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Sudoku, as the name suggests – each number can only appear once. Sudoku is a number puzzle that originated in Switzerland at the end of the 18th century, developed in the United States, and developed in Japan. The Sudoku board is a nine-house board, and each house is divided into nine sub-squares.

In these 81 grids, certain known numbers and solution conditions are given, and the numbers from 1 to 9 are filled in the other spaces using logic and reasoning. Make each number from 1 to 9 appear only once in each row, column, and house. This kind of game comprehensively tests the observation and reasoning skills of the problem-solver, although the gameplay is simple, but the arrangement of numbers is ever-changing, so many educators think that Sudoku is an excellent way to train the mind.

Sudoku solutions are all derived from rules, and the basic solutions are divided into two types of ideas, one is the elimination method and the other is the unique method. More complex solutions will eventually fall into these two categories. The following is a brief introduction to several solutions with an illustration, as long as you take a few minutes to look at it, you can start doing Sudoku immediately.

The main Sudoku intuitive solution techniques are: unique solution, basic elimination, block elimination, remainder solution, rectangular elimination, unit elimination, remainder test, etc.

Resources.

Enter the Sudoku problem, click to solve the problem, and it's OK.

Sudoku Calculator is a special Sudoku tool, which tries to provide a user-friendly Sudoku solution method, completely simulates the thinking process of the human brain, and can explain the reasons for each step step by step.

We hope that the Sudoku calculator will become a good tool for solving Sudoku using logical methods, and you can master better Sudoku solving skills from the operation process of Sudoku Assistant, as a tool for teaching Sudoku skills.

The Sudoku calculator can perform a step-by-step calculation, a specified number of steps, a one-time calculation, and gives a detailed explanation for each step of the calculation. For Sudoku problems with multiple solutions, prompts are given and manual intervention is possible. A list of steps is generated for each step calculation, and you can go back to any step to study.

Sudoku can entertain itself, and the next whole calculator is required?

The formula of Sudoku is the rule of 45, and it is not difficult to understand that each row and column in Sudoku and each 3x3 must have 1 9 without repeating each other, which means that the sum of the numbers in each row and row house is 45, 1 2 + 3 + 4 + 5 + 6 + 7 + 8 9 45.

Due to each column, row, nine-square grid.

You can only fill in 1-9, so the sum must be 45. Using this rule, you can help solve many problems. For example, the first number is a number and the second number is a cell number.

Benefits of Sudoku.

1. Cultivate mathematical thinking.

Improve number sense, lay a good foundation for future mathematics results, cultivate mathematical thinking, cultivate number sense, learning mathematics is important to discover arithmetic, find out the rules. Sudoku adopts very simple rules, which can help children begin to understand what the rules of mathematics are, and cultivate mathematical thinking and number sense from an early age.

2. Sudoku is a great logic game to improve logical reasoning.

ability, do things more logical thinking ability.

That is, the ability to observe, compare, analyze, generalize, and reason about things. People with strong logical thinking do things in a more orderly mannerMathematics is not only arithmetic, but also the core of logical reasoning.

3. Improve children's concentration.

Observation & reflexivity, so that children have the ability to go further and improve concentration, in life, many children have procrastination in writing homework and losing things.

Fourth, problems such as lack of concentration in class, in fact, these are all manifestations of lack of concentration. Carefully observe the top students and work efficiency around us.

Particularly high.

Sudoku is used to calculate the "rule of 45":

Sum of numbers per row = 45

The sum of the numbers in each column = 45

The sum of the numbers for each house = 45

Moreover, Sudoku calculations are generally only used in killer sudoku, and other forms of problems are not used.

The horizontal row is A-I from top to bottom, and the vertical row is 1-9 from left to right.

Crack the formula -1: use the same row of numbers and the same nine-square grid number cannot be repeated. In particular, if there are two identical numbers within the three nine-square squares of a horizontal line or straight line, there is a chance to find a position for the third one. Here are some examples:

Crack Formula -2: Note that if there is a vertical or horizontal row in any nine-square grid, when all are blank, the numbers associated with the same row of other nine-square grids should appear in other positions in the nine-square grid. Here are some examples:

Note that the F horizontal row, since F1-F3 are spaces, the 4, 6, 8, and numbers in the same row should be in other positions in the nine-square grid of F1-F3, that is, D1, D2, E3. Since i2=6, b2=4, e9=4, d2=8, e3=6, d1=4.

Crack Equation -4: Now you need to exclude the possible numbers in the space in the nine-square grid from the numbers in the same row. Remember to make assumptions from fewer squares and then exclude impossible numbers from the comparison. (Remember to compare the horizontal, straight, and nine-square grids with each other).

Generally, on high difficulty, you will need to use 5 spaces, that is, only 4 numbers appear. Here are some examples:

The remaining spaces in the horizontal row of h are 1, 4, 5, 7, and the 5th vertical row has 4, 5, 7, so h5=1

Sudoku is also called the nine-square grid, that is, the nine numbers of 1 9 are put into each row and each column, and the same palace grid is 1+2+3+4+5+6+7+8+9, and the same row and column can not appear in the same square grid. Sudoku does not have a fixed formula, it is necessary to reason horizontally and vertically according to the number it gives, and introduce other numbers. It can reflect a person's logical thinking ability.

The formula for calculating Sudoku is that the sum of each horizontal, vertical, and diagonal row is equal to 15.

Sudoku does not have a fixed formula for calculation, but rather a game of logical reasoning. To play Sudoku, you need to deduce the value of an unknown number according to the rules based on the existing numbers. The rules are:

The row, column, and nine-square grid where each number is located must contain numbers from 1 to 9, and there can be no duplicate numbers in the same row, column, or nine-square grid. Therefore, playing Sudoku requires logical reasoning, elimination, and other ways of thinking to solve Sudoku puzzles step by step.

The rule of 45 is a technique often used in killer Sudoku, and it is not difficult to understand that each row and column in Sudoku and each 3x3 must have 1 9 not repeat each other, which means that the sum of the numbers in each row and row of the palace is 45 (1+2......+9=45)。Rule of 45: Since each column, row, and nine-square grid can only be filled in 1-9, the sum must be 45 (1+2+3+..)9)。

Rule of 45: Since each column, row, and nine-square grid can only be filled in 1-9, the sum must be 45 (1+2+3+..)9)。

Using this rule, you can help solve many problems. For example, the first number is a number and the second number is a cell number.

Sudoku does not have a specific calculation formula, there is a logical formula, through which the number of spaces is judged.

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As can be seen from Figure 6, glyphosate ripening treatment had a relatively small effect on the formation of rapeseed yield compared with paraquat. Glyphosate was an endogenous herbicide with a slower effect, while paraquat was a contact herbicide with a faster effect, which quickly reduced the water content of rapeseed straw by dehydration and drying, disrupted the normal process of photosynthesis, and promoted rapeseed maturation. 3 Discussion Glyphosate and paraquat are two different types of ripening drugs used for chemical ripening of oilseed rape, and their mechanisms of action and modes of action are different.

Glyphosate competitively inhibits the activity of 5-enolacetone shikimic acid-3-phosphate synthetase in the shikimic acid pathway, resulting in the obstruction of the synthesis of aromatic amino acids in plants, resulting in the lack of corresponding proteins to promote the death of sobs and plants, and the drug response is slow, and it generally takes effect after 7 10 days of administration [5]. The mechanism of action can explain the slow ripening effect of glyphosate in this study, which has little damage to the growth and development of rapeseed, and the changes of 1000-grain weight and oil content of rapeseed after ripening are not obvious compared with the control. Paraquat relies primarily on its divalent cation to be reduced to a monovalent cation (PQ+) by light and systems, which rapidly reduces oxygen to peroxide, which produces a hydroxyl group through a Haberweiss reaction, leading to plant cell death [6]. Its drug response is very fast, and obvious symptoms of drug damage can be seen after a few hours of spraying.

In this study, paraquat treatment had a significant adverse effect on the 1000-grain weight and oil content of rapeseed, mainly because paraquat rapidly caused a sharp decrease in chlorophyll and carotenoids in the peel of rapeseed horn, followed by a rapid decrease in photosynthesis rate and a large inhibition of dry matter accumulation, resulting in a significant decrease in 1000-grain weight, oil content and yield. Based on the effects of the two drugs on the growth and development of rapeseed, the author believes that the ripening effect of glyphosate is slow, but the damage to the later development of rapeseed is small, and the spraying is better about 12 days before the harvest of rapeseed. Paraquat has a rapid effect on the later development of oilseed rape, which is suitable for spraying 5 days before harvesting, but if it is rainy after spraying, it may make it difficult to harvest oilseed rape after ripening, and there is a certain production risk. In addition, the two ripening drugs are chemical herbicides, and the impact of residues in the seeds and soil after ripening on food and the next crop must be considered in practical application to ensure the safety of food and ecological environment.

1. There are two ways to play Sudoku, that is, the intuitive method and the intuitive method candidate number method

1. Intuitive method: without making any marks, directly observing clues from Sudoku's disk potential, and deducing the answer.

2. Candidate number method: delete the numbers that have appeared in the allele group box, and fill in the blanks with the remaining fillable numbers as a reference for solving clues, and the fillable numbers are called candidates, or candidate numbers.

3. The intuitive method and the candidate number method are only the difference between whether there is a note when filling in, according to personal habits, and is not the standard for identifying the difficulty of the question or the difficulty of the technique.

2. Sudoku is basically composed of three consecutive houses.

Columns, which are divided into large rows and large columns.

First Row: Consists of the first, second, and third houses.

Second major line: by the fourth house.

The fifth and sixth houses are composed.

Third major line: consists of the seventh, eighth, and ninth houses.

The first column: consists of the first, fourth, and seventh houses.

Second column: consists of the second, fifth, and eighth houses.

Third column: consists of the third, sixth, and ninth houses.

3. Basic solution of Sudoku:

1. Elimination method: use numbers to find the only fillable blank in the unit, which is called the elimination method, and the only space that can be filled in by numbers is called hidden single

1) The number can be filled in the only blank in the palace unit is called hidden single in box, also known as the palace exclusion method.

2) Numbers can be filled in unique blanks in the row unit called hidden single in row, also known as row elimination.

3) Numbers can be filled in with unique blanks in the column unit called the column elimination method (hidden single in column), also known as the column exclusion method of the year.

2. Unique remainder method: Use the grid to find the only fillable number, which is called the remainder method, and the only fillable number in the grid is called the only remainder solution.

Second, the law is that only one solution is needed to produce the number through the basic solution, the elimination method or the only residual method, beyond this range and the advanced solution needs to be applied, the solution point needs the advanced solution to assist the basic solution to meet the implicit uniqueness or explicit uniqueness to produce the number, and the solution of the solution point needs to be completed by multiple steps, so it is called the combined solution.

3. In addition, in 2006 Gary McGuire wrote a program in an attempt to pass the law of violence.

To prove the existence of a Sudoku with 16 hints, the method is very simple, since Berram Felgenhauer and Frazer Jarvis have calculated the total number of unequal finalists to be 5,472,730,538, then run every case where the finale is 16 hints, and if no Sudoku with 16 hints is found, then it can be proved that the minimum number of hints is 17.