 100%. Examples of solving such crosswords will also be considered.

Where to begin?

Obvious cases

First of all, we are looking for empty or completely filled rows and columns with one number equal to 0 or the width (height) of the crossword puzzle:

What's next?

Partial filling

In most cases, you will not be able to unambiguously paint a row or column. But some conclusions about the filled cells can usually be drawn. Here are some examples.

1 ... No matter how the group of 10 cells is located in a row 15 cells long, 5 cells in a row will necessarily be black - this can be seen from the figure.

The counting method also helps in this case: 15 (line length) - 10 (group length) \u003d 5 (indent from the edge of the line on each side).

2 ... We are looking for unambiguously filled cells for two groups of cells ...

3 ... And for three groups ...

Something is painted over

So, in the previous cases, we identified uniquely filled cells in the rows (columns) of the Japanese crossword puzzle. Quite often, from this one can draw conclusions about unambiguously unstained cells.

We have a group of 10 cells, two filled.

Obviously, we can extend the group to the right by a maximum of 8 cells:

This means that the three cells on the right must be white:

Something is not painted over

The information about unpainted cells can be used quite easily. Let's try to demonstrate this.

The white cell divides the row (column) of the crossword puzzle into two parts, allowing you to search for an “independent” solution for each of the parts.

In this case, to the left of the white cell is a group of two black cells, to the right - of ten. We find unambiguously filled cells:

Have you noticed that recently many around you have begun to solve not ordinary, but Japanese crosswords? And there is an explanation for this. Regular crosswords and their light version - scanwords have not made you strain your intellect for a long time. From newspaper to newspaper the same wordings like "parrot of 3 letters" or "clothes for the walls" wander. Boring ...

And what are the “Japanese” good at? Oh, this is a completely different level, each task is unique, and as a result, you get moral satisfaction not from remembering all the words you know, but from seeing a picture you yourself have drawn, and the more difficult the crossword puzzle, the more detailed will be drawn all its details.

The rules for solving such crosswords are not complicated. Let's learn? So…

A Japanese crossword puzzle is a picture encrypted using numbers. The numbers opposite each row (column) indicate the number of filled cells in this row (column). If more than one number is written in a row, it means that this row (column) contains several groups of filled cells, between which there is at least one unpainted cell. The order of the numbers is the same as the order of the colored groups. Your goal is to determine the place of all groups of numbers on the field and get a drawing as a result. The crossword puzzle can only have one solution, therefore, if something does not fit, we go back a step and carefully check all our steps. That's all the rules.

Everything seems to be simple. But in practice, many questions arise. In magazines and newspapers that publish Japanese crosswords, very primitive pictures are given as examples. And it often happens that you cannot solve any of the proposed options on your own. Therefore, I propose to start learning with an example of a more complex picture, for example, 15 × 15 cells.

1. Start by looking for the largest digit, or group of numbers. This is line number 14.
We count 14 cells from left to right and put a point. We repeat the countdown from right to left and also put a point. We connect them and paint over the whole group. We got 13 filled cells. Where the 14th cell will be located - to the right or to the left - we do not yet know.

2. We repeat the countdown for the line with the number 9, also from left to right and vice versa. We paint over 3 cells:

3. Now let's look at the lowest line with numbers 8 and 4. This entry means that this line contains a group of 8 cells, then a gap of at least one cell, and a group of 4 cells. Let's try to calculate them.

From left to right we count 8 cells, put a full stop, skip one cell and continue counting 4 cells. We put a point. Now from right to left: we count 4 cells (point), skip one and count 8 cells (point). We connect in pairs the points related to the eight and four, and we get groups of 6 and 2 cells. We paint over them. In which direction each of the groups will continue, is still unknown.
Please note that when we count several groups in a row or column, we always skip 1 intermediate cell, although after completing the solution you will see that there are sometimes more of them. But we will always use such a counting mechanism if we want everything to work out. Let's go further.

4. The same counting algorithm is applied to the line "4 - 7". You should end up with groups of one and four cells - these are pieces from 4 and 7, respectively.

5. Now let's see the big picture:

Pay attention to the columns. Many of them end with the number 1. This means that the lowest group of cells in these columns is equal to one. Therefore, in the line "8 - 4" you can safely mark those "units" that have automatically emerged in our country, and "twos" that you can safely draw. At the same time, we remember that between the groups of numbers there must be at least 1 open cell and agree that we will mark such cells with crosses. Such cells will not be painted over under any conditions.

6. Next, let's do it yourself:
- column "2-1-6-2" - after the bottom "two" comes the "six". We count 6 cells and paint over it completely. It all came together by itself. Do not forget to put a cross at the end of the group;
- column "1-3-5-2" - we do the same with "five";
- line "9" - we have two filled cells closer to the right edge. From there we count 9 cells, put a dot and connect it with a group of 2 cells. Let's paint over and see that we have 7 of 9 filled cells. Since we have only one group in this line, we leave 2 cells free from its supposed left edge, and mark the rest with crosses. There won't be anything anyway;
- we check the vertical and notice the appeared "triplets" (columns "1-1-3-1", "1-3-1-3-1" and "2-1-2-3-1"), paint over them and do not we forget to separate them with crosses;
- in the line "1-6" we count the "six": from right to left we count six cells (point) and from the cross from left to right also 6 cells and put a dot. To the connections, paint over 5 of 6 cells. We do not pay attention to the "unit" in this line yet;
- we also recalculate the line "7-1", as a result we paint over 6 of 7 cells;
- do the same with lines "1-5" and "7";
- then check the verticals and complete the groups that begin immediately after the crosses. After each move, check how the picture changes, paint the positions that appear, and you should get the following intermediate picture:

Think logically in the process of solving. If in the line "1-6" there is only one position for one, then it is also part of the "two" from the first column. Therefore, leave room for the completion of the "two", and mark the rest of the column with crosses. Now you can finish line "14" and once again count the rows and columns, marking those positions with crosses where, well, the colored cells cannot be. Draw the line "4-1-1", count the columns "1-3-5-2" and "1-3-1-3-1", and then argue logically and be careful, all the cells will appear with each next step ... As a result, we have a drawing of a mouse in a boot.

