76



42

Assuming standard Minesweeper rules, here’s one solution (with $ X $ = a mine): EDIT: In response to Euphoric in the comments, I solved this purely by logical deduction with a bit of educated guessing to make things easier on me. But if you really want to know how I did it, here’s a rigorous solution:


21

Many Minesweeper games, including the one that ships with Windows, do not allow the first square you click to be a mine. The lower-left-hand corner is not necessarily safe, but if it's the first square you click, then it will be safe.


18

Although the puzzle is most likely to be solved without a computer, and we already have a winner, here are all 16 solutions, just for the record: There are some symmetries in there, of course. Whether rotations and flips should count as "different boards" is a matter of interpretation. Found with the following (quick and dirty) Java program that jus ...


15

I think that yes, it is possible. You can create a custom grid with a ratio of more than 8 bombs per empty square, then, by the pigeonhole principle, there exists a bomb with no empty square next to it, since each empty square can be adjacent to at most 8 bombs. I don't have my own picture but I found this on the internet: Source


13

There are 50 different possible ways that the unknown mines next to the revealed region could be configured: Here, the green cells are clear (no mines), while the X's around the perimeter indicate the different ways the mines could potentially be placed. If we consider each of these to be of equal probability (probably not quite true, because the total ...


13

The crossed bomb corresponds to a square where a flag had been placed while no bomb was on it. Therefore it is not actually a bomb and this solves the problem.


13

How about (horrible ascii depiction):


11

The 2 down-right from your bad flag should have tipped you off; it is touching two bombs you had already flagged. That would show the one next to it (which you triggered) to be a bomb; the two under that one would clear the one left of it (above the 4), leaving just the four bombs around the 4. You could also have figured out the 4's surroundings just from ...


10

My answer is: This was found:


9

(I did this without looking at the CW. I claim no credit for imposing arbitrary restrictions on myself, but it means any mistakes are my own :-).) The final grid is as follows: which obeys the following constraint: If we interpret we get "First", "Second", etc., are of course When groups of cells are referred to collectively, Note: in the course of ...


8

As GentlePurpleRain says in their excellent answer, there are $50$ different possible placements for the mines in the squares around the solved region. However they make the assumption that each of these possibilities is equally likely. This is not correct. The possibilities that GentlePurpleRain lists contain either $4$, $5$, $6$, or $7$ mines in the ...


8

This answer, although it does address the question itself, is more of an interesting observation coming from analysing the situation by expressing the system in terms of simple linear equations (eg/ using capitals for the reds, you might say A+B=1 to say that exactly one of A and B can be a mine, or F+G+H+I=2 because there must be exactly two mines amongst ...


8

The most you can do according to these new rules is 8 tiles, with the following grid: 1 2 3 3 3 2 1 2 # # # # # 2 3 # ? ? ? # 3 3 # ? 7 ? # 3 3 # ? ? ? # 3 2 # # # # # 2 1 2 3 3 3 2 1 # represents an already-discovered mine. To show that this is maximal, look at the "information-conveying" tiles required by the instructions. We'll call these "useful tiles"...


8

Code: Some sample outputs: .


8

First: Now, an interesting step: Some more logic sprouts off of the same area: And hey, wait a second...


7

I can get this much: which is to say, Here's how it goes. Then After this [EDITED to add:] Here's a sketch of how to prove that Note that I am writing this after reading other people's solutions :-) but I haven't read them in much depth and am not deliberately copying anything. So, first of all, What about the top region? Well, So the only question ...


7

Given your current situation, I believe that I would therefore guess that Diagram:


7

Here is another way of completing this puzzle:


6

If you're going by Microsoft Minesweeper rules (or any where the number of mines are known), and assuming we aren't limited by the artificial limitation Microsoft provides on board creation, the answer is which happens to be and is a trivial solution. Once you mark the opening move, which will be an 8, the board is solved, either automatically in the case ...


6

Here is the solved grid: but I'm not sure (yet) what to do next ...


6

The solved grid (solved independently of @Glorfindel - pipped to the initial posting of the completed grid by seconds!) is as follows: What's crucial here is to: This then gives us: What do we have now? Well, notice that these numbers:


6

Answer: The techniques are mostly from minesweeper. Here are the steps:


5

It feels like there's more slack in here for other solutions 1. 2. 3.


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