The Most Commonly Used Basic Formulas

Let's assume that there are no marked mines around the number to be determined (in the case of mines, please refer to the "subtraction principle" later).

(Unrelated numbers are hidden from the picture. The blue dots represent empty spaces and the red dots represent mines.)

One-Headed Fixed Form

"One end" refers to one side of a number (three vertical squares) being empty or bordered.

1. Two at one end, two mines;

(Right border of 2 in the figure)

(Inference) Equation 22: If 22 is at one end, then the third grid contains no mine. (Image is temporarily omitted)


2. Formula 11: If 11 is at one end, then the three squares on the other side contain no mines;

(11 in the figure, left border)

(The left side of 11 in the figure is clearly empty)

(Inference) Formula 111: If there are three 1s or 2s, then the middle one is a mine, and the other two are not mines. (Image is temporarily omitted)

Arbitrary Position Formula

3. At any position, there is no mine on the outer side of 1 and one mine on the outer side of 2;



4. 3 in the middle, three mines;



5. 121 At any location, two 1s have mines, and 2 has no mines;



6. 1221 at any position: Two 2s with mines, 1 without a mine.



The above formula applies in the same direction for both horizontal and vertical orientations.

Subtraction Principle:

If mines are already marked around the number, subtract the number of mines around the number first, keeping these spaces blank in your mind, and then apply the formula.

Figure below: It is actually a fixed 11 formula, and the green dot can be opened.



Below: There are two mines around 3 with a ratio of 3-2=1, and one mine around 2 with a ratio of 2-1=1. Therefore, it simplifies to 11 mode, and the two grids for marking can be directly opened.



Below: After subtraction, there are 12 fixed formulas, with red dots indicating mines.



Below: According to the number 3 located at the top of the figure, if there is only one mine in the two unknown squares enclosed by the ellipse, then the number 3 below becomes 2, using the 12 formula. The blue dot is not a mine, and the red dot is a mine.