The whole border at once
Sometimes no small group of numbers proves anything, and only all the numbers of a border together prove a cell.
Follow the border from one end: place a mine or not, and see what each number then forces in the next cell. Some choices run into a number they cannot satisfy. The cells that come out the same in every choice that reaches the other end are proven. It is slow, so try it only when nothing simpler works.
How it works
No group of up to four of these numbers proves anything. Look at the whole border.
Your turn
Each board is a real position from a game. Tap or click to open; right-click, long-press or switch on Flag to place a flag. If you are not sure, take a hint: the first one only shows where to look.
Which hidden cells can you be sure of?
How the exercises were chosen
A computer checked every board: in what you see, no group of up to four numbers proves anything; all the numbers of the border together prove exactly the marked cells.