Skip to content

Minesweeper Rules [WIP]

vockek edited this page Feb 6, 2024 · 4 revisions

Minesweeper

Minesweeper is a puzzle with cells that are either filled or contain a hidden bomb. Your goal is to mark the locations of all bombs and filled cells based on the rules of minesweeper.

Rules

Here are the direct rules of the puzzle

  1. All cells containing a number are not a bomb.
  2. The number of a cell indicates the total number of bombs contained in the cells adjacent to it (sharing an edge or a vertex).

LEGUP Proof Rules

Case Rules

Bomb or Filled

J09ME8b.th.jpg

If a tile can either be filled or a bomb based on the current state of the board, create a split in the tree where the tile is filled in one path, and a bomb in the other to show the different cases.

Satisfy Flag

J0HKgxS.jpg

Create a different path for each valid way to mark bombs and filled cells around a flag.

Contradiction Rules

Insufficient Bombs

J0HGuVI.th.jpg

There cannot be less bombs around a flag than the specified number.

Bomb Surplus

J0HhMFI.th.jpg

There cannot be more bombs around a flag than the specified number.

Direct Rules

Fill Bombs

J0H8WT7.th.jpg

Fill the rest of the blank spaces around a flag with bombs if it would satisfy the number specified by the flag.

Fill Surrounding

J0HQXB2.th.jpg

Fill the rest of the blank spaces around a flag with non-bombs if the number specified by the flag is already satisfied.

Covered Flag

J0J31Fs.th.jpg

If the number of remaining bombs around a flag are covered by another flag, fill the cells not covered by that flag with non-bombs.

Difference of Three

J0JtU3N.jpg

If the numbers of two adjacent cells (sharing an edge, not a vertex) have a difference of three, fill the outside of the lower flag with non-bombs and the outside of the higher flag with bombs.

1-2-1 Rule

J13642a.jpg

If there are three flags in a line with numbers 1, 2, and 1 respectively, then fill the outside and middle columns with non-bombs.

Clone this wiki locally