I congratulate you on your first success!
I hope you enjoyed it and join our ranks of Japanese crossword lovers!

Each of us chooses an occupation to our liking. Someone likes to cross stitch. Someone - to make crafts from a variety of materials. Another hobby option is crosswords.

Now there are many periodicals completely devoted to crosswords. Almost every newspaper has a page for those who like to test their erudition. One of the most popular types of crosswords in recent years is the Japanese crossword puzzle.

The technique of how to solve Japanese crosswords is quite complex. But if you figure it out once, you can always keep yourself occupied and train your brains.

What is the difference between the Japanese crossword puzzle and the usual

In ordinary crosswords, we guess the words, and in Japanese, we need to decipher a hidden drawing. The scheme of the Japanese crossword puzzle looks like this:

The numbers indicate how many cells in a row should be crossed out. For example, there should be nine of them on the first line. The first column contains eight.

What you need to know

The entire field of a Japanese crossword puzzle is usually divided into squares of five cells. That is, you do not need to count one cell at a time, you can count it as fives. Thus, we can calculate that our drawing is 14 by 15 cells.
The order of the numbers does not change. In what order they stand, in this order they will be crossed out in a row or column.
There must be at least one space between the filled numbers. There may be more, but there should be a gap of one cell. For convenience, they can be crossed out with crosses or marked with dots.
It is better to draw crosses with a pencil, because then there will be an opportunity to erase them and see a beautiful picture.

Instructions for solving the Japanese crossword puzzle

We proceed, in fact, to the very technique of how to solve Japanese crosswords. Find the largest numbers first. In our case, it is 9 on the first line. Now you need to determine where to cross out these 9 cells in the first line? We need to find out which cells will be crossed out 100%. To do this, we count 9 cells from the left like this:

And now there are nine cells on the right:

Those cells that are at the intersection will be crossed out:

Now we look at the columns in which the crossed out cells fall. These are the sixth, seventh, eighth and ninth columns. Each of them has a number one - that is, one cell. One cell has already been crossed out, which means that there must be a gap under it. We mark them with crosses, and cross out the number so as not to get confused later:

We do the same with the next descending numbers. We have it 9 in the last column, 8 in the first and 7 in the last row:

Please note that the last line consists of 14 cells, and therefore seven on the left and seven on the right give exactly half, which means there will be no intersection.

Now is it clear how to solve Japanese crosswords? Moving on. Now let's look horizontally, what the filled cells give us. In the seventh line, we have one cell painted over to the right. So, we cross out the rightmost unit and put a cross in front of the cell - we mark the gap:

Eighth line. Two units - two filled cells. Mark the gaps and cross them out. Congratulations, the eighth line has been solved! This means that we can cross out all the space between them.

Let's see what it gives us. In the seventh and ninth columns, we see the number five. Five cells should be filled after the one we have already crossed out. We look at the distance between the crosses in these columns ... Exactly five cells! The question arises why they cannot be in the lower part of the field, after the crosses. Let's go back to the rules once again: the numbers are listed in order. That is, if from the very top we painted over one cell, then there must be five, and only then 4 cells one by one. So, feel free to paint over these cells:

Checking the lines horizontally. Alas, in the third and fourth lines this does not give us anything - it is impossible to determine whether this is one cell or, perhaps, two. But we can definitely put a cross between them, since there cannot be three in a row in a line:

But in the fifth line, we can put as many as three crosses and cross out two ones. In this case, it doesn't matter which ones, since the entire line consists of units, and the picture will not go astray:

Checking the sixth line gives us only a cross between the black stripes, the seventh line doesn't give us anything yet. We skip the eighth, since it has already been solved, and in the ninth we put a cross in the penultimate cell and cross out one.

Further, alas, while we can not cross out anything horizontally. Let's go back vertically. Checking the first six columns gives us nothing. At first glance, the seventh too, but if you look closely ... We have 4 units left. And there are six empty cells in the column. That is, just enough space to accommodate the four filled cells and the gaps between them. The situation is the same with the ninth column:

The art of how to solve Japanese crossword puzzles is to constantly check yourself. Now let's go back to the horizontal again and see what the crossed out cells in the bottom field give us. In the ninth line we get a cross. Nothing in the tenth yet. In the eleventh there is also no reliable information, as in the twelfth. But in the thirteenth, we can sketch a cell between the two already sketched, because we have the number 5. It cannot be somewhere on the side, because there are units on the sides. And even if we put units on the sides, the gap recedes - and five cells will not fit.

We look further on the last two lines. In the very last one, where 7 cells should be drawn, we can cross out something. Since the cells in the seventh and ninth columns are crossed out in the middle, the cell between them will also be painted over. Three out of seven. We retreat hypothetically possible four left and right, and mark everything else with crosses:

And then we act in the same spirit. Again and again checking horizontally and vertically, calculating all the options, cross out new cells. When you have almost one unit left, you need to look at the drawing itself, as a rule, the picture looms and you can understand what the author wanted to say and where you need to sketch the cell. Here's what you should end up with: