?

Log in

   Journal    Friends    Archive    Profile    Memories
 

Battleship theory - Problem-A-Day

nahtmmmMar. 12th, 2008 03:06 pm Battleship theory1 comment - Leave a commentPrevious Entry Share Next Entry

Comments:

From:nekura_ca
Date:March 14th, 2008 02:55 am (UTC)
(Link)
Hidden

There are 8 possible setups for his ships:
+--------+ +--------+ +--------+ +--------+
|........| |........| |........| |........|
|..AAAAA.| |..BBBCCC| |..BBBCCC| |..BBBCCC|
|....B...| |....A...| |........| |........|
|....B...| |....A...| |........| |........|
|....B...| |....A...| |..DDD...| |..DDD...|
|..CCCDDD| |....ADDD| |..AAAAA.| |...AAAAA|
|........| |....A...| |........| |........|
|........| |........| |........| |........|
+--------+ +--------+ +--------+ +--------+

+--------+ +--------+ +--------+ +--------+
|........| |........| |........| |........|
|..BBBCCC| |..BBBCCC| |..BBBCCC| |..BBBCCC|
|....D...| |....D...| |........| |........|
|....D...| |....D...| |........| |........|
|....D...| |....D...| |...DDD..| |...DDD..|
|..AAAAA.| |...AAAAA| |..AAAAA.| |...AAAAA|
|........| |........| |........| |........|
|........| |........| |........| |........|
+--------+ +--------+ +--------+ +--------+

In four cases, everything is connected, so
any shot that hits will kill everything, in
the other four cases, there are two 3-ships
connected, and the other 3-ship and the
5-ship are connected, so taking out the
group with the 5-ship is best. Looking at
the overlap of all the groups that we want
to hit, we get this set of targets:
+--------+
|........|
|........|
|........|
|........|
|....*...|
|....***.|
|........|
|........|
+--------+

The only one that hasn't already been hit,
and the one that does the most damage, is
therefore F6.