Step 1: Starting in the upper left, open up all the squares adjacent to any blank square.  That reveals 36 spaces.


Step 2: Identify spaces that have to be mines.


The spaces indicated here all must be mines.  The two to the left, because they each border a “1” for which they are the only remaining open space.  On the upper right side, we know that the two mines cannot be in adjacent spaces, otherwise more than one “2” would be present.  So the configuration shown is the only possibility.


Step 3: Open all spaces adjacent to known “1” spaces that are not mines. Then open additional safe spaces that were subsequently revealed (as either being adjacent to a new blank space, or adjacent to a “1” that already has its mine found.)



Step 4: Identify more spaces that must be mines.


The first two new mine additions are both the only remaining square adjacent to a “1” without a mine, and the two in the bottom right are the only 2 open squares adjacent to the “2” there. We now have 8 definite mines identified.


Step 5: Once again, open all spaces that must be safe, because they border a numbered space that has already has its mine quota filled. Then continue opening the safe spaces that were subsequently revealed.



Step 6: Identify one more definite mine (we should be up to 9 now), because it’s the only open space next to one of the “1” squares.



Step 7: Open up more safe squares, as in previous steps.


Step 8: Since we know there are only 10 mines, that means only one undiscovered mine remains.  It MUST be adjacent to the “3”, since that only has 2 mines currently marked next to it.  It must also be adjacent to BOTH of the “2” squares in the lower left, because neither has had its second mine marked.  That means it can only be in the square that is adjacent to all three of those.