Solution to Problem 6: Battleships

When a ship square is identified, its diagonal neighbors will be assumed to be water squares without comment.  Also, when unknown squares in a given row or column must either all be ships or water to make a count work out properly, that is also generally done without comment.

There must be ship squares at BK, CM, and GQ.  The unknown squares are all water in rows B and F and column Q
The battleship is either on row E or column M.   Assume it is in row E.  Then the only places for the cruisers will be row G and row I.  GN must be blank, since row G is finshed by the cruiser at GP-GR.  The cruiser on row I must include either IM or IO, so HN and JN are both blank.  But then there cannot be three ship squares in column N.  Therefore, DM and EM are the final battleship squares.
Either HN or JN must have a ship square, so IO is water.  If there were a cruiser in row E, then row A could not legally have three ship squares.  Therefore, the two cruisers are in row GP-GR and HN-JN.  

AS and AT must be ship squares, as must CO, EO, and IL.

If EP were a water square, then there would be submarines at CO, EK, EO, ES, IS, and IP.  This is too many, so EP is a ship square.  This accounts for the final cruiser, so IK is a water square.  

The submarines are at CO, EK, IL, IS.

Notes:  I spent just a few minutes looking at this during the test, but then went on to other things.  It wound up taking me a while once I started on it afterwards, so I guess I'm happy to have not wasted time on it.