Beautiful solution with the binomial encoding. Apparently, "at most k" is a well known problem http://www.sat4j.org/maven233/apidocs/org/sat4j/tools/encodi...
Kaboom: an unusual Minesweeper
31–40 of 71 posts
Re: Kaboom: an unusual Minesweeper
#32How can I choose which square has the mine without guessing here? https://imgur.com/gallery/GlAgExv
According to the rules of the game, both positions are safe.
The golden rule of this variant is: If a tile could contain a mine, it does.
Except: If there are no more tiles that can be guaranteed to be safe given the information on the board, you have to guess.
When you're forced into guessing, the rule is inverted: If the tile could be safe, then it will be safe. Again, this only applies if there are NO other guaranteed safe tiles on the board.
So click whichever you prefer.
Re: Kaboom: an unusual Minesweeper
#33> One of the bottom squares contain a mine, but it's impossible to say which one. You have to select one of them. But according to what I just said, that would mean certain death! I wanted the game to be cruel, but now it's unwinnable. So I'll modify the idea a bit and say you are allowed to guess, but only if there are no safe squares left. This way, the game will be cruel, but fair.
The situation when your only move possible is a guess is exactly the same we have in the very beginning of the game so I would rather make such fields guaranteed safe the way the first click is.
Re: Kaboom: an unusual Minesweeper
#34> One of the bottom squares contain a mine, but it's impossible to say which one. You have to select one of them. But according to what I just said, that would mean certain death! I wanted the game to be cruel, but now it's unwinnable. If it's not stalemate, haven't you won at that point? The tiles are practically in a state of quantum superposition where they are both safe and unsafe at the same time. You can't know…
Read further down.
> So I'll modify the idea a bit and say you are allowed to guess, but only if there are no safe squares left. This way, the game will be cruel, but fair.
Re: Kaboom: an unusual Minesweeper
#35Earlier quoted context omitted.
I wouldn't say it's "easier", since random chance of failure isn't a difficulty level, it's a lack of difficulty: Your gameplay has no effect on the outcome. If anything, this is Minesweeper as it should have been: A game of perception and deduction with no chance of random failure. As a huge minesweeper fan, I think this is fantastic.
Yes. I've always bemoaned the fact that people's first experience with the game is the one bundled in Windows. Because the player knows the game sometimes requires guessing, they never learn which situations actually require guessing and which are actually solvable; they just decide they need to guess because there is no number surrounded by the same number of empty squares, and never discover the math about possibil…
I learned on Windows and 1. Never guessed if avoidable, 2. If guessing always considered both odds and potential reward for each option, at least heuristically. I feel in this context for saying "never" you deserve to click a mine ;-)
Re: Kaboom: an unusual Minesweeper
#36I have been playing this obsessively the last few weeks without knowing about the implementation. I thought it expresses the known facts about the board configuration as a system of linear equations and uses one of the classic algorithms for solving these. Anyone know if that would be infeasible for some reason?
I was thinking along the same lines when the systems of linear equations came up. The difficulty is that the variables are 0-1 while the equations are over the integers. So this is not quite as simple as solving a system over F_2, but is instead feasibility testing of an IP with 0-1 variables and a 0-1 matrix.
I wonder if solving the LP-relaxation might lead to a rounding based approach.
Re: Kaboom: an unusual Minesweeper
#37The original minesweeper had a smiley face up the top, which would turn dead if you lost, and would have a :o face while picking a cell.
Having the face change if there are safe cells available would give the face a purpose.
Re: Kaboom: an unusual Minesweeper
#38Given that guessing is always safe when it's required, it means you have a choice in e.g. the initial play. Is it more efficient to click tiles on a line, or to click them in a cluster?
I've found it easier to hug the corners when possible, since it reduces the surface area in which you have to look for overlaps that might generate safe squares. In general, the game is easier when there are fewer places in the border.
Re: Kaboom: an unusual Minesweeper
#39Earlier quoted context omitted.
I wouldn't say it's "easier", since random chance of failure isn't a difficulty level, it's a lack of difficulty: Your gameplay has no effect on the outcome. If anything, this is Minesweeper as it should have been: A game of perception and deduction with no chance of random failure. As a huge minesweeper fan, I think this is fantastic.
I'm not entirely sure the software's working correctly. I lost my first game, and I'm fairly certain that there was a different possible orientation of mines: https://imgur.com/gallery/hg1Mcwq
In your screenshot, look at the green squares. Those are the spaces that are guaranteed to be safe based on the available information. The game wants you to click those before you do anything else.
Once there are no more guaranteed squares anywhere on the board, then you can guess. And if you guess somewhere that could be valid, it will be valid. But only if there are no other guaranteed spaces left.
Re: Kaboom: an unusual Minesweeper
#40> One of the bottom squares contain a mine, but it's impossible to say which one. You have to select one of them. But according to what I just said, that would mean certain death! I wanted the game to be cruel, but now it's unwinnable. If it's not stalemate, haven't you won at that point? The tiles are practically in a state of quantum superposition where they are both safe and unsafe at the same time. You can't know…
Read further down. > So I'll modify the idea a bit and say you are allowed to guess, but only if there are no safe squares left. This way, the game will be cruel, but fair.
That's not quite the same though. The computer's rolling a dice on that one. My thinking was that the final state comes from a random player at the other side of the world.