# In Minesweeper, does every bomb have to have at least one neighboring number?

In a classic Minesweeper game (say, the one from Windows), is this situation possible? This is the bottom-right corner of a board:

1 2 2
2 B B
2 B B


I'm specifically asking about the bomb in the bottom-right corner because it does not have any neighboring numbers.

• In the version of Minesweeper that I have been playing, this situation certainly is possible. – Gamow Sep 12 '17 at 10:40
• I'd say it is possible; even if it isn't, I'd bet that the vast majority of minesweeper games allow this to happen. – Wen1now Sep 12 '17 at 10:49
• Note that because the total number of bombs is known, it is sometimes possible that such a situation can be solved by pure logic. – supinf Sep 12 '17 at 12:56
• @supinf, however, sometimes you can have one bomb left, but two such corners. – rus9384 Sep 12 '17 at 13:02
• In my experience, this never happened in the Windows version. At least not on the standard preset fields. It may be possible if you customized a field – Kevin Sep 12 '17 at 20:42

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:

• Not sure spoiler markup is needed, here. The question seems to be an enquiry about the game, rather than a puzzle to be solved. – David Richerby Sep 12 '17 at 11:44
• It's nice using the pigeonhole principle to prove the program isn't coded to explicitly avoid the situation. But even with 4 mines in total it's possible, however unlikely, to have situation the OP described. The best way to achieve this without a custom game is to play in advanced difficulty and open tiles away from the top left corner. This is because the board is initialised before clicking on the first tile and if you happen to hit on a mine with your first click, it'll be moved to the top left. This slightly increases your chances of seeing that configuration than in other other corner. – Reti43 Sep 12 '17 at 12:19

Of course, it is possible.
As it is a game for the numbers, which tell how many bombs are in their range in 1 step vertical and horizontal. So it's on the randomness of the game. You can also get that form and this you can know after getting all the bombs as it is in bottom right-corner.
Getting this type of image takes a huge amount of time as you can't predict randomness.

• Is the randomness uniform, though? – boboquack Sep 12 '17 at 21:53
• No, it's as random bombs which takes its place and then numbering is done – Asterisk Sep 13 '17 at 4:41
• I seems to recall that certain boards (look up the Dreamboard) come up way more often than others. – boboquack Sep 13 '17 at 5:29
• Some minesweeper game can allow us to make custom , in which u can defined the height, width and the percent of mines in it. – Asterisk Sep 13 '17 at 5:49