Strategy: reasoning without guessing
In brief
Three deductions are enough to solve many grids: a number with as many hidden neighbors as its value (all contain mines), a number that already has all its flags (the rest are safe), and two neighboring numbers where one “contains” the other. The mine counter helps near the end of the game. When none applies, you have to guess.
The grids on this page are generated by the app (Beginner, 9 × 9, 10 mines); each deduction was played by the app's engine without hitting a mine, then checked by a second program.
- hidden cell
- open cell
- flag
- number used
- deduced safe cell
- deduced mine
A number that needs every hidden neighbor: all contain mines
The number in column 4, row 4 has a value of 1 and only 1 hidden neighbor (not counting flags already placed around it). Its mines have to go somewhere: this square contains a mine.
A satisfied number: the rest are safe
Once this flag is placed, the number in column 4, row 3, whose value is 1, has as many flags around it as its value. Its other hidden neighbors cannot contain mines: 1 safe square. In the app, tapping this number opens that square immediately (chording).
Two neighboring numbers
Later in the same game, no single number is enough. The number in column 1, row 7 still needs its mines to be placed among squares that all also touch the number in column 2, row 7. These two numbers require the same number of mines still to be placed: all the second number's mines must therefore lie within the first number's area, and its other hidden neighbors are safe, here 1 square.
The same reasoning sometimes identifies mines: when the second number requires as many additional mines as it has additional squares.
The mine counter
The counter shows mines minus flags. Near the end of the game, it can sometimes settle the question: in this other Beginner grid, all flags have been placed and 1 hidden square remains; the counter is at zero, so it is safe.
When you have to guess
The app's generator places mines randomly, without checking whether a grid can be solved logically. In the grid below, after 16 reasoning steps, 4 hidden squares remain and the mine counter shows 2. Trying every way to place them reveals 2 arrangements that satisfy all the numbers, and no square is safe in every arrangement: you have to choose.
When you have to guess, a few guidelines:
- first open any safe squares elsewhere: a new area may resolve the uncertainty;
- prefer a square that will give you information if it is safe, rather than an isolated square;
- accept the loss: losing a game on a forced guess says nothing about your reasoning.