How to Win at MineSweeper: Complex Elimination

This is a continuation of previous posts.

Finding a Safe Square:  Complex Elimination

I define Complex Elimination as having to use the information from two squares to find a safe square.  Here’s how it gets used in this area:

We know one of those two squares conceals a mine.  While we should not use a flag because we do not know for certain which one has the flag, we can take advantage of the question mark feature (double right-click):

Use of the Question Mark

 But consider the square right below this one.  It is also a 1.  What could that mean?

Using Info from a 2nd Square

There is only 1 mine in this area as well.  We already know the mine must be located in one of the two upper squares of this area (as per the question marks).  Therefore, the bottom square must be a safe square (marked with a ‘x’):

Complex Elimination

 So, let’s reveal this safe square and see what we get:

Safe Square Revealed

This new information may not seem very useful.  There are 2 mines in the area of the square we just revealed, but there are still 6 squares unrevealed squares in the area.  One of them we know is a mine (marked with a flag), so there is one more mine in the 5 remaining squares.  How is that helpful?

We’ll have to use Complex Elimination again.  We will have to use the square next to it that is marked with a 3.  There are only 3 mines in the area of this square, two of which have already been located.  There is only one more, and it must be located in one of two possible squares:

Question Mark Again

These question marks are the only possible locations for the 2nd mine in the area of the square marked ‘2′.  All the other squares in the area of ‘2′ must be safe. 

Can you find the safe squares?

 Do you see the safe squares?:

Complex Elimination Again

Here is my next move (again using complex elimination to find more safe squares):

Minesweeper

Next, I will write about how the same type of reasoning can be used to locate mines (and not just safe squares).  Thanks for reading.

~The Witch Doctor

Tags: game, microsoft, mine, minesweeper, sweeper, win, windows