In a standard game of battleships, what is the minimum number of strikes you will need to make to guarantee hitting at least one boat?

Battleships is played on a 10x10 Grid,
You are allowed:-
1 Battle Ship (4x1)
2 Cruisers (3x1)
3 Destroyers (2x1) and
3 Submarines (1x1)

NOTE:-These rules are slightly different than those of the board game, I am using these so that all members can give the same answer.

Justin seems to be thinking along lines of density but I haven't properly taken time to think his assumptions.

I'm not doing this justice either, but I offer it as a 'springboard'.

This is my 'contrived' grid for analysis: (bold chars may distort the presentation)

0  0  0  0  0  0  0  0  0  0

0  4  4  4  4  0  3  3  3  0

0  0  0  0  0  0  0  0  0  0

0  3  3  3  0  1  0  2  2  0

0  0  0  0  0  0  0  0  0  0

1  0  1  0  2  2  0  2  2  0

0  0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0  0

I have packed my fleet as tightly as possible toward the top of the grid ensuring that a first 'hit' cannot be made within the first row.

By virtue of my layout, cell occupancy is denser at the top of the grid.  I therefore reason, without due proof, that, even though I might shuffle a few pieces, like the middle destroyer 2 2(lowest occupied row) to somewhere lower, or have more blank rows at the top of the grid, then I can develop a determined strategy.

On the basis that there are 19 cells occupied out of the 100, c. 20%, it seems like a 1 in 5 probability of a hit.  But that is no guarantee.

I had considered dismissing the 4 innermost cells and concentrate only upon the 12 which surround them.  I can void that concept by ensuring that the 4 middle rows are blank.

Carry On.

Edited on July 24, 2005, 9:29 am

Posted by brianjn on 2005-07-24 06:46:08