Info about
MineSweeper
Assuming that you know about the Mine Sweeper game, find where mines can be in the following two scenarios:
1)
S S S S S
S 1 2 1 S
S X X X S
2)
S S S S S S
S 1 2 2 1 S
S X X X X S
Find for which 'n' values the following scenario is solvable for mines, where n represents the number of 2's.
S S S ........ S S S
S 1 2 ........ 2 1 S
S X X ........ X X S
In the above scenarios, S can be filled with a mine or a number and X can be filled only with a number.
1) 1m2m1 2) 01mm10 m = mine
11211 012210
00000 000000
Scenarios where 'n' is not a multiple of 3 appear solvable.
Where 'n' is a multiple of 3, there appears two
possible solutions where the mines may be:
3) 01mm2m1 1m2mm10
0122211 or 1122210
0000000 0000000
Where 'n' = 3k  2, such that k is an integer value of 1 or greater, the top row of each scenario has a pattern of '1x1' with x being a number of 'm2m' for each k.
Where 'n' = 3k  1, such that k is an integer value of 1 or greater, the top row of each scenario has a pattern of '01mxm10' with x being a number  1 of 'm2m' for each k.
Where 'n' = 3k, such that k is an integer value of 1 or greater, the top row of each scenario has either a pattern of '01mx1' OR '1xm10' with x being a number of 'm2m' for each k.
By selecting either of the two end positions in the top or middle row, which are minefree, the solvable pattern is revealed. Thus, ALL scenarios for 'n' are actually solvable.
Edited on February 16, 2009, 9:14 pm

Posted by Dej Mar
on 20090216 19:40:37 