Help yourself to solve a difficult face by solving a neighboring face.
The 3 digits in the middle of each face are the same for the adjacent face of the cube.
Every Sudoku is tested and has a single solution.
4 difficulty levels that are suitable for both beginners and professionals.
Additional functions of the game are enabled by long pressing without the need to open the menu.
Sudoku is a popular puzzle game based on the logical arrangement of numbers. Sudoku is a logic game that does not require calculations or special mathematical skills. All you need is your brain, mindfulness and the ability to focus.
The first prototype of Sudoku was invented by a mathematician from Switzerland, Leonard Euler. He called the game "Latin square".
In the 70s of the last century, new puzzles were developed based on it in the United States of America. From there they got to Japan, where they quickly became popular. After that, the magic squares spread all over the world.
Later, an electronic version of the game appeared with many useful features and a 3D mode.
Consider the seventh square. There are only four free cells, so something can be filled quickly. "8" on D3 blocks the filling of H3 and J3; similarly, "8" on G5 closes G1 and G2. With a clear conscience, we put "8" on H1
After viewing the squares for obvious solutions, we move on to the columns and rows. Consider the "4" on the field. It is clear that it will be somewhere in line A. We have a "4" on G3 that closes A3, there is a "4" on F7 that removes A7. And another "4" in the second square prohibits its repetition on A4 and A6. The "last hero" for our "4" is A2
Sometimes there are several reasons for a particular location. The "4" in J8 would be a great example. The blue arrows indicate that this is the last possible number in the square. The red and blue arrows give us the last number in column 8. The green arrows give us the last possible number in row J. As you can see, we have no choice but to put this "4" in place.
It is easier to fill in the numbers using the methods described above. However, checking the number as the last possible value also gives results. The method should be used when it seems that all the numbers are there, but something is missing. The "5" in B1 is placed based on the fact that all the numbers from "1" to "9", except "5", are in the row, column and square (marked in green). In the jargon, this is a "naked loner". If you fill in the field with possible values (candidates), then this number will be the only possible one in the cell. Developing this technique, you can search for "Hidden Singles" — numbers unique to a particular row, column or square.
A "naked pair" is a set of two candidates located in two cells belonging to one common block: a row, a column, a square. It is clear that the correct solutions to the puzzle will be only in these cells and only with these values, while all other candidates from the general block can be removed. In this example, there are several "naked couples". Cells A2 and A3 are highlighted in red in row A, both containing "1" and "6". I don't know exactly how they are located here yet, but I can safely remove all the other "1" and "6" from line A (marked in yellow). Also A2 and A3 belong to a common square, so we remove "1" from C1.
"Naked threes" is a complicated version of "naked couples".
Any group of three cells in one block containing three candidates in total is a "bare three". When such a group is found, these three candidates can be removed from other cells of the block.
Combinations of candidates for the "naked three" can be as follows:
[abc] [abc] [abc] // three numbers in three cells.
[abc] [abc] [ab] // any combinations.
[abc] [ab] [ab] // any combinations.
[ab] [ac] [bc]
In this example, everything is pretty obvious. In the fifth square, cells E4, E5, E6 contain [5,8,9], [5,8], [5,9] accordingly. It turns out that in general these three cells have [5,8,9], and only these numbers can be there. This allows us to remove them from the other candidates of the block. This trick gives us the "3" solution for cell E7.
The "naked four" is a very rare phenomenon, especially in full form, and still gives results when detected. The logic of the solution is the same as that of the "naked triples".
In this example, in the first square, cells A1, B1, B2 and C1 generally contain [1,5,6,8], so these numbers will occupy only these cells and no others. We remove the candidates highlighted in yellow.
A great way to uncover the field is to search for hidden pairs. This method allows you to remove unnecessary candidates from the cell and give development to more interesting strategies.
In this puzzle we see that 6 and 7 are in the first and second squares. In addition, 6 and 7 are in column 7. Combining these conditions, we can say that cells A8 and A9 will have only these values and we remove all other candidates.
A more interesting and complex example of hidden pairs. The pair [2,4] in D3 and E3 is highlighted in blue, removing 3, 5, 6, 7 of these cells. Two hidden pairs consisting of [3,7] are highlighted in red. On the one hand, they are unique for two cells in column 7, on the other hand, for row E. The candidates highlighted in yellow are removed.
We can develop hidden pairs to hidden triples or even hidden fours. The hidden triple consists of three pairs of numbers located in one block. Such as [a,b,c], [a,b,c] and [a,b,c]. However, as in the case of "bare threes", there need not be three numbers in each of the three cells. Only three numbers in three cells will work. For example [ab], [ac], [bc]. Hidden triples will be masked by other candidates in the cells, so first you need to make sure that the triple is applicable to a specific block.
In this complex example, there are two hidden triples. The first one marked in red is in column A. Cell A4 contains [2,5,6], A7 — [2,6] and cell A9 -[2,5]. These three cells are the only ones where there can be 2, 5 or 6, so they will be the only ones there. Therefore, we remove unnecessary candidates.
The second one is in column 9. [4,7,8] are unique for cells B9, C9 and F9. Using the same logic, we remove the candidates.
A perfect example of hidden fours. [1,4,6,9] in the fifth square can only be in four cells D4, D6, F4, F6. Following our logic, we remove all other candidates (marked yellow).
As an example, I will show this puzzle. In the third square, "3" is only in B7 and B9. Following statement #1, we remove candidates from B1, B2, B3. Similarly, "2" from the eighth square removes a possible value from G2.
A special puzzle. It is very difficult to solve, but if you look closely, you can notice several pointing pairs. It is clear that it is not always necessary to find all of them in order to advance in the solution, however, each such finding makes our task easier.
This strategy involves careful analysis and comparison of rows and columns with the contents of squares (Rules No. 3, No. 4).
Consider the string A. "2" is only possible in A4 and A5. Following rule No. 3, we remove "2" of them B5, C4, C5.
Let's continue to solve the puzzle. We have a single arrangement of "4" within one square in the 8th column. According to rule No. 4, we remove unnecessary candidates and, in addition, we get a solution "2" for C7.
