Minesweeper that never makes you guess
Ordinary boards routinely end in a coin flip. Every board here is checked to be clearable by reasoning alone before you see it — if you are stuck, there is a deduction you have not spotted.
Click to open · right-click or long-press to flag · arrow keys and space work too · click a number with its flags placed to open the rest
How a board is checked before you see it
Mines are placed at random, and then the board is played by a solver that uses only what the revealed numbers imply — never the mine layout. If that solver clears the board, it is kept. If it gets stuck, the board is thrown away and another is generated.
The solver knows two rules. Counting: a cell showing 3 with three flags beside it has no more mines nearby, so its other neighbours are safe; and a cell showing 3 with exactly three unopened neighbours left has mines in all of them. Subsets: when one cell's unopened neighbours are entirely contained in another's, the difference between what the two need often settles the extra cells. That second rule is what cracks the 1-2-1 wall pattern, and without it a solver rejects boards any competent player finds routine.
It is worth knowing how often this matters. Of a hundred and fifty ordinary nine-by-nine boards with a clear opening, measured directly, about a quarter cannot be finished without guessing at some point. That is the situation this removes.
The first click is always a zero with an empty neighbourhood. Without an opening area there is nothing to reason from, so the first move would itself be a guess.
The 1-2-1 pattern is the one worth learning
A row of three numbers reading 1, 2, 1 along a wall of unopened cells has exactly one arrangement: mines under the two 1s, and the cell under the 2 is safe. It follows from the subset rule rather than from counting, which is why so many players never notice it and end up guessing there.
The hint button uses the same two rules in the same order, so what it shows you is always something you could have worked out. It never looks at where the mines actually are.
Why flags matter more here
Flagging is optional in most versions and largely cosmetic. Here it is how you make progress: the counting rule works from flags, so a number with its mines marked lets you clear everything else around it in one move. Clicking a satisfied number opens its remaining neighbours all at once.
The consequence is that a flag in the wrong place blocks the reasoning rather than just being untidy. If the hint says nothing is available, a misplaced flag is almost always why.
Related
Nonograms and logic grids use the same kind of elimination, and neither needs a guess either.
Questions people actually ask
Do I really never have to guess?
Never, and it is enforced rather than hoped for. After the mines are placed, a solver plays the board using only what the revealed numbers imply — never the mine layout — and the board is discarded unless that alone clears it. If you are stuck, there is a deduction you have not spotted, and the hint button will show it.
How often would an ordinary board strand me?
About a quarter of the time. Measured directly on a hundred and fifty randomly-placed nine-by-nine boards with a clear opening, roughly one in four reaches a position where two arrangements fit every number on screen and the only way on is a coin flip.
What is the 1-2-1 pattern?
Three numbers reading 1, 2, 1 along a wall of unopened cells. There is exactly one arrangement that fits: mines under the two 1s, and the cell under the 2 is safe. It comes from comparing what neighbouring cells need rather than from counting, which is why it is easy to miss.
Does the hint know where the mines are?
No, and that is deliberate. It works from the same information you have — the numbers showing and the flags you have placed — using the same two rules the generator's solver uses. Anything it tells you, you could have worked out.
Why does it say no deduction is available?
Almost always a flag in the wrong place. The counting rule works from your flags, so a misplaced one actively blocks the reasoning rather than just being untidy. Removing your least certain flags normally reopens it.
Why is the first click free?
Because without an opening area there is nothing to reason from, so the first move would itself be a guess. Every board is built so the opening cell is a zero with an empty neighbourhood around it.