## "X-[X+3] in space" Pattern

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## Are you aware of this pattern?

Yes! I've mastered this pattern already
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100%
Yes. I've heard of it, but not mastered it yet
0
No. I haven't even heard of it
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ChallengeSpaceYard
Posts: 2
Joined: Tue Jan 25, 2011 10:58 pm

### "X-[X+3] in space" Pattern

I wonder how many of you sweepers know this pattern. The pattern basically forces all the tiles only the X has to be safe, and the tiles only the [X+3] has to be mines.

Information has been relocated to here as Google Sites doesn't specify dimensions of a picture, making it impossible to put images on the board.

Summary: All tiles touching only the X must be safe, and all the tiles touching only the 4 must be mines.
Last edited by ChallengeSpaceYard on Thu Feb 24, 2011 2:15 am, edited 1 time in total.

EWQMinesweeper
Posts: 411
Joined: Sun Nov 30, 2008 11:50 pm

### Re: "X-[X+3] in space" Pattern

pretty easy pattern. pattern recognition shouldn't be the big deal. recognising the several ways to solve a pattern and being able to find the solutions that a) take the fewest clicks or b) are the fastest is quite more difficult.
„Das perlt jetzt aber richtig über, ma sagn. Mach ma' noch'n Bier! Wie heißt das? Biddä! Bidddää! Biddddäää! Reiner Weltladen!“

wylx
Posts: 30
Joined: Mon Jan 24, 2011 12:02 am
Location: Cambridge, Massachusetts

### Re: "X-[X+3] in space" Pattern

On the topic of the original poster's post, though, it can be generalized that given any two horizontally or vertically adjacent revealed numbers, the difference in the number of mines in the two sets of three squares on the extreme sides of the numbers is the respective difference between the two numbers. For example, given a 2 to the left of a 4, there is at most one mine in the three squares to the left of the 2, and that amount plus two mines in the squares to the right of the 4. The remaining mines, if any, are distributed among the squares covered by both the 2 and the 4.

There are many corollaries to this; for example, no two horizontally or vertically adjacent squares could bear numbers with a difference of greater than three.

ChallengeSpaceYard
Posts: 2
Joined: Tue Jan 25, 2011 10:58 pm

### Re: "X-[X+3] in space" Pattern

wylz's reply gives some useful insight with two adjacent safe tiles. If there is a revealed safe tile next to only the 4, the other tiles touching only the 4 have to be mines, and the tiles only the 2 touch have to be safe.

Likewise, if the difference between the two safe tiles is 1, then if two of the tiles adjacent only to the bigger of the two control tiles are safe, then the third tile has to be a mine, and the tiles on the other side have to be safe. Basically the 1-2 pattern stripped.

Both of these are available along with the 1-4 pattern on a seperate webpage.
Last edited by ChallengeSpaceYard on Thu Feb 24, 2011 2:28 am, edited 1 time in total.

EWQMinesweeper
Posts: 411
Joined: Sun Nov 30, 2008 11:50 pm

### Re: "X-[X+3] in space" Pattern

@CSP: images make it easier to follow. although your pattern examination is correct, the Os, -s and Xs make an ugly sight. minesweeper clone has a cheat mode, in which you are able to set the mines' positions and can then play this board in UPK mode and take a screencap of the pattern you want to show us.
„Das perlt jetzt aber richtig über, ma sagn. Mach ma' noch'n Bier! Wie heißt das? Biddä! Bidddää! Biddddäää! Reiner Weltladen!“

Tjips
Posts: 72
Joined: Sat Apr 18, 2009 1:15 am
Location: South Africa

### Re: "X-[X+3] in space" Pattern

ChallengeSpaceYard: You are correct in that this pattern, and it's many fellows, exist. It is in actual fact simply a generalization of the 11 pattern, along with such famous patterns as the 12 and 121 patterns (and even the 1 in a hole pattern). The thing is that most players learn the idea that these are equivalent at some point during their development, and thus all the top players (top200 say) are aware of this case. The fact that you mention it bodes well for your development . If you really want to understand where this pattern comes in I suggest reading Raphael Collet's paper "Playing the Minesweeper with Constraints". It beautifully explains the underlying logic involved in a human player's solution of a minesweeper board.

Hope you enjoy it
The number of minesweeper boards:
Exp: 140055249834355336357264746443955277014822625680974475320364702381803619892657792049596418323789908370400 (1.4e104)
Int: 13115156192346373485000211099954895788134532256 (1.3e46) &
Beg: 18934455246 (1.9e10)