# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

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Duke Gnome
Daedalian Member

 Posted: Mon May 17, 2004 8:27 am    Post subject: 1 I enjoy playing Minesweeper, and I try to avoid possibly unsafe sqyares but eventually I generally need to guess. Often though, I think it is probably uneccesary. This image is taken from a recent game. I cannot see any guaranteed mines or guaranteed safe squares, but with all the corners and edges around there probably is. Are there any guarenteed safe squares and if so, what technique did you use to spot them? Thanks.
kevinatilusa
Daedalian Member

 Posted: Mon May 17, 2004 8:37 am    Post subject: 2 One technique to get more squares marked: If you have a smaller number bordering a higher number, and not that many more squares surrounding the higher number are open than those around the smaller number, squares near the higher number may be able to be marked. A typical example is when you have (with all other nearby squares marked ) 221 ABCD A must be a bomb since only one of B and C can be a bomb. D must be safe since at least one of B and C must be a bomb. Near the bottom of your picture you have 10001X212 111233312 ????????? Because the rightmost 1 is adjacent to the 2, at least one square with a bomb must be adjacent to the 2 and not the 1. This can only be the square below the leftmost 3. Conversely, at least one square without a bomb must be adjacent to the 1 and not the two, and this can only be the square below the second 1. Similarly, there is only one more marked square adjacent to the rightmost three than to the 1 adjacent to that 3. Therefore we must have both: A bomb next to the 3 which is not next to the 1...this must be below the middle three. A safe square next to the 1 which is not next to the three...this must be below and to the right of the 1. [This message has been edited by kevinatilusa (edited 05-17-2004 07:37 AM).]
Intentionally left blank

 Posted: Mon May 17, 2004 10:08 am    Post subject: 3 I think this is necessary to point out that no matter how good you'll get, you'll never beat me in Beginner!
Quailman
His Postmajesty

 Posted: Mon May 17, 2004 10:46 am    Post subject: 4 On the far right, there are three 1's in a column. Directly to the right of the middle one is a safe square. It's based on the 3 beneath having two remaining bombs next to it, so the 1 above it will be abutting one of them. For that matter, directly to the right of the lower of those two 3's is a bomb. Also, where there is a bomb three rows from the bottom, there is not a bomb to the right of it. Starting directly above this space, there are possibilities of bomb-bomb-safe-bomb, bomb-safe-bomb-safe, or safe-bomb-bomb-safe. In the lowest row, there are three 3's in a row. There is a bomb beneath the left-most 3, because of the 1 & 2 to its left. There's a bomb beneath the middle 3 because of the 3 & 1 to its right. To the right of that bomb is safe-bomb-safe-safe. To the left of the first bomb, starting beneath the 2, are safe-bomb-safe-safe. Rats. I just noticed that Kevin posted all that.[/e] [This message has been edited by Quailman (edited 05-17-2004 06:48 AM).]
DMTsurel
The Other Israeli

 Posted: Mon May 17, 2004 2:54 pm    Post subject: 5 I've beaten Macnut!!! You see, practice makes perfect. [This message has been edited by DMTsurel (edited 05-17-2004 01:34 PM).]
Lepton
1:41+ Arse Scratcher

 Posted: Mon May 17, 2004 5:55 pm    Post subject: 6 i am the "l33t"est minesweeperer here
mikegoo
Daedalian Member

 Posted: Mon May 17, 2004 7:40 pm    Post subject: 7 Thank you Lepton...I almost cried laughing at that.
i_h8_evil_stuff
Daedalian Member

 Posted: Tue May 18, 2004 10:06 pm    Post subject: 8 I usually just look for every possibility, but I'm good at that logic stuff. I have a couple of my "tricks" below. I have 2 examples in the above picture, in which I have labled some of the squares (and increased the size). The first method will prove that spot E is safe. Both of the spots A and B tell you crucial data. A says "There must be exactly 1 mine split between spaces C and D," and B says "There must be exactly 1 mine split between spaces C, D, and E." Logically adding the phrases together lets you eliminate spot E. A similar case is true for the lower part. Spots a snd b, when added together, show that there is one mine between c and d, and one mine on e. I probably will add more later, but I'm too lazy right now to think. Edit: Yeah, uh, I just realized that you used a technique similar to mine in your above game. Sorry. [This message has been edited by i_h8_evil_stuff (edited 05-18-2004 07:05 PM).]
Mikko
Daedalian Member

 Posted: Tue May 18, 2004 10:47 pm    Post subject: 9 One thing to look out for, apart from safe squares, are situation like the one on the top two rows in Duke Gnome's picture. One of the squares next to the 1 and 3 is a mine and the other one isn't. You will not get any more information about it no matter how the mines are placed. Because of this you might as well do the guessing now instead of putting it off.
Zealot
Daedalian Member

 Posted: Wed May 19, 2004 12:11 am    Post subject: 10 Guessing may not be necessary in that situation. If a setup like that is in a corner with no possible additional information, then guess right away, but in this case it's possible that the unsolved section can be worked toward from the right side.
Duke Gnome
Daedalian Member

 Posted: Wed May 19, 2004 3:08 pm    Post subject: 11 Thanks for the advice. Mikko is right, though, Zealot. No combination of numbers on the squares 2 spaces to the right of the 1/3 would give any additional info.
Bicho the Inhaler
Daedalian Member

 Posted: Wed May 19, 2004 6:54 pm    Post subject: 12 Yes...all of the unplayed squares are adjacent to either none of those two or to both of them. What this means is that no square on the board can differentiate between those two squares (the only ones that could have done that have already been determined to contain mines). If you have N squares that you can't differentiate between, the maximum information you can obtain about them is the number of those squares that are mines. You already have that maximum amount of information.
Daedalian Member

 Posted: Wed May 19, 2004 9:34 pm    Post subject: 13 h8's "lower case" solution can be taken one step further. Since the 1 mine in the square directly above e already has a mine, that means d and the square that might be labelled f do not have mines. That leaves only square c to have the other mine for square b. In fact, this works for any 1-2-1 combination (Even without a wall present, as long as there are three unknown squares for the 2, all on one side like that): The mines must be adjacent to the 1's, and the space adjacent to the 2 must be open. ------------------ The sooner you accept one simple truth, the sooner we can all get along with our lives. I'm right.
groza528
No Place Like Home

 Posted: Sun May 23, 2004 2:07 pm    Post subject: 14 I don't want to find what everyone else has pointed out to make sure I'm not repeating it, so instead of offering specific examples I'll give a general idea. If you get stuck in a particular area, use the question mark to your advantage (right-click twice to get a question mark.) Use it to mean "What if this was a bomb?" Then try to fill in where the other bombs would be down the line. Sometimes you'll find that it will contradict something you already have, and the first one you marked can be considered safe.
DMTsurel
The Other Israeli

 Posted: Mon May 24, 2004 6:22 am    Post subject: 15 The question mark is just a waste of time.
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