TECHNIQUES FOR SOLVING MINESWEEPER PUZZLES

In this discussion, the following cell types will be referred to:-
  • HAZARD These contain a triangular flag with a number which indicates the number of adjacent cells (horizontally, vertically and diagonally) which contain a mine.

  • PENDING Cells which have not yet been declared as CLEAR or MINED. The default color for these cells is light gray.

  • MINED Cells which have been declared as MINED. By default, they have a white background, and containe a graphic image of a Mine.

  • CLEAR Cells which have been declared as not containing a Mine. The default color for these cells is white.

  • When specific cells need to be referred to, they will be designated as C4-R3 which means the 4th cell in row 3.
The following presents a number of strategies which you should apply in turn. Note that the successful application of a strategy opens up new opportunities which permit the successful application of other strategies within the list. Consequently, if the puzzle is not solved after the first pass through the list, you should continue to repeat the process, until the puzzle is solved.

For a description of MINESWEEPER puzzles, refer to  Building Minesweeper Puzzles 

Required Clear

This is one of the most fundamental strategies available for the solving of Minesweeper puzzles. If you make a puzzle having a difficulty level of 1, then you will be able to solve it completely using only this strategy plus the Required Mine strategy.

The five cells highlighted in blue draw your attention to the hazard cell containing a 1. This cell requires a single adjacent mine, and reference to cell C3-R4 shows that this requirement has already been met. As no further mines are required, the highlighted cells may all be cleared.


Required Mine

Look at the hazard cell immediately below the highlighted cell. It requires mines in two of its adjacent cells. It already has one mine, and since the highlighted cell is the only pending adjacent cell it must also be mined.

Invalid Clear

Imagine that the highlighted cell were to be cleared. Then the hazard cell immediately above it would still require two adjacent mined cells. The only candidate cells for this purpose are C1-R1, C1-R2 and C3-R1. However these are all adjacent to the hazard cell at C2-R1, and consequently only one of them can have a mine. This would leave the hazard cell at C2-R2 with only a single mine. Therefore our original action of clearing the highlighted cell was invalid. It must in fact be a mine.

Implied Mine

The hazard cell immediately above the highlighted cell requires two more mines, and the candidate cells for this purpose are C4-R2, C4-R4 and C3-R4. However, two of these cells are adjacent to the hazard cell at C5-R3, and so only one of them is available. This implies that the highlighted cell must in fact be a mine.

Implied Clear

The hazard cell at C5-R4 requires a single mine which can only be placed at C4-R4 or C6-R5. At this point we don't know which one it will be, but in either case it will be adjacent to the hazard cell at C5-R5 and will completely satisfy its requirement. No further mines will be required, and this implies that the three highlighted cells must be cleared.

Invalid Mine

If a mine were to be placed into the highlighted cell, it would satisfy the requirements of the hazard cell at C5-R3, which in turn would mean that cells C4-R2 and C4-R4 would have to be cleared. This would leave the hazard cell at C3-R3 with no way of satisfying its requirement for two additional mines. It follows then that a mine must not be placed into the highlighted cell.

Astute solvers may find other, more obscure strategies which they can apply. However, the strategies listed here are guaranteed to solve any MINESWEEPER puzzle created by Magnum Opus.