Symbols and Terms For Rules
Each cell is surrounded by at most eight other cells. Relative to these adjacent
cells, each cell has associated with it the following fields:
| ADJMINE |
# Adjacent mines (fixed at start of each game) |
| ADJFLAG |
# Adjacent cells marked with a flag |
| ADJEXPO |
# Adjacent exposed cells |
| ADJUNEX |
# Adjacent unexposed/unflagged cells |
| REST = ADJMINE - ADJFLAG |
# still buried mines |
| Note: ADJFLAG + ADJEXPO + ADJUNEX = 8 |
| Rn |
The 3 x 3 rectangle surrounding cell n. |
| Rn INT Rm |
Set of cells formed by intersection of Rn and Rm (this
set is also a rectangle, possibly empty) |
| #Rn |
Number of unexposed and unflagged cells in Rn |
| Rn \ Rm |
Set of cells in Rn but not in Rm (this set is not necessarily
a rectangle) |
Legend:
 = unexposed
 = unexposed, but we
know is a blank
 = unexposed, but we know
is a mine.
 = flagged as a mine
Implemented Rules
MySweeper implements one-level rules, not transitive cases. That is, it doesn't
act upon hints, only exposed cells and (possibly incorrectly) flagged cells.
However, throughout this discussion, it is assumed that there are no incorrectly
flagged cells.
| 1. |
Prose: |
If an exposed cell has all its adjacent mines flagged,
the remaining unexposed cells are empty. |
|
Technical: |
If for any exposed cell, ADJMINE == ADJFLAG,
then none of the ADJUNEX cells are mines. |
|
Example: |
In the following configuration, the cells marked with a
are known to be blank:
|
| 2. |
Prose: |
If an unexposed cell has the same number of unexposed
adjacent cells as there are unexposed mines, the remaining unexposed
cells are all mines. |
|
Technical: |
If for any exposed cell, ADJMINE == (ADJFLAG +
ADJUNEX), then all of the ADJUNEX cells are mines. |
|
Example: |
In the following configuration, the cells marked with a
are known to be mines:
|
| 3. |
Prose: |
If the unexposed cells surrounding cell #1 are a subset
of the unexposed cells surrounding cell #2, and they have the same
number of still buried (unflagged) mines, then none of the unexposed
cells in R2 \ R1 are mines. |
|
Technical: |
Relative to the original cell(#1), for any exposed
(within two cell radius) cells(#2) other than the current cell(#1)
If (#(R2 INT R1) == #R1
&& REST1 == REST2)
Then all of the unexposed and unflagged cells in R2 \ R1
are blank. |
|
Example: |
In the following configuration, the cells marked with a
are known to be blank:
|
| 4. |
Prose: |
If the still buried mines around cell #1 are fewer
than the number of unexposed unflagged cells common to R2
and R1, and the difference between the number of unflagged
mines between the two cells is the same as the number of unexposed
unflagged cells in R2 \ R1, then all of the unexposed cells
in R2 \ R1 are mines. |
|
Technical: |
Relative to the original cell(#1), for any exposed (within two
cell radius) cells(#2) other than the current cell(#1)
If (REST1 < #(R2 INT R1)
&& (REST2 - REST1) == #(R2 \ R1))
Then all of the unexposed and unflagged cells in R2 \
R1 are mines and none of the unexposed and unflagged cells
in R1 \ R2 are mines.
|
|
Example: |
In the following configuration, the cells marked with a
are known to be mines, and the cells marked with a
are known to be blanks:
|
Unimplemented Rules
5. |
The program does not as yet handle the following case:
In this case, the 
on the bottom means that the two s
to its left and above left contain one mine. This means that the two s
above and to the above left of the 
also contain one mine. Finally, the
at the top left absorbs this last mine and thus the cells marked
are blanks. To handle this, likely we need to recurse at each stage, or
as has been suggested by Dave Rusin
(),
solve a set of simultaneous linear equations.
|
6. |
For the moment, no endgame rules have been implemented. For example
If there's only one mine remaining, it's the cell marked .
Using Dave Rusin's scheme this can be accomplished with one more simultaneous
linear equation.
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