Portal   Forum   Members   Market   Gallery   Events

minesweeper mental exercise

Discussion in 'Chit Chat' started by Jakeman, Mar 23, 2009.

  1. Jakeman

    Jakeman MSC Founder and Donator

    Joined:
    Feb 26, 2000
    Messages:
    25,761
    Likes Received:
    27
    Market Rating:
    16
    Most people dismiss minesweeper as a mindless game that is used to pass the time when you are bored. But I play it for hours on end. It is very mentally engaging if you play it right.

    Exercise - prove that the yellow squares are clear of mines.

    msproof2.png

    Hint #1 - use proof by contradiction.

    More hints will follow if no one is able to solve the problem.

    This is a custom game that I play. It has 50% more squares and 100% more mines than expert mode which gives it a 33% higher mine density than expert. I have only beaten it once.

    Height: 24
    Width: 30
    Mines: 198
     
  2. Jakeman

    Jakeman MSC Founder and Donator

    Joined:
    Feb 26, 2000
    Messages:
    25,761
    Likes Received:
    27
    Market Rating:
    16
    Hint #2 - test the pink squares. Can we know that there is a mine in one of those squares?

    msproof3.png
     
  3. Jakeman

    Jakeman MSC Founder and Donator

    Joined:
    Feb 26, 2000
    Messages:
    25,761
    Likes Received:
    27
    Market Rating:
    16
    Hint #3 - assume the pink squares are empty. What happens?

    msproof4.png
     
  4. Potente

    Potente Peasant

    Joined:
    Mar 24, 2009
    Messages:
    1
    Likes Received:
    0
    Market Rating:
    0
    omg solutions

    Here's my solution. First, some notation:
    - A green square is completely safe.
    - An orange square may contain a mine.
    - A white, highlighted number is used to reference that particular square.

    1. The white square has two marked mines and two orange spaces.
    2. The white square has one marked mine and three orange spaces.
    3. An intersection yields the square where mines can occur. We can mark one yellow square as safe.

    Now, moving up a bit

    4. We can see that the white squares share a common area containing exactly one mine.
    5. Two more mines need to be accounted for, and they are spread in three additional squares.
    6. To clarify, I'll shade the three distinct groups.
    7. The are now two possible solutions, both of which make the remaining yellow squares safe.
     

    Attached Files:

  5. Jakeman

    Jakeman MSC Founder and Donator

    Joined:
    Feb 26, 2000
    Messages:
    25,761
    Likes Received:
    27
    Market Rating:
    16
    Maybe I am wrong:

    http://www.youtube.com/watch?v=MPKXNLkDz10

    I am shocked at the comments in this video. It seems many people don't know how to play the game and they hate it because they think it's random. Are people ****ing retarded?
     
  6. Wiezzen

    Wiezzen Peasant

    Joined:
    Sep 15, 2008
    Messages:
    140
    Likes Received:
    0
    Market Rating:
    0
  7. Jakeman

    Jakeman MSC Founder and Donator

    Joined:
    Feb 26, 2000
    Messages:
    25,761
    Likes Received:
    27
    Market Rating:
    16
  8. Wiezzen

    Wiezzen Peasant

    Joined:
    Sep 15, 2008
    Messages:
    140
    Likes Received:
    0
    Market Rating:
    0
    I don't think they were being literal.
    Default map is 100 squares with 10 mines so it's only a 10% chance you'll hit a mine. I hit a mine on the first square maybe every 1/20 times.
     
  9. Jakeman

    Jakeman MSC Founder and Donator

    Joined:
    Feb 26, 2000
    Messages:
    25,761
    Likes Received:
    27
    Market Rating:
    16
    I play minesweeper many times every day. The first square is never a mine. I hit a mine on the first square 0% of the time. The custom game mode I play now has a 31% chance to hit a mine and it's never the first one.

    I beat my original custom game mode several times and got bored with it, so now I play this:

    Height: 24
    Width: 30
    Mines: 223

    That is 50% more squares and 125% more mines than expert mode which gives it a 50% higher mine density than expert. I have yet to beat this one, but I have come within 20 mines.
     
  10. Wiezzen

    Wiezzen Peasant

    Joined:
    Sep 15, 2008
    Messages:
    140
    Likes Received:
    0
    Market Rating:
    0
    odd. I could've sworn I've hit a mine on the first click a few times.
     
  11. Wiezzen

    Wiezzen Peasant

    Joined:
    Sep 15, 2008
    Messages:
    140
    Likes Received:
    0
    Market Rating:
    0
    Just tested it out with a 9x9 grid with 67 mines. First two times I didnt hit a mine, but on the third game I hit a mine on the first click.

    Perhaps the new version that comes with Windows Vista was changed?
     

    Attached Files:

  12. Jakeman

    Jakeman MSC Founder and Donator

    Joined:
    Feb 26, 2000
    Messages:
    25,761
    Likes Received:
    27
    Market Rating:
    16
    Must be. That is different than the version I play.
     

Hitometer: 54,663,938 since 1995