The every-arrangement technique says: take a group of numbers that share hidden squares, and work through every way the mines could sit among those squares. A square that’s safe in all of them is safe; one that’s a mine in all of them is a mine. It finds everything the numbers can tell you, but it’s slow, so it’s for when nothing simpler works anywhere.
This is the last of the Minesweeper techniques.
The rule
- Check that no simpler technique finds anything, anywhere on the board.
- Pick a group of numbers whose hidden squares overlap: the smaller the group, the quicker this is.
- Try one hidden square as a mine, and follow the consequences with the simple checks. Then try it as safe.
- Keep only the ways that fit every number in the group. Any square that’s the same in all of them is settled.
In a real game
On the Expert board every technique page follows, it’s needed at step 206, near the end. Only 20 squares are still hidden, and 18 of them form a pocket at the top of the board, ringed by nineteen numbers. No simpler technique finds anything anywhere. But only 11 ways of placing the mines in the pocket fit all nineteen numbers, and all 11 agree on two mines and one safe square, all in column 23.
How often you’ll need it
Rarely, until Expert: on 1 of 200 Beginner boards, 3 Intermediate and 19 Expert. On the Expert board here it’s needed twice, both in this pocket.