Dec 7, 2009
Problem of the Week
for Monday, December 7, 2009
Now Coco and Charmaine are playing three-dimensional battleship. The board is a 5 x 5 x 5 cube. Charmaine has hidden her submarine (2 units long) somewhere in the cube, and Coco will try to guess its location. What is the fewest number of guesses Coco needs to make to guarantee that she will hit Charmaine's sub no matter where it is? How many guesses are needed to guarantee that she will sink it?
(Note: Three-dimensional battleship is played on a 3-D grid labeled with letters and numbers as shown. A guess is a coordinate description such as "A-c-3." The other player responds with either "hit" or "miss." Guessing continues until the submarine is sunk, meaning both of its grid squares have been guessed)