Solving sudoku and minesweeper by logic

The same skeleton

Sudoku and minesweeper look different but do the same work. You hold a set of candidates for each square and eliminate the impossible ones using the given constraints. When one candidate remains, the square is settled, and settled squares shrink the candidates elsewhere. That chain is what drives the solve.

Two ways to look at sudoku

You can work from the square or from the number. When one direction stalls, the other often opens it up.

• By square: is there only one number that fits here
• By number: is there only one square in this line where 7 fits
• If two squares hold only the same two candidates, remove them elsewhere in that line
• Pencilling in candidates makes the chain visible

What the numbers say in minesweeper

A number tells you how many mines sit among the eight surrounding squares. Two certainties follow. If the number equals the count of closed neighbours, all of them are mines; if the flags already placed equal the number, every remaining closed neighbour is safe. Those two rules alone resolve a large share of any board.

Overlapping two numbers

When a single number is not enough, look at squares shared by two adjacent numbers. If a one and a two are adjacent and share squares, you can work out whether the mine already accounted for by the one is also counted by the two, and settle the rest. Most intermediate situations resolve through this overlap.

Squares logic cannot reach

Minesweeper can end with too little information, leaving a probabilistic choice. There, counting remaining mines against remaining closed squares and taking the lower-probability option is the best available move. A well-made sudoku, by contrast, has a unique answer reachable by logic alone, so needing to guess usually means a clue was missed.