This topic mainly examines the application of logical reasoning and analytical reasoning ability. The key to solve this problem is to judge from which squares have no numbers and which ones have no smiling faces.
For example, 1 in the lower left corner means that only one of the eight around is a smiling face.
But there is only one square around it in the title, so the square in the upper right corner must be a smiling face, so the answer is
Extended data
This is a sudoku problem in elementary school olympiad. Mastering some Sudoku problem-solving skills can solve this kind of problem faster:
1. Intrauterine exclusion
Exclusion method is a method to exclude the same number from other squares of the same row, column and palace by using the rule that rows, columns and palaces in Sudoku cannot fill in the same number.
Intrauterine exclusion is a method that aims at a uterus, excludes it with a certain number, and finally gets that only one cell in this uterus has a number. Skills diagram:
As shown in the above figure, 1 in cells A2, B4 and F7 does not include the third house. At this time, only C9 cells in the third house can be filled with 1. This legend is the exclusion method used by Mimiya.
2. Row and column exclusion method
Row-column exclusion method is a method to exclude a row or a column with a certain number as the goal, and finally get that only one cell in the row and column has the number. Skills diagram:
As shown in the above figure, both 6 and B8 of D2 do not include the F line. At this time, only F5 can fill in 6 in line F. This legend is the exclusion method used for the F line.
3. Block exclusion method
Block exclusion method is to form a block in a palace by intrauterine exclusion method, and then use the exclusion of this block to determine that only one box in a palace has other known numbers. Skills diagram:
As shown above, 7 in B4 excludes the fifth house, and a block containing the number 7 is formed in the fifth house. No matter whether the F5 cell in this block is 7 or the F6 cell is 7, the 7 of other cells in the F row can be excluded. Combining the 7 in the H7 grid and excluding the Sixth Hospital, it is concluded that only the D8 grid in the Sixth Hospital can be filled with 7.
4. Occupation method of intrauterine number pair
The number pair occupation method means that two numbers only appear in two communities in a certain area. At this time, although the position of these two numbers can't be judged, the occupation of these two numbers can be used to exclude other numbers from appearing in these two cells, and then the next number can be filled indirectly by combining the exclusion method. Skills diagram:
As shown in the figure, the known numbers 3 and 5 in row D and column 7 are used to exclude the sixth house, and a number pair is formed in cells E8 and F8, which excludes other numbers from filling these two cells. At this time, seven of D4 and F 1 are used to exclude the sixth house, and it is concluded that the sixth house can only be filled with E7.
5. Congruence solution
The remainder method takes advantage of the possibility that each cell in Sudoku has only nine numbers. If there are 8 kinds of numbers in a cell, you can only fill in the only one that does not appear. Skills diagram:
As shown in the above figure, the numbers 1 and 2 are known on line C; The numbers of the third house are 3, 4 and 5; 9 lists the known numbers 5, 6, 7 and 8. The above eight different numbers affect the C9 grid at the same time, so that the C9 grid cannot be filled with these eight numbers, and only the number 9 can be filled in the C9 grid. Otherwise, there will be the same number in the same industry, the same column and the same palace.