Minesweeper

Minesweeeper is a puzzle where each cell is a mine, empty, unknown, or number. The goal of the puzzle is to determine if each unknown cell must contain a mine or be empty according to the rules.

The cycle of tiles is { Unset, Mine, Empty }. Left clicking on the tile will advance the cycle by one state (Unset -> Mine or Mine -> Empty or Empty -> Unset) and right clicking on a tile will detract the cycle by one state (Empty -> Mine or Mine -> Unset or Unset -> Empty).

Rules

1. Each unset cell must be changed to either Mine or Empty
2. Each number cell (cell with a number 1-8) must see that number of Mine cells. A cell sees its eight neighbors.
3. A cell that does not see any number cells may either be mine or empty

Notice: LEGUP minesweeper is a bit different from minesweeper on other platforms. In order to make it possible to do proofs, randomness and revealed information do not exist in LEGUP minesweeper.

LEGUP Proof Rules

Direct Rules

Finish With Mines

For at least one of the numbers that the an unset cell sees, the amount of unset tiles plus the number of mine tiles in the number cell's vision must be equal to its number for the cell to be a mine.

Finish with Empty

For at least one of the numbers that an unset cell sees, the amount of mines that the number sees must be equal to its number for the unset cell to be empty.

Non Touching Shared Mine

Adjacent cells with numbers have the same difference in mines in their unshared regions as the difference in their numbers

Non Touching Shared Empty

Adjacent cells with numbers have the same difference in mines in their unshared regions as the difference in their numbers

Case Rules

Mine Or Empty

An unset cell must either contain a mine or be empty

Satisfy Number

Every possible way for the unset cells around a number to be filled with a mine or empty according to its number

Contradiction Rules

Too Few Mines

A number cell can not have less than it's number of mines around it

Too Many Mines

A number cell can not have more than it's number of mines around